CSS Values and Units Module Level 4

1. Introduction

The value definition field of each CSS property can contain keywords, data types (which appear between < and >), and information on how they can be combined. Generic data types (<length> being the most widely used) that can be used by many properties are described in this specification, while more specific data types (e.g., <spacing-limit>) are described in the corresponding modules.

1.1. Module Interactions

This module replaces and extends the data type definitions in [CSS2] sections 1.4.2.1, 4.3, and A.2.

2. Value Definition Syntax

The value definition syntax described here is used to define the set of valid values for CSS properties (and the valid syntax of many other parts of CSS). A value so described can have one or more components.

2.1. Component Value Types

Component value types are designated in several ways:

1. Keyword values (such as auto, disc, etc.) and at-keywords representing the start of an at-rule, which appear literally, without quotes (e.g. auto or @media).

   Note: It is possible, with escaping, to construct a CSS identifier whose value ends with ( or starts with @. Such a token is an <ident-token> (i.e. a keyword), not a <function-token> or an <at-keyword-token>.

2. Basic data types, which appear between < and > (e.g., <length>, <percentage>, etc.). For numeric data types, this type notation can annotate any range restrictions using the bracketed range notation described below.

3. Property value ranges, which represent the same pattern of values as a property bearing the same name. These are written as the property name, surrounded by single quotes, between < and >, e.g., <'border-width'>, <'background-attachment'>, etc.

   These types do not include CSS-wide keywords such as inherit. Additionally, if the property’s value grammar is a comma-separated repetition, the corresponding type does not include the top-level comma-separated list multiplier. (E.g. if a property named pairing is defined as [ <custom-ident> <integer>? ]#, then <'pairing'> is equivalent to [ <custom-ident> <integer>? ], not [ <custom-ident> <integer>? ]#.)

   Why remove the multiplier?

   The top-level multiplier is ripped out of these value types because top-level comma-separated repetitions are mostly used for coordinating list properties, and when a shorthand combines several such properties, it needs the unmultiplied grammar so it can construct its own comma-separated repetition.

   Without this special treatment, every such longhand would have to be defined with an ad-hoc production just for the inner value, which makes the grammars harder to understand overall.

4. Functional notations and their arguments. These may be written literally as defined in § 2.6 Functional Notation Definitions, or referenced by a non-terminal using the function’s name, followed by an empty parentheses pair, between < and >, e.g. <calc()>, and references the correspondingly-named functional notation.

5. Other non-terminals. These are written as the name of the non-terminal between < and >, as in <spacing-limit>. Notice the distinction between <border-width> and <'border-width'>: the latter represents the grammar of the border-width property, the former requires an explicit expansion elsewhere. The definition of a non-terminal is typically located near its first appearance in the specification.

6. Delimiters, which represent their corresponding tokens. Slashes (/), commas (,), colons (:), semicolons (;), parentheses (( and )), and braces ({ and }) are written literally. Other delimiters must be written enclosed in single quotes (such as '+').

Commas specified in the grammar are implicitly omissible in some circumstances, when used to separate optional terms in the grammar. Within a top-level list in a property or other CSS value, or a function’s argument list, a comma specified in the grammar must be omitted if:

• all items preceding the comma have been omitted
• all items following the comma have been omitted
• multiple commas would be adjacent (ignoring white space/comments), due to the items between the commas being omitted.

example( first? , second? , third? )

All CSS properties also accept the CSS-wide keyword values as the sole component of their property value. For readability these are not listed explicitly in the property value syntax definitions. For example, the full value definition of border-color under CSS Cascading and Inheritance Level 3 is <color>{1,4} | inherit | initial | unset (even though it is listed as <color>{1,4}).

Note: This implies that, in general, combining these keywords with other component values in the same declaration results in an invalid declaration. For example, background: url(corner.png) no-repeat, inherit; is invalid.

2.2. Component Value Combinators

Component values can be arranged into property values as follows:

• Juxtaposing components means that all of them must occur, in the given order.
• A double ampersand (&&) separates two or more components, all of which must occur, in any order.
• A double bar (||) separates two or more options: one or more of them must occur, in any order.
• A bar (|) separates two or more alternatives: exactly one of them must occur.
• Brackets ([ ]) are for grouping.

Juxtaposition is stronger than the double ampersand, the double ampersand is stronger than the double bar, and the double bar is stronger than the bar. Thus, the following lines are equivalent:

  a b   |   c ||   d &&   e f
[ a b ] | [ c || [ d && [ e f ]]]

For reorderable combinators (||, &&), ordering of the grammar does not matter: components in the same grouping may be interleaved in any order. Thus, the following lines are equivalent:

a || b || c
b || a || c

Note: Combinators are not associative, so grouping is significant. For example, a || b || c and a || [ b || c ] are distinct grammars: the first allows a value like b a c, but the second does not.

2.3. Component Value Multipliers

Every type, keyword, or bracketed group may be followed by one of the following modifiers:

• An asterisk (*) indicates that the preceding type, word, or group occurs zero or more times.
• A plus (+) indicates that the preceding type, word, or group occurs one or more times.
• A question mark (?) indicates that the preceding type, word, or group is optional (occurs zero or one times).
• A single number in curly braces ({A}) indicates that the preceding type, word, or group occurs A times.
• A comma-separated pair of numbers in curly braces ({A,B}) indicates that the preceding type, word, or group occurs at least A and at most B times. The B may be omitted ({A,}) to indicate that there must be at least A repetitions, with no upper bound on the number of repetitions.
• A hash mark (#) indicates that the preceding type, word, or group occurs one or more times, separated by comma tokens (which may optionally be surrounded by white space and/or comments). It may optionally be followed by the curly brace forms, above, to indicate precisely how many times the repetition occurs, like <length>#{1,4}.
• An exclamation point (!) after a group indicates that the group is required and must produce at least one value; even if the grammar of the items within the group would otherwise allow the entire contents to be omitted, at least one component value must not be omitted.

The + and # multipliers may be stacked as +#; similarly, the # and ? multipliers, {A} and ? multipliers, and {A,B} and ? multipliers may be stacked as #?, {A}?, and {A,B}?, respectively. These stacks each represent the later multiplier applied to the result of the earlier multiplier. (These same stacks can be represented using grouping, but in complex grammars this can push the number of brackets beyond readability.)

For repeated component values (indicated by *, +, or #), UAs must support at least 20 repetitions of the component. If a property value contains more than the supported number of repetitions, the declaration must be ignored as if it were invalid.

2.4. Combinator and Multiplier Patterns

There are a small set of common ways to combine multiple independent component values in particular numbers and orders. In particular, it’s common to want to express that, from a set of component value, the author must select zero or more, one or more, or all of them, and in either the order specified in the grammar or in any order.

All of these can be easily expressed using simple patterns of combinators and multipliers:

Note that all of the "any order" possibilities are expressed using combinators, while the "in order" possibilities are all variants on juxtaposition.

2.5. Component Values and White Space

Unless otherwise specified, white space and/or comments may appear before, after, and/or between components combined using the above combinators and multipliers.

Note: In many cases, spaces will in fact be required between components in order to distinguish them from each other. For example, the value 1em2em would be parsed as a single <dimension-token> with the number 1 and the identifier em2em, which is an invalid unit. In this case, a space would be required before the 2 to get this parsed as the two lengths 1em and 2em.

