---
title: Calculations
introduction: >
  Calculations are how Sass represents the `calc()` function, as well as similar
  functions like `clamp()`, `min()`, and `max()`. Sass will simplify these as
  much as possible, even if they're combined with one another.
---

{% compatibility 'dart: "1.40.0"', 'libsass: false', 'ruby: false' %}
  LibSass, Ruby Sass, and versions of Dart Sass prior to 1.40.0 parse `calc()`
  as a [special function] like `element()`.

  [special function]: /documentation/syntax/special-functions#element-progid-and-expression

  LibSass, Ruby Sass, and versions of Dart Sass prior to 1.31.0 parse `clamp()`
  as a [plain CSS function] rather than supporting special syntax within it.
  Versions of Dart Sass between 1.31.0 and 1.40.0 parse `clamp()` as a [special
  function] like `element()`.

  [plain CSS function]: /documentation/at-rules/function/#plain-css-functions
{% endcompatibility %}

{% codeExample 'calculations', false %}
  @debug calc(400px + 10%); // calc(400px + 10%)
  @debug calc(400px / 2); // 200px
  @debug min(100px, calc(1rem + 10%)); // min(100px, 1rem + 10%)
  ===
  @debug calc(400px + 10%)  // calc(400px + 10%)
  @debug calc(400px / 2)  // 200px
  @debug min(100px, calc(1rem + 10%) ; // min(100px, 1rem + 10%)
{% endcodeExample %}

{% markdown %}
  Calculations use a special syntax that's different from normal SassScript.
  It's the same syntax as the CSS `calc()`, but with the additional ability to
  use [Sass variables] and call [Sass functions]. This means that `/` is always
  a division operator within a calculation!

  [Sass variables]: /documentation/variables
  [Sass functions]: /documentation/modules

  {% funFact %}
    The arguments to a Sass function call use the normal Sass syntax, rather
    than the special calculation syntax!
  {% endfunFact %}

  You can also use [interpolation] in a calculation. However, if you do, nothing
  in the parentheses that surround that interpolation will be simplified or
  type-checked, so it's easy to end up with extra verbose or even invalid CSS.
  Rather than writing `calc(10px + #{$var})`, just write `calc(10px + $var)`!

  [interpolation]: /documentation/interpolation

  ## Simplification

  Sass will simplify adjacent operations in calculations if they use units that
  can be combined at compile-time, such as `1in + 10px` or `5s * 2`. If
  possible, it'll even simplify the whole calculation to a single number—for
  example, `clamp(0px, 30px, 20px)` will return `20px`.

  {% headsUp %}
    This means that a calculation expression won't necessarily always return a
    calculation! If you're writing a Sass library, you can always use the
    [`meta.type-of()`] function to determine what type you're dealing with.

    [`meta.type-of()`]: /documentation/modules/meta#type-of
  {% endheadsUp %}

  Calculations will also be simplified within other calculations. In particular,
  if a `calc()` end up inside any other calculation, the function call will be
  removed and it'll be replaced by a plain old operation.
{% endmarkdown %}

{% codeExample 'simplification' %}
  $width: calc(400px + 10%);

  .sidebar {
    width: $width;
    padding-left: calc($width / 4);
  }
  ===
  $width: calc(400px + 10%)

  .sidebar
    width: $width
    padding-left: calc($width / 4)
  ===
  .sidebar {
    width: calc(400px + 10%);
    padding-left: calc((400px + 10%) / 4);
  }
{% endcodeExample %}

{% markdown %}
  ## Operations

  You can't use calculations with normal SassScript operations like `+` and `*`.
  If you want to write some math functions that allow calculations just write
  them within their own `calc()` expressions—if they're passed a bunch of
  numbers with compatible units, they'll return plain numbers as well, and if
  they're passed calculations they'll return calculations.

  This restriction is in place to make sure that if calculations *aren't*
  wanted, they throw an error as soon as possible. Calculations can't be used
  everywhere plain numbers can: they can't be injected into CSS identifiers
  (such as `.item-#{$n}`), for example, and they can't be passed to Sass's
  built-in [math functions]. Reserving SassScript operations for plain numbers
  makes it clear exactly where calculations are allowed and where they aren't.

  [math functions]: /documentation/modules/math
{% endmarkdown %}

{% codeExample 'calc-operations', false %}
  $width: calc(100% + 10px);
  @debug $width * 2; // Error!
  @debug calc($width * 2); // calc((100% + 10px) * 2);
  ===
  $width: calc(100% + 10px);
  @debug $width * 2; // Error!
  @debug calc($width * 2); // calc((100% + 10px) * 2);
{% endcodeExample %}

{% markdown %}
  ## Constants

  {% compatibility 'dart: "1.60.0"','libsass: false', 'ruby: false' %}{% endcompatibility %}

  Calculations can also contain constants, which are written as CSS identifiers.
  For forwards-compatibility with future CSS specs, *all* identifiers are
  allowed, and by default they're just treated as unquoted strings that are
  passed-through as-is.
{% endmarkdown %}

{% codeExample 'calc-constants', false %}
  @debug calc(h + 30deg); // calc(h + 30deg);
  ===
  @debug calc(h + 30deg)  // calc(h + 30deg);
{% endcodeExample %}

{% markdown %}
  Sass automatically resolves a few special constant names that are specified in
  CSS to unitless numbers:

  * `pi` is a shorthand for the [mathematical constant *π*].