2.6. Functional Notation Definitions

The syntax of a functional notation is defined as a sequence of:

1. The function’s name written as an identifier followed by an open parenthesis (such as example(), or the <function-token> production to indicate a function with an arbitrary name.

2. The function’s arguments, if any, expressed using the value definition syntax.

3. A literal closing parenthesis.

The function’s arguments are considered implicitly grouped, as if surrounded by brackets ([ ... ]).

example( <length> , <length> )

<pseudo-class-selector> = : <ident-token> | : <function-token> <any-value> )

2.7. Property Value Examples

Below are some examples of properties with their corresponding value definition fields

2.8. Non-Terminal Definitions and Grammar Production Blocks

The precise grammar of non-terminals, like <position> or <calc()>, is often specified in a CSS grammar production block. These are conventionally represented in a preformatted block of definitions like this:

<foo> = keyword | <bar> |
        some-really-long-pattern-of-stuff
<bar> = <length>

Each definition starts on its own line, and consists of the non-terminal to be defined, followed by an =, followed by the fragment of value definition syntax to which it expands. A definition can stretch across multiple lines, and terminates before the next line that starts a new grammar production or at the end of the grammar production block (whichever comes first).

3. Combining Values: Interpolation, Addition, and Accumulation

Some procedures, for example transitions and animations, combine two CSS property values. The following combining operations—​on the two computed values V_A and V_B yielding the computed value V_result—​are defined. For operations that are not commutative (for example, matrix multiplication, or accumulation of mismatched transform lists) V_A represents the first term of the operation and V_B represents the second.

interpolation

Given two property values V_A and V_B, produces an intermediate value V_result at a distance of p along the interval between V_A and V_B such that p = 0 produces V_A and p = 1 produces V_B.

The range of p is (−∞, ∞) due to the effect of timing functions. As a result, this procedure must also define extrapolation behavior for p outside [0, 1].

addition

Given two property values V_A and V_B, returns the sum of the two properties, V_result.

Note: While addition can often be expressed in terms of the same weighted sum function used to define interpolation, this is not always the case. For example, interpolation of transform matrices involves decomposing and interpolating the matrix components whilst addition relies on matrix multiplication.

If a value type does not define a specific procedure for addition or is defined as not additive, its addition operation is simply V_result = V_B.

accumulation

Given two property values V_A and V_B, returns the result, V_result, of combining the two operands such that V_B is treated as a delta from V_A.

Note: For many types of animation such as numbers or lengths, accumulation is defined to be identical to addition.

A common case where the definitions differ is for list-based types where addition may be defined as appending to a list whilst accumulation may be defined as component-based addition. For example, the filter list values blur(2) and blur(3), when added together would produce blur(2) blur(3), but when accumulated would produce blur(5).

If a value type does not define a specific procedure for accumulation, its accumulation operation is identical to addition.

These operations are only defined on computed values. (As a result, it is not necessary to define, for example, how to add a <length> value of 15pt with 5em since such values will be resolved to their canonical unit before being passed to any of the above procedures.)

3.1. Range Checking

Interpolation can result in a value outside the valid range for a property, even if all of the inputs to interpolation are valid; this especially happens when p is outside the [0, 1] range, but some easing functions can cause this to occur even within that range. If the final result after interpolation, addition, and accumulation is out-of-range for the target context the value is being used in, it does not cause the declaration to be invalid. Instead, the value must be clamped to the range allowed in the target context, exactly the same as math functions (see § 10.12 Range Checking).

Note: Even if interpolation results in an out-of-range value, addition/accumulation might "correct" the result and bring it back into range. Thus, clamping is only applied to the final result of applying all interpolation-related operations.

4. Textual Data Types

The textual data types include various keywords and identifiers as well as strings (<string>) and URLs (<url>). Aside from the casing of pre-defined keywords or as explicitly defined for a given property, no normalization is performed, not even Unicode normalization: the specified and computed value of a property are exactly the provided Unicode values after parsing (which includes character set conversion and escaping). [UNICODE] [CSS-SYNTAX-3]

CSS identifiers, generically denoted by <ident>, consist of a sequence of characters conforming to the <ident-token> grammar. [CSS-SYNTAX-3] Identifiers cannot be quoted; otherwise they would be interpreted as strings. CSS properties accept two classes of identifiers: pre-defined keywords and author-defined identifiers.

Note: The <ident> production is not meant for property value definitions—​<custom-ident> should be used instead. It is provided as a convenience for defining other syntactic constructs.

All textual data types interpolate as discrete and are not additive.

4.1. Pre-defined Keywords

In the value definition fields, keywords with a pre-defined meaning appear literally. Keywords are identifiers and are interpreted ASCII case-insensitively (i.e., [a-z] and [A-Z] are equivalent).

Value: collapse | separate

table { border-collapse: separate }

4.1.1. CSS-wide keywords: initial, inherit and unset

As defined above, all properties accept the CSS-wide keywords, which represent value computations common to all CSS properties. These keywords are normatively defined in the CSS Cascading and Inheritance Module.

Other CSS specifications can define additional CSS-wide keywords.

4.2. Unprefixed Author-defined Identifiers: the <custom-ident> type

Some properties accept arbitrary author-defined identifiers as a component value. This generic data type is denoted by <custom-ident>, and represents any valid CSS identifier that would not be misinterpreted as a pre-defined keyword in that property’s value definition. Such identifiers are fully case-sensitive (meaning they’re compared using the "identical to" operation), even in the ASCII range (e.g. example and EXAMPLE are two different, unrelated user-defined identifiers).

The CSS-wide keywords are not valid <custom-ident>s. The default keyword is reserved and is also not a valid <custom-ident>. Specifications using <custom-ident> must specify clearly what other keywords are excluded from <custom-ident>, if any—​for example by saying that any pre-defined keywords in that property’s value definition are excluded. Excluded keywords are excluded in all ASCII case permutations.

When parsing positionally-ambiguous keywords in a property value, a <custom-ident> production can only claim the keyword if no other unfulfilled production can claim it.

Note: When designing grammars with <custom-ident>, the <custom-ident> should always be “positionally unambiguous”, so that it’s impossible to conflict with any keyword values in the property. Such conflicts can alternatively be avoided by using <dashed-ident>.

4.3. Prefixed Author-defined Identifiers: the <dashed-ident> type

Some contexts accept both author-defined identifiers and CSS-defined identifiers. If not handled carefully, this can result in difficulties adding new CSS-defined values; UAs have to study existing usage and gamble that there are sufficiently few author-defined identifiers in use matching the new CSS-defined one, so giving the new value a special CSS-defined meaning won’t break existing pages.

While there are many legacy cases in CSS that mix these two values spaces in exactly this fraught way, the <dashed-ident> type is meant to be an easy way to distinguish author-defined identifiers from CSS-defined identifiers.

The <dashed-ident> production is a <custom-ident>, with all the case-sensitivity that implies, with the additional restriction that it must start with two dashes (U+002D HYPHEN-MINUS).

<dashed-ident>s are reserved solely for use as author-defined names. CSS will never define a <dashed-ident> for its own use.

.foo {
  --fg-color: blue;
}

@color-profile --foo { src: url(https://example.com/foo.icc); }
.foo {
  color: color(--foo 1 0 .5 / .2);
}

4.4. Quoted Strings: the <string> type

Strings are denoted by <string>. When written literally, they consist of a sequence of characters delimited by double quotes or single quotes, corresponding to the <string-token> production in the CSS Syntax Module [CSS-SYNTAX-3].

content: "this is a 'string'.";
content: "this is a \"string\".";
content: 'this is a "string".';
content: 'this is a \'string\'.'

It is possible to break strings over several lines, for aesthetic or other reasons, but in such a case the newline itself has to be escaped with a backslash (\). The newline is subsequently removed from the string. For instance, the following two selectors are exactly the same:

a[title="a not s\
o very long title"] {/*...*/}
a[title="a not so very long title"] {/*...*/}

Since a string cannot directly represent a newline, to include a newline in a string, use the escape "\A". (Hexadecimal A is the line feed character in Unicode (U+000A), but represents the generic notion of "newline" in CSS.)

4.5. Resource Locators: the <url> type

The <url> type, written with the url() and src() functions, represents a URL, which is a pointer to a resource.

The syntax of <url> is:

<url> = <url()> | <src()>

<url()> = url( <string> <url-modifier>* ) | <url-token>
<src()> = src( <string> <url-modifier>* )

body { background: url("http://www.example.com/pinkish.gif") }

A url() can be written without quotation marks around the URL value, in which case it is specially-parsed as a <url-token>; see CSS Syntax 3 § 4.3.6 Consume a url token. [CSS-SYNTAX-3]

Note: Because of this special parsing, url() can only express its value literally. To provide a URL by functions such as var(), use the src() notation, which does not have this special parsing rule.

background: url("http://www.example.com/pinkish.gif");
background: url(http://www.example.com/pinkish.gif);

background: src("http://www.example.com/pinkish.gif");
--foo: "http://www.example.com/pinkish.gif";
background: src(var(--foo));

--foo: "http://www.example.com/pinkish.gif";
background: url(var(--foo));

Note: The unquoted url() syntax cannot accept a <url-modifier> argument and has extra escaping requirements: parentheses, whitespace characters, single quotes (') and double quotes (") appearing in a URL must be escaped with a backslash, e.g. url(open\(parens), url(close\)parens). (In quoted <string> url()s, only newlines and the character used to quote the string need to be escaped.) Depending on the type of URL, it might also be possible to write these characters as URL-escapes (e.g. url(open%28parens) or url(close%29parens)) as described in [URL].

Some CSS contexts (such as @import) also allow a <url> to be represented by a bare <string>, without the function wrapper. In such cases the string behaves identically to a url() function containing that string.

@import url("base-theme.css");
@import "base-theme.css";

4.5.1. Relative URLs

In order to create modular style sheets that are not dependent on the absolute location of a resource, authors should use relative URLs. Relative URLs (as defined in [URL]) are resolved to full URLs using a base URL. RFC 3986, section 3, defines the normative algorithm for this process. For CSS style sheets, the base URL is that of the style sheet itself, not that of the styled source document. Style sheets embedded within a document have the base URL associated with their container.

Note: For HTML documents, the base URL is mutable.

When a <url> appears in the computed value of a property, it is resolved to an absolute URL. The computed value of a URL that the UA cannot resolve to an absolute URL is the specified value.

body { background: url("tile.png") }

http://www.example.org/style/basic.css

http://www.example.org/style/tile.png

4.5.1.1. Fragment URLs

To enable element ID references to work in CSS regardless of base URL changes or shadow DOM, <url>s have special behavior when they contain only a fragment.

If a <url>’s value starts with a U+0023 NUMBER SIGN (#) character, then the URL additionally has its local url flag set, and is a tree-scoped reference for the URL’s fragment.

When matching a <url> with the local url flag set:

• if the URL’s fragment is an element ID reference (rather than, say, a media fragment), resolve it as a tree-scoped reference with the tree’s IDs as the associated tree-scoped names: specifically, resolve to the first element in tree order among the associated node tree’s descendants with the URL’s fragment as its ID. (And, as usual for tree-scoped references, continuing up to the host’s tree if needed.)

  If no such element is found, the URL fails to resolve.

• otherwise, resolve the fragment against the current document.

Possibly reference find a potential indicated element, but that is defined specifically for Documents, not ShadowRoots.

Note: This means that such fragments will resolve against the contents of the current document (or whichever node tree the stylesheet lives in, if shadow DOM is involved) regardless of how such relative URLs would resolve elsewhere (ignoring, for example, base elements changing the base URL, or relative URLs in linked stylesheets resolving against the stylesheet’s URL).

<!DOCTYPE html>
<base href="http://example.com/">
...
<a href="#anchor" style="background-image: url(#image)">link</a>

When serializing a url() with the local url flag set, it must serialize as just the fragment.

4.5.2. Empty URLs

If the value of the <url> is the empty string (like url("") or url()), the url must resolve to an invalid resource (similar to what the url about:invalid does).

Its computed value is url("") or src(""), whichever was specified, and it must serialize as such.

Note: This matches the behavior of empty urls for embedded resources elsewhere in the web platform, and avoids excess traffic re-requesting the stylesheet or host document due to editing mistakes leaving the url() value empty, which are almost certain to be invalid resources for whatever the url() shows up in. Linking on the web platform does allow empty urls, so if/when CSS gains some functionality to control hyperlinks, this restriction can be relaxed in those contexts.

4.5.3. URL Modifiers

<url>s support specifying additional <url-modifier>s, which change the meaning or the interpretation of the URL somehow. A <url-modifier> is either an <ident> or a functional notation.

This specification does not define any <url-modifier>s, but other specs may do so.

Note: A <url> that is either unquoted or not wrapped in url() notation cannot accept any <url-modifier>s.

4.5.4. URL Processing Model

When interpreting URLs expressed in CSS, the URL parser’s encoding argument must be omitted (i.e. use the default, UTF-8), regardless of the stylesheet encoding.

Note: In other words, a URL written in CSS will always percent-encode non-ASCII codepoints using UTF-8 in the URL object (and thus whenever using the URL value for e.g. network requests), regardless of the stylesheet’s own encoding. Note that this occurs after decoding the stylesheet into Unicode code points.

5. Numeric Data Types

Numeric data types are used to represent quantities, indexes, positions, and other such values. Although many syntactic variations can exist in expressing the quantity (numeric aspect) in a given numeric value, the specified and computed value do not distinguish these variations: they represent the value’s abstract quantity, not its syntactic representation.

The numeric data types include <integer>, <number>, <percentage>, and various dimensions including <length>, <angle>, <time>, <frequency>, and <resolution>.

Note: While general-purpose dimensions are defined here, some other modules define additional data types (e.g. [css-grid-1] introduces fr units) whose usage is more localized.

The precision and supported range of numeric values in CSS is implementation-defined, and can vary based on the property or other context a value is used in. However, within the CSS specifications, infinite precision and range is assumed. When a value cannot be explicitly supported due to range/precision limitations, it must be converted to the closest value supported by the implementation, but how the implementation defines "closest" is implementation-defined as well.

If an <angle> must be converted due to exceeding the implementation-defined range of supported values, it must be clamped to the nearest supported multiple of 360deg.

5.1. Range Restrictions and Range Definition Notation

Properties can restrict numeric values to some range. If the value is outside the allowed range, then unless otherwise specified, the declaration is invalid and must be ignored. Range restrictions can be annotated in the numeric type notation using CSS bracketed range notation—​[min,max]—​within the angle brackets, after the identifying keyword, indicating a closed range between (and including) min and max. For example, <integer [0,10]> indicates an integer between 0 and 10, inclusive, while <angle [0,180deg]> indicates an angle between 0deg and 180deg (expressed in any unit).