    [mathematical constant *π*]: https://en.wikipedia.org/wiki/Pi

  * `e` is a shorthand for the [mathematical constant *e*].

    [mathematical constant *e*]: https://en.wikipedia.org/wiki/E_(mathematical_constant)

  * `infinity`, `-infinity`, and `NaN` represent the corresponding
    floating-point values.
{% endmarkdown %}

{% codeExample 'unitless-numbers', false %}
  @use 'sass:math';

  @debug calc(pi); // 3.1415926536
  @debug calc(e);  // 2.7182818285
  @debug calc(infinity) > math.$max-number;  // true
  @debug calc(-infinity) < math.$min-number; // true
  ===
  @use 'sass:math'

  @debug calc(pi)  // 3.1415926536
  @debug calc(e)   // 2.7182818285
  @debug calc(infinity) > math.$max-number   // true
  @debug calc(-infinity) < math.$min-number  // true
{% endcodeExample %}

{% markdown %}
  ## `min()` and `max()`

  {% compatibility 'dart: ">=1.11.0 <1.42.0"', 'libsass: false', 'ruby: false', 'feature: "Special function syntax"' %}
    LibSass, Ruby Sass, and versions of Dart Sass prior to 1.11.0 *always* parse
    `min()` and `max()` as Sass functions. To create a plain CSS `min()` or
    `max()` call for those implementations, you can write something like
    `unquote("min(#{$padding}, env(safe-area-inset-left))")` instead.

    Versions of Dart Sass between 1.11.0 and 1.40.0, and between 1.40.1 and
    1.42.0 parse `min()` and `max()` functions as [special functions] if they're
    valid plain CSS, but parse them as Sass functions if they contain Sass
    features other than interpolation, like variables or function calls.

    Dart Sass 1.41.0 parses `min()` and `max()` functions as calculations, but
    doesn't allow unitless numbers to be combined with numbers with units. This
    was backwards-incompatible with the global `min()` and `max()` functions, so
    that behavior was reverted.

    [special functions]: /documentation/syntax/special-functions
  {% endcompatibility %}

  CSS added support for [`min()` and `max()` functions] in Values and Units
  Level 4, from where they were quickly adopted by Safari [to support the
  iPhoneX]. But Sass supported its own [`min()`] and [`max()`] functions long
  before this, and it needed to be backwards-compatible with all those existing
  stylesheets. This led to the need for extra-special syntactic cleverness.

  [`min()` and `max()` functions]: https://drafts.csswg.org/css-values-4/#calc-notation
  [to support the iPhoneX]: https://webkit.org/blog/7929/designing-websites-for-iphone-x/
  [`min()`]: /documentation/modules/math#min
  [`max()`]: /documentation/modules/math#max

  If a `min()` or `max()` function call is a valid calculation expression, it
  will be parsed as a calculation. But as soon as any part of the call contains
  a SassScript feature that isn't supported in a calculation, like the [modulo
  operator], it's parsed as a call to Sass's core `min()` or `max()` function
  instead.

  Since calculations are simplified to numbers when possible anyway, the only
  substantive difference is that the Sass functions only support units that can
  be combined at build time, so `min(12px % 10, 10%)` will throw an error.

  [modulo operator]: /documentation/operators/numeric
{% endmarkdown %}

{% headsUp %}
  Other calculations don't allow unitless numbers to be added to, subtracted
  from, or compared to numbers with units. `min()` and `max()` are different,
  though: for backwards-compatibility with the global Sass `min()` and `max()`
  functions which allow unit/unitless mixing for historical reasons, these units
  can be mixed as long as they're contained directly within a `min()` or `max()`
  calculation.
{% endheadsUp %}

{% codeExample 'min-max' %}
  $padding: 12px;

  .post {
    // Since these max() calls are valid calculation expressions, they're
    // parsed as calculations.
    padding-left: max($padding, env(safe-area-inset-left));
    padding-right: max($padding, env(safe-area-inset-right));
  }

  .sidebar {
    // Since these use the SassScript-only modulo operator, they're parsed as
    // SassScript function calls.
    padding-left: max($padding % 10, 20px);
    padding-right: max($padding % 10, 20px);
  }
  ===
  $padding: 12px

  .post
    // Since these max() calls are valid calculation expressions, they're
    // parsed as calculations.
    padding-left: max($padding, env(safe-area-inset-left))
    padding-right: max($padding, env(safe-area-inset-right))


  .sidebar
    // Since these use the SassScript-only modulo operator, they're parsed as
    // SassScript function calls.
    padding-left: max($padding % 10, 20px)
    padding-right: max($padding % 10, 20px)
{% endcodeExample %}