Note: CSS values generally do not allow open ranges; thus only square-bracket notation is used.

CSS theoretically supports infinite precision and infinite ranges for all value types; however in reality implementations have finite capacity. UAs should support reasonably useful ranges and precisions. Range extremes that are ideally unlimited are indicated using ∞ or −∞ as appropriate. For example, <length [0,∞]> indicates a non-negative length.

If no range is indicated, either by using the bracketed range notation or in the property description, then [−∞,∞] is assumed.

Values of −∞ or ∞ must be written without units, even if the value type uses units. Values of 0 can be written without units, even if the value type doesn’t allow “unitless zeroes” (such as <time>).

Note: At the time of writing, the bracketed range notation is new; thus in most CSS specifications any range limitations are described only in prose. (For example, “Negative values are not allowed” or “Negative values are invalid” indicate a [0,∞] range.) This does not make them any less binding.

5.2. Integers: the <integer> type

Integer values are denoted by <integer>.

When written literally, an integer is one or more decimal digits 0 through 9 and corresponds to a subset of the <number-token> production in the CSS Syntax Module [CSS-SYNTAX-3]. The first digit of an integer may be immediately preceded by - or + to indicate the integer’s sign.

Unless otherwise specified, in the CSS specifications rounding to the nearest integer requires rounding in the direction of +∞ when the fractional portion is exactly 0.5. (For example, 1.5 rounds to 2, while -1.5 rounds to -1.)

5.2.1. Computation and Combination of <integer>

Unless otherwise specified, the computed value of a specified <integer> is the specified abstract integer.

Interpolation of <integer> is defined as V_result = round((1 - p) × V_A + p × V_B); that is, interpolation happens in the real number space as for <number>s, and the result is converted to an <integer> by rounding to the nearest integer.

Addition of <integer> is defined as V_result = V_A + V_B

5.3. Real Numbers: the <number> type

Number values are denoted by <number>, and represent real numbers, possibly with a fractional component.

When written literally, a number is either an integer, or zero or more decimal digits followed by a dot (.) followed by one or more decimal digits; optionally, it can be concluded by the letter “e” or “E” followed by an integer indicating the base-ten exponent in scientific notation. It corresponds to the <number-token> production in the CSS Syntax Module [CSS-SYNTAX-3]. As with integers, the first character of a number may be immediately preceded by - or + to indicate the number’s sign.

The value <zero> represents a literal number with the value 0. Expressions that merely evaluate to a <number> with the value 0 (for example, calc(0)) do not match <zero>; only literal <number-token>s do.

5.3.1. Computation and Combination of <number>

Unless otherwise specified, the computed value of a specified <number> is the specified abstract number.

Interpolation of <number> is defined as V_result = (1 - p) × V_A + p × V_B

Addition of <number> is defined as V_result = V_A + V_B

5.4. Numbers with Units: dimension values

The general term dimension refers to a number with a unit attached to it; and is denoted by <dimension>.

When written literally, a dimension is a number immediately followed by a unit identifier, which is an identifier. It corresponds to the <dimension-token> production in the CSS Syntax Module [CSS-SYNTAX-3]. Like keywords, unit identifiers are ASCII case-insensitive.

CSS uses <dimension>s to specify distances (<length>), durations (<time>), frequencies (<frequency>), resolutions (<resolution>), and other quantities.

5.4.1. Compatible Units

When serializing computed values [CSSOM], compatible units (those related by a static multiplicative factor, like the 96:1 factor between px and in, or the computed font-size factor between em and px) are converted into a single canonical unit. Each group of compatible units defines which among them is the canonical unit that will be used for serialization.

When serializing resolved values that are used values, all value types (percentages, numbers, keywords, etc.) that represent lengths are considered compatible with lengths. Likewise any future API that returns used values must consider any values that represent distances/durations/frequencies/etc. as compatible with the relevant class of dimensions, and canonicalize accordingly.

5.4.2. Combination of Dimensions

Interpolation of compatible dimensions (for example, two <length> values) is defined as V_result = (1 - p) × V_A + p × V_B

Addition of compatible dimensions is defined as V_result = V_A + V_B

5.5. Percentages: the <percentage> type

Percentage values are denoted by <percentage>, and indicates a value that is some fraction of another reference value.

When written literally, a percentage consists of a number immediately followed by a percent sign %. It corresponds to the <percentage-token> production in the CSS Syntax Module [CSS-SYNTAX-3].

Percentage values are always relative to another quantity, for example a length. Each property that allows percentages also defines the quantity to which the percentage refers. This quantity can be a value of another property for the same element, the value of a property for an ancestor element, a measurement of the formatting context (e.g., the width of a containing block), or something else.

5.5.1. Computation and Combination of <percentage>

Unless otherwise specified (such as in font-size, which computes its <percentage> values to <length>), the computed value of a percentage is the specified percentage.

Interpolation of <percentage> is defined as V_result = (1 - p) × V_A + p × V_B

Addition of <percentage> is defined as V_result = V_A + V_B

5.6. Mixing Percentages and Dimensions

In cases where a <percentage> can represent the same quantity as a dimension in the same component value position, and can therefore be combined with them in a calc() expression, the following convenience notations may be used in the property grammar:

<length-percentage>

Equivalent to [ <length> | <percentage> ], where the <percentage> will resolve to a <length>.

<frequency-percentage>

Equivalent to [ <frequency> | <percentage> ], where the <percentage> will resolve to a <frequency>.

<angle-percentage>

Equivalent to [ <angle> | <percentage> ], where the <percentage> will resolve to an <angle>.

<time-percentage>

Equivalent to [ <time> | <percentage> ], where the <percentage> will resolve to a <time>.

Note: Specifications should never alternate <percentage> in place of a dimension in a grammar unless they are compatible.

Note: More <type-percentage> productions can be added in the future as needed. A <number-percentage> will never be added, as <number> and <percentage> can’t be combined in calc().

5.6.1. Computation and Combination of Percentage and Dimension Mixes

The computed value of a percentage-dimension mix is defined as

• a computed dimension if the percentage component is zero or is defined specifically to compute to a dimension value

• a computed percentage if the dimension component is zero

• a computed calc() expression otherwise

Interpolation of percentage-dimension value combinations (e.g. <length-percentage>, <frequency-percentage>, <angle-percentage>, <time-percentage> or equivalent notations) is defined as

• equivalent to interpolation of <length> if both V_A and V_B are pure <length> values
• equivalent to interpolation of <percentage> if both V_A and V_B are pure <percentage> values
• equivalent to converting both values into a calc() expression representing the sum of the dimension type and a percentage (each possibly zero) and interpolating each component individually (as a <length>/<frequency>/<angle>/<time> and as a <percentage>, respectively)

Addition of <percentage> is defined the same as interpolation except by adding each component rather than interpolating it.

5.7. Ratios: the <ratio> type

Ratio values are denoted by <ratio>, and represent the ratio of two numeric values. It most often represents an aspect ratio, relating a width (first) to a height (second).

When written literally, a ratio has the syntax:

<ratio> = <number [0,∞]> [ / <number [0,∞]> ]?

The second <number> is optional, defaulting to 1. However, <ratio> is always serialized with both components.

The computed value of a <ratio> is the pair of numbers provided.

If either number in the <ratio> is 0 or infinite, it represents a degenerate ratio (and, generally, won’t do anything).

If two <ratio>s need to be compared, divide the first number by the second, and compare the results. For example, 3/2 is less than 2/1, because it resolves to 1.5 while the second resolves to 2. (In other words, “tall” aspect ratios are less than “wide” aspect ratios.)

5.7.1. Combination of <ratio>

The interpolation of a <ratio> is defined by converting each <ratio> to a number by dividing the first value by the second (so a ratio of 3 / 2 would become 1.5), taking the logarithm of that result (so the 1.5 would become approximately 0.176), then interpolating those values. The result during the interpolation is converted back to a <ratio> by inverting the logarithm, then interpreting the result as a <ratio> with the result as the first value and 1 as the second value.

If either <ratio> is degenerate, the values cannot be interpolated.

start  = log(5);   // ≈ 0.69897
end    = log(1.5); // ≈ 0.17609
interp = 0.69897*.5 + 0.17609*.5; // ≈ 0.43753
final  = 10^interp; // ≈ 2.73

Note: Interpolating over the logarithm of the ratio means the results are scale-independent (5 / 1 to 300 / 200 would give the same results as above), that they’re symmetrical over "wide" and "tall" variants (interpolating from 1 / 5 to 2 / 3 would give a ratio approximately equal to 1 / 2.73 at the halfway point), and that they’re symmetrical over whether the width is fixed and the height is based on the ratio or vice versa. These properties are not shared by many other possible interpolation strategies.

Note: Due to the properties of logarithms, any log can be used; the example here uses base-10 log, but if, say, the natural log and e was used, the intermediate results would be different but the final result would be the same.

Addition of <ratio>s is not possible.

6. Distance Units: the <length> type

Lengths refer to distance measurements and are denoted by <length> in the property definitions. A length is a dimension.

For zero lengths the unit identifier is optional (i.e. can be syntactically represented as the <number> 0). However, if a 0 could be parsed as either a <number> or a <length> in a property (such as line-height), it must parse as a <number>.

Properties may restrict the length value to some range. If the value is outside the allowed range, the declaration is invalid and must be ignored.

While some properties allow negative length values, this may complicate the formatting and there may be implementation-specific limits. If a negative length value is allowed but cannot be supported, it must be converted to the nearest value that can be supported.

In cases where the used length cannot be supported, user agents must approximate it in the actual value.

There are two types of length units: relative and absolute. The specified value of a length (specified length) is represented by its quantity and its unit. The computed value of a length (computed length) is the specified length resolved to an absolute length, and its unit is not distinguished: it can be represented by any absolute length unit (but will be serialized using its canonical unit, px).

While the exact supported precision of numeric values, and how they are rounded to match that precision, is generally implementation-defined, <length>s in border-width and a few other properties are rounded in a specific fashion to ensure reasonable visual display. (This algorithm is called by individual properties explicitly.)

6.1. Relative Lengths

Relative length units specify a length relative to another length. Style sheets that use relative units can more easily scale from one output environment to another.

The relative units are:

Child elements do not inherit the relative values as specified for their parent; they inherit the computed values.

6.1.1. Font-relative Lengths: the em, rem, ex, rex, cap, rcap, ch, rch, ic, ric, lh, rlh units

The font-relative lengths refer to the font metrics either of the element on which they are used (for the local font-relative lengths) or of the root element (for the root font-relative lengths).

em

Equal to the computed value of the font-size property of the element on which it is used.

The rule:

h1 { line-height: 1.2em }

means that the line height of h1 elements will be 20% greater than the font size of h1 element. On the other hand:

h1 { font-size: 1.2em }

means that the font size of h1 elements will be 20% greater than the computed font size inherited by h1 elements.

rem

Equal to the computed value of the em unit on the root element.

Tests

• calc-rem-lang.html (live test) (source)

ex

Equal to the used x-height of the first available font [CSS3-FONTS]. The x-height is so called because it is often equal to the height of the lowercase "x". However, an ex is defined even for fonts that do not contain an "x". The x-height of a font can be found in different ways. Some fonts contain reliable metrics for the x-height. If reliable font metrics are not available, UAs may determine the x-height from the height of a lowercase glyph. One possible heuristic is to look at how far the glyph for the lowercase "o" extends below the baseline, and subtract that value from the top of its bounding box. In the cases where it is impossible or impractical to determine the x-height, a value of 0.5em must be assumed.

Tests

• ex-unit-001.html (live test) (source)
• ex-unit-002.html (live test) (source)
• ex-unit-003.html (live test) (source)
• numbers-units-007.xht (live test) (source)
• numbers-units-009.xht (live test) (source)
• numbers-units-010.xht (live test) (source)
• numbers-units-011.xht (live test) (source)
• numbers-units-012.xht (live test) (source)
• numbers-units-013.xht (live test) (source)
• numbers-units-015.xht (live test) (source)
• numbers-units-019.xht (live test) (source)
• units-001.xht (live test) (source)
• units-002.xht (live test) (source)
• units-003.xht (live test) (source)
• units-004.xht (live test) (source)
• units-005.xht (live test) (source)
• calc-ch-ex-lang.html (live test) (source)

rex

Equal to the value of the ex unit on the root element.

cap

Equal to the used cap-height of the first available font [CSS3-FONTS]. The cap-height is so called because it is approximately equal to the height of a capital Latin letter. However, a cap is defined even for fonts that do not contain Latin letters. The cap-height of a font can be found in different ways. Some fonts contain reliable metrics for the cap-height. If reliable font metrics are not available, UAs may determine the cap-height from the height of an uppercase glyph. One possible heuristic is to look at how far the glyph for the uppercase “O” extends below the baseline, and subtract that value from the top of its bounding box. In the cases where it is impossible or impractical to determine the cap-height, the font’s ascent must be used.

rcap

Equal to the value of the cap unit on the root element.

ch

Represents the typical advance measure of European alphanumeric characters, and measured as the used advance measure of the “0” (ZERO, U+0030) glyph in the font used to render it. (The advance measure of a glyph is its advance width or height, whichever is in the inline axis of the element.)

Note: This measurement is an approximation (and in monospace fonts, an exact measure) of a single narrow glyph’s advance measure, thus allowing measurements based on an expected glyph count.

Note: The advance measure of a glyph depends on writing-mode and text-orientation as well as font settings, text-transform, and any other properties that affect glyph selection or orientation.

In the cases where it is impossible or impractical to determine the measure of the “0” glyph, it must be assumed to be 0.5em wide by 1em tall. Thus, the ch unit falls back to 0.5em in the general case, and to 1em when it would be typeset upright (i.e. writing-mode is vertical-rl or vertical-lr and text-orientation is upright).

Tests

• ch-unit-001.html (live test) (source)
• ch-unit-002.html (live test) (source)
• ch-unit-003.html (live test) (source)
• ch-unit-004.html (live test) (source)
• ch-unit-008.html (live test) (source)
• ch-unit-009.html (live test) (source)
• ch-unit-010.html (live test) (source)
• ch-unit-011.html (live test) (source)
• ch-unit-012.html (live test) (source)
• ch-unit-016.html (live test) (source)
• ch-unit-017.html (live test) (source)
• line-break-ch-unit.html (live test) (source)
• calc-ch-ex-lang.html (live test) (source)

rch

Equal to the value of the ch unit on the root element.

ic

Represents the typical advance measure of CJK letters, and measured as the used advance measure of the “水” (CJK water ideograph, U+6C34) glyph found in the font used to render it.

Note: This measurement is a typically an exact measure (in the few fonts with proportional fullwidth glyphs, an approximation) of a single fullwidth glyph’s advance measure, thus allowing measurements based on an expected glyph count.

In the cases where it is impossible or impractical to determine the ideographic advance measure, it must be assumed to be 1em.

Tests

• ic-unit-001.html (live test) (source)
• ic-unit-002.html (live test) (source)
• ic-unit-003.html (live test) (source)
• ic-unit-004.html (live test) (source)
• ic-unit-008.html (live test) (source)
• ic-unit-009.html (live test) (source)
• ic-unit-010.html (live test) (source)
• ic-unit-011.html (live test) (source)
• ic-unit-012.html (live test) (source)

ric

Equal to the value of the ic unit on the root element.

lh

Equal to the computed value of the line-height property of the element on which it is used, converting normal to an absolute length by using only the metrics of the first available font.

Tests

• lh-rlh-on-root-001.html (live test) (source)
• lh-unit-001.html (live test) (source)
• lh-unit-002.html (live test) (source)

rlh

Equal to the value of the lh unit on the root element.

Note: Setting the height of an element using either the lh or the rlh units does not enable authors to control the actual number of lines in that element. These units only enable length calculations based on the theoretical size of an ideal empty line; the size of actual lines boxes may differ based on their content. In cases where an author wants to limit the number of actual lines in an element, the max-lines property can be used instead.

Tests

• lh-rlh-on-root-001.html (live test) (source)

When used in the value of any font-* property on the element they refer to, the font-relative lengths resolve against the computed metrics of the parent element—​or against the computed metrics corresponding to the initial values of the font and line-height properties, if the element has no parent. Similarly, when lh or rlh units are used in the value of the line-height property or font-* properties on the element they refer to, they resolve against the computed line-height and font metrics of the parent element—​or the computed metrics corresponding to the initial values of the font and line-height properties, if the element has no parent. (The other font-relative lengths continue to resolve against the element’s own metrics when used in line-height.)

When used outside the context of an element (such as in media queries), the font-relative lengths units refer to the metrics corresponding to the initial values of the font and line-height properties. Similarly, when specified in a document with no root element, the root font-relative lengths are resolved assuming the initial values of the font and line-height properties.

Note: Font-relative units such as ch and ic can trigger font downloads, if a required font is not yet loaded.

The font-relative lengths are calculated in the absence of shaping.

Some user-agents allow users to apply additional restrictions to font sizes in a document, such as setting minimum font sizes to ensure readability. Such restrictions must be applied to the used value of the affected properties only; they must not affect the resolution of font-relative lengths used in properties. However, in other contexts (such as in media queries), to the extent that they would impact the used font metrics, such restrictions do affect the resolution of font-relative lengths.

Note: In general, respecting a user’s preferences, like minimum font sizes, is desirable; it’s useful for a media query like (min-width: 40em) to use the actual font size the document will be displayed in. However, having these preferences affect font-relative lengths in properties on an element was found to not be Web-compatible; too many pages expect these units to be exact multiples of the specified font-size, rather than the actual font-size after applying user preferences.

Some user-agents apply restrictions to the line-height values on form controls. These must have no effect on the lh and rlh units. The effect on their descendants, however, is implementation-defined.

6.1.2. Viewport-percentage Lengths: the *vw, *vh, *vi, *vb, *vmin, *vmax units

The viewport-percentage lengths are relative to the size of the initial containing block—​which is itself based on the size of either the viewport (for continuous media) or the page area (for paged media). When the height or width of the initial containing block is changed, they are scaled accordingly.

6.1.2.1. The Large, Small, and Dynamic Viewport Sizes

There are four variants of the viewport-percentage length units, corresponding to three (possibly identical) notions of the viewport size.

large viewport

The large viewport-percentage units (lv*) and default viewport-percentage units (v*) are defined with respect to the large viewport size: the viewport sized assuming any UA interfaces that are dynamically expanded and retracted to be retracted. This allows authors to size content such that it is guaranteed to fill the viewport, noting that such content might be hidden behind such interfaces when they are expanded.

The sizes of the large viewport-percentage units are fixed (and therefore stable) unless the viewport itself is resized.

For example, on phones, where screen real-estate is at a premium, browsers will often hide part or all of the title and address bar once the user starts scrolling the page. The large viewport-percentage units are sized relative to this larger everything-retracted space, so content using these units will fill the entire visible page when these UI elements are hidden. However, when these retractable elements are shown, they can obscure content that is sized or positioned using these units.

small viewport

The small viewport-percentage units (sv*) are defined with respect to the small viewport size: the viewport sized assuming any UA interfaces that are dynamically expanded and retracted to be expanded. This allows authors to size content such that it can fit within the viewport even when such interfaces are present, noting that such content might not fill the viewport when such interfaces are retracted.

The sizes of the small viewport-percentage units are fixed (and therefore stable) unless the viewport itself is resized.

An element that is sized as height: 100svh, for example, will fill the screen perfectly, without any of its content being obscured, when all the dynamic UI elements of the UA are shown.

Once those UI elements start being hidden, however, there will be extra space around the element. The small viewport-percentage units units are thus “safer” in general, but might not produce the most attractive layout once the user starts interacting with the page.

dynamic viewport

The dynamic viewport-percentage units (dv*) are defined with respect to the dynamic viewport size: the viewport sized with dynamic consideration of any UA interfaces that are dynamically expanded and retracted. This allows authors to size content such that it can exactly fit within the viewport whether or not such interfaces are present.

The sizes of the dynamic viewport-percentage units are not stable even while the viewport itself is unchanged. Using these units can cause content to resize e.g. while the user scrolls the page. Depending on usage, this can be disturbing to the user and/or costly in terms of performance.

The UA is not required to animate the dynamic viewport-percentage units while expanding and retracting any relevant interfaces, and may instead calculate the units as if the relevant interface was fully expanded or retracted during the UI animation. (It is recommended that UAs assume the fully-retracted size for this duration.)

Whether the expansion/retraction of a particular interface (A) changes the sizes of all of the viewport-percentage lengths (and the initial containing block) simultaneously or (B) contributes to the differences between the large viewport size and small viewport size is largely UA-dependent. However:

• Changes in interface that happen as a result of scrolling or other frequent page interactions that would disturb the user if they resulted in substantial layout changes must be categorized as the latter (B).

• Changes in interface that have a sufficiently steady state that re-laying out the document into the adjusted space would be beneficial to the user must be categorized as the former (A).

• Additionally, UAs may have some dynamically-shown interfaces that intentionally overlay content and do not cause any shifts in layout—​and therefore have no effect on any of the viewport-percentage lengths. (Typically on-screen keyboards will fit into this category.)

In all cases, if the value of overflow or scrollbar-gutter on the root element in either axis would cause scrollbars to appear (or space to be reserved for them) unconditionally (for example, overflow: scroll, but not overflow: auto), the computed values of the viewport-percentage lengths in that axis are reduced in accordance with the initial containing block. Otherwise, and always in the case of media queries, the viewport-percentage lengths are sized assuming that scrollbars do not exist (even if this diverges from the initial containing block).

Note: The value of overflow on the body element can sometimes affect the presence of scrollbars on the root element. This does not affect the size of viewport units, however.

6.1.2.2. The Various Viewport-relative Units

The viewport-percentage length units are:

vw

svw

lvw

dvw

Equal to 1% of the width of the large viewport size, small viewport size, large viewport size, and dynamic viewport size, respectively.

In the example below, if the width of the viewport is 200mm, the font size of h1 elements will be 16mm (i.e. (8×200mm)/100).

h1 { font-size: 8vw }

vh

svh

lvh

dvh

Equal to 1% of the height of the large viewport size, small viewport size, large viewport size, and dynamic viewport size, respectively.

vi

svi

lvi

dvi

Equal to 1% of the size of the large viewport size, small viewport size, large viewport size, and dynamic viewport size (respectively) in the box’s inline axis.

vb

svb

lvb

dvb

Equal to 1% of the size of the initial containing block large viewport size, small viewport size, large viewport size, and dynamic viewport size (respectively) in the box’s block axis.

vmin

svmin

lvmin

dvmin

Equal to the smaller of *vw or *vh.

vmax

svmax

lvmax

dvmax

Equal to the larger of *vw or *vh.

Note: The original (unprefixed) viewport units were defined relative to the initial containing block, which in continuous media always matched the (singular) viewport size. The dynamism of browser chrome shifting in and out during scrolling was invented later, and following Safari’s lead, most UAs mapped these units to the larger size. Defining it this way is prettier in many cases, but can also block critical content (such as toolbars, headers, and footers) in others. It’s therefore not entirely clear whether this was the best mapping, and thus earlier editions of this specifications allowed UAs to choose the mapping of these default units. However at this point the mapping to the large viewport-percentage units is presumed to be required for Web compatibility.

In situations where there is no element or it hasn’t yet been styled (such as when evaluating media queries), the *vi and *vb units use the initial value of the writing-mode property to determine which axis they correspond to.

6.2. Absolute Lengths: the cm, mm, Q, in, pt, pc, px units

The absolute length units are fixed in relation to each other and anchored to some physical measurement. They are mainly useful when the output environment is known. The absolute units consist of the physical units (in, cm, mm, pt, pc, Q) and the visual angle unit (pixel unit) (px):

h1 { margin: 0.5in }      /* inches  */
h2 { line-height: 3cm }   /* centimeters */
h3 { word-spacing: 4mm }  /* millimeters */
h3 { letter-spacing: 1Q } /* quarter-millimeters */
h4 { font-size: 12pt }    /* points */
h4 { font-size: 1pc }     /* picas */
p  { font-size: 12px }    /* px */

Note: Lengths in publishing contexts are sometimes written like 2p3, indicating a length of 2 picas and 3 points. These can be written in CSS as calc(2pc + 3pt) (see § 10.1 Basic Arithmetic: calc()).

All of the absolute length units are compatible, and px is their canonical unit.

For a CSS device, these dimensions are anchored either

1. by relating the physical units to their physical measurements, or
2. by relating the pixel unit to the reference pixel.

For print media at typical viewing distances, the anchor unit should be one of the physical units (inches, centimeters, etc). For screen media (including high-resolution devices), low-resolution devices, and devices with unusual viewing distances, it is recommended instead that the anchor unit be the pixel unit. For such devices it is recommended that the pixel unit refer to the whole number of device pixels that best approximates the reference pixel.

Note: If the anchor unit is the pixel unit, the physical units might not match their physical measurements. Alternatively if the anchor unit is a physical unit, the pixel unit might not map to a whole number of device pixels.

Note: This definition of the pixel unit and the physical units differs from the earlier editions of CSS1 and CSS2. In particular, in previous versions of CSS the pixel unit and the physical units were not related by a fixed ratio: the physical units were always tied to their physical measurements while the pixel unit would vary to most closely match the reference pixel. (This unfortunate change was made because too much existing content relies on the assumption of 96dpi, and breaking that assumption broke the content.)

Note: Units are ASCII case-insensitive and serialize as lowercase, for example 1Q serializes as 1q.

The reference pixel is the visual angle of one pixel on a device with a device pixel density of 96dpi and a distance from the reader of an arm’s length. For a nominal arm’s length of 28 inches, the visual angle is therefore about 0.0213 degrees. For reading at arm’s length, 1px thus corresponds to about 0.26 mm (1/96 inch).

The image below illustrates the effect of viewing distance on the size of a reference pixel: a reading distance of 71 cm (28 inches) results in a reference pixel of 0.26 mm, while a reading distance of 3.5 m (12 feet) results in a reference pixel of 1.3 mm.

This second image illustrates the effect of a device’s resolution on the pixel unit: an area of 1px by 1px is covered by a single dot in a low-resolution device (e.g. a typical computer display), while the same area is covered by 16 dots in a higher resolution device (such as a printer).

A device pixel is the smallest unit of area on the device output capable of displaying its full range of colors. For typical color screens, it’s a square or somewhat rectangular region containing a red, green, and blue subpixel. Many non-traditional outputs exist that can blur this definition, such as by displaying some colors at higher resolutions. Such devices still expose some equivalent notion of "device pixel", however.

7. Other Quantities

7.1. Angle Units: the <angle> type and deg, grad, rad, turn units

Angle values are <dimension>s denoted by <angle>. The angle unit identifiers are:

deg

Degrees. There are 360 degrees in a full circle.

grad

Gradians, also known as "gons" or "grades". There are 400 gradians in a full circle.

rad

Radians. There are 2π radians in a full circle.

turn

Turns. There is 1 turn in a full circle.

For example, a right angle is 90deg or 100grad or 0.25turn or approximately 1.57rad.

All <angle> units are compatible, and deg is their canonical unit.

Note: For legacy reasons, some uses of <angle> allow a bare 0 to mean 0deg. This is not true in general, however, and will not occur in future uses of the <angle> type.

7.2. Duration Units: the <time> type and s, ms units

Time values are dimensions denoted by <time>. The time unit identifiers are:

s

Seconds.

ms

Milliseconds. There are 1000 milliseconds in a second.

All <time> units are compatible, and s is their canonical unit.

Properties may restrict the time value to some range. If the value is outside the allowed range, the declaration is invalid and must be ignored.

7.3. Frequency Units: the <frequency> type and Hz, kHz units

Frequency values are dimensions denoted by <frequency>. The frequency unit identifiers are:

Hz

Hertz. It represents the number of occurrences per second.

kHz

KiloHertz. A kiloHertz is 1000 Hertz.

For example, when representing sound pitches, 200Hz (or 200hz) is a bass sound, and 6kHz (or 6khz) is a treble sound.

All <frequency> units are compatible, and hz is their canonical unit.

Note: Units are ASCII case-insensitive and serialize as lowercase, for example 1Hz serializes as 1hz.

7.4. Resolution Units: the <resolution> type and dpi, dpcm, dppx units

Resolution units are dimensions denoted by <resolution>. The resolution unit identifiers are:

dpi

Dots per inch.

dpcm

Dots per centimeter.

dppx

x

Dots per px unit.

The <resolution> unit represents the size of a single "dot" in a graphical representation by indicating how many of these dots fit in a CSS in, cm, or px. For uses, see e.g. the resolution media query in [MEDIAQ] or the image-resolution property defined in [CSS3-IMAGES].

All <resolution> units are compatible, and dppx is their canonical unit.

The allowed range of <resolution> values always excludes negative values, in addition to any explicit ranges that might be specified.

Note that due to the 1:96 fixed ratio of CSS in to CSS px, 1dppx is equivalent to 96dpi. This corresponds to the default resolution of images displayed in CSS: see image-resolution.

@media (min-resolution: 2dppx) { ... }

8. Data Types Defined Elsewhere

Some data types are defined in their own modules. This example talks about some of the most common ones used across several specifications.

8.1. Colors: the <color> type

The <color> data type is defined in [CSS-COLOR-4]. UAs must interpret <color> as defined therein.

8.1.1. Combination of <color>

Interpolation of <color> is defined in CSS Color 4 §  12. Color Interpolation. Interpolation is done between premultiplied colors, as defined in CSS Color 4 § 12.3 Interpolating with Alpha.

The <color> type is not additive.

Note: the CSS WG is interested to hear use-cases for addition of <color>, and may consider making <color> additive in the future.

8.2. Images: the <image> type

The <image> data type is defined in [CSS3-IMAGES]. UAs that support CSS Images Level 3 or its successor must interpret <image> as defined therein. UAs that do not yet support CSS Images Level 3 must interpret <image> as <url>.

8.2.1. Combination of <image>

Note: Interpolation of <image> is defined in CSS Images 3 § 6 Interpolation.

Images are not additive.

8.3. 2D Positioning: the <position> type

The <position> value specifies the position of a object area (e.g. background image) inside a positioning area (e.g. background positioning area). It is computed and interpreted as specified for background-position. [CSS3-BACKGROUND]

<position> = [
  [ left | center | right | top | bottom | <length-percentage> ]
|
  [ left | center | right ] && [ top | center | bottom ]
|
  [ left | center | right | <length-percentage> ]
  [ top | center | bottom | <length-percentage> ]
|
  [ [ left | right ] <length-percentage> ] &&
  [ [ top | bottom ] <length-percentage> ]
]

Note: The background-position property also accepts a three-value syntax. This has been disallowed generically because it creates parsing ambiguities when combined with other length or percentage components in a property value.

8.3.1. Parsing <position>

When specified in a grammar alongside other keywords, <length>s, or <percentage>s, <position> is greedily parsed; it consumes as many components as possible.

8.3.2. Serializing <position>

When serializing the specified value of a <position>:

If only one component is specified:

• The implied center keyword is added, and a 2-component value is serialized.

If two components are specified:

• Keywords are serialized as keywords.

• <length-percentage>s are serialized as <length-percentage>s.

• Components are serialized horizontal first, then vertical.

If four components are specified:

• Keywords and offsets are both serialized.

• Components are serialized horizontal first, then vertical.

Note: <position> values are never serialized as a single value, even when a single value would produce the same behavior, to avoid causing parsing ambiguities in some grammars where a <position> is placed next to a <length>, such as transform-origin.

Note: Computed values are always serialized as two offsets (without keywords) because the computed value does not preserve syntactic distinctions.

8.3.3. Combination of <position>

Interpolation of <position> is defined as the independent interpolation of each component (x, y) normalized as an offset from the top left corner as a <length-percentage>.

Addition of <position> is likewise defined as the independent addition each component (x, y) normalized as an offset from the top left corner as a <length-percentage>.

9. Functional Notations

A functional notation is a type of component value that can represent more complex types or invoke special processing. The syntax starts with the name of the function immediately followed by a left parenthesis (i.e. a <function-token>) followed by the argument(s) to the notation followed by a right parenthesis. Like keywords, function names are ASCII case-insensitive. White space is allowed, but optional, immediately inside the parentheses. Functions can take multiple arguments, which are formatted similarly to a CSS property value. See § 2.6 Functional Notation Definitions.

Note: Some legacy functional notations, such as rgba(), use commas unnecessarily, but generally commas are only used to separate items in a list, or pieces of a grammar that would be ambiguous otherwise. If a comma is used to separate arguments, white space is optional before and after the comma.

background: url(http://www.example.org/image);
color: rgb(100, 200, 50 );
content: counter(list-item) ". ";
width: calc(50% - 2em);

The math functions are defined below. Other functional notations are defined in their own modules; for example the <color> functions are defined in [CSS-COLOR-4] and [CSS-COLOR-5].

10. Mathematical Expressions

The math functions (calc(), clamp(), sin(), and others defined in this chapter) allow numeric CSS values to be written as mathematical expressions.

A math function represents a numeric value, one of:

• <length>,

• <frequency>,

• <angle>,

• <time>,

• <flex>,

• <resolution>,

• <percentage>,

• <number>,

• <integer>

...or the <length-percentage>/etc mixed types, and can be used wherever such a value would be valid.

10.1. Basic Arithmetic: calc()

The calc() function is a math function that allows basic arithmetic to be performed on numerical values, using addition (+), subtraction (-), multiplication (*), division (/), and parentheses.

A calc() function contains a single calculation, which is a sequence of values interspersed with operators, and possibly grouped by parentheses (matching the <calc-sum> grammar), which represents the result of evaluating the expression using standard operator precedence rules (* and / bind tighter than + and -, and operators are otherwise evaluated left-to-right). The calc() function represents the result of its contained calculation.

Components of a calculation can be literal values (such as 5px), other math functions, or other expressions, such as var(), that evaluate to a valid argument type (like <length>).

section {
  float: left;
  margin: 1em; border: solid 1px;
  width: calc(100% / 3 - 2 * 1em - 2 * 1px);
}

.fade {
  background-image: linear-gradient(silver 0%, white 20px,
                                    white calc(100% - 20px), silver 100%);
}

:root {
  font-size: calc(100vw / 35);
}

.aspect-ratio-box {
  --ar: calc(16 / 9);
  --w: calc(100% / 3);
  --h: calc(var(--w) / var(--ar));
  width: var(--w);
  height: var(--h);
}

10.2. Comparison Functions: min(), max(), and clamp()

The comparison functions of min(), max(), and clamp() compare multiple calculations and represent the value of one of them.

The min() or max() functions contain one or more comma-separated calculations, and represent the smallest (most negative) or largest (most positive) of them, respectively.

The clamp() function takes three calculations—​a minimum value, a central value, and a maximum value—​and represents its central calculation, clamped according to its min and max calculations, favoring the min calculation if it conflicts with the max. (That is, given clamp(MIN, VAL, MAX), it represents exactly the same value as max(MIN, min(VAL, MAX))).

Either the min or max calculations (or even both) can instead be the keyword none, which indicates the value is not clamped from that side. (That is, clamp(MIN, VAL, none) is equivalent to max(MIN, VAL), clamp(none, VAL, MAX) is equivalent to min(VAL, MAX), and clamp(none, VAL, none) is equivalent to just calc(VAL).)

For all three functions, the argument calculations can resolve to any <number>, <dimension>, or <percentage>, but must have a consistent type or else the function is invalid; the result’s type will be the consistent type.

.type {
  /* Set font-size to 10x the average of vw and vh,
     but don’t let it go below 12px. */
  font-size: max(10 * (1vw + 1vh) / 2, 12px);
}

.type {
  /* Force the font-size to stay between 12px and 100px */
  font-size: clamp(12px, 10 * (1vw + 1vh) / 2, 100px);
}

.type {
  /* Force the font-size to be at least 12px */
  font-size: clamp(12px, 10 * (1vw + 1vh) / 2, none);
}

10.3. Stepped Value Functions: round(), mod(), and rem()

The stepped-value functions,