---
title: Numeric Operators
table_of_contents: true
introduction: >
  Sass supports the standard set of mathematical operators for
  [numbers](../values/numbers). They automatically convert between compatible
  units.
---

* `<expression> + <expression>` adds the first [expression][]'s value to the
  second's.
* `<expression> - <expression>` subtracts the first [expression][]'s value from
  the second's.
* `<expression> * <expression>` multiplies the first [expression][]'s value by
  the second's.
* `<expression> / <expression>` divides the first [expression][]'s value by the
  second's.
* `<expression> % <expression>` returns the remainder of the first
  [expression][]'s value divided by the second's. This is known as the [*modulo*
  operator][].

[expression]: ../syntax/structure#expressions
[*modulo* operator]: https://en.wikipedia.org/wiki/Modulo_operation

<% example(autogen_css: false) do %>
  @debug 10s + 15s; // 25s
  @debug 1in - 10px; // 0.8958333333in
  @debug 5px * 3px; // 15px*px
  @debug (12px/4px); // 3
  @debug 1in % 9px; // 0.0625in
  ===
  @debug 10s + 15s  // 25s
  @debug 1in - 10px  // 0.8958333333in
  @debug 5px * 3px  // 15px*px
  @debug (12px/4px)  // 3
  @debug 1in % 9px  // 0.0625in
<% end %>

Unitless numbers can be used with numbers of any unit.

<% example(autogen_css: false) do %>
  @debug 100px + 50; // 150px
  @debug 4s * 10; // 40s
  ===
  @debug 100px + 50  // 150px
  @debug 4s * 10  // 40s
<% end %>

Numbers with incompatible units can't be used with addition, subtraction, or
modulo.

<% example(autogen_css: false) do %>
  @debug 100px + 10s;
  //     ^^^^^^^^^^^
  // Error: Incompatible units px and s.
  ===
  @debug 100px + 10s
  //     ^^^^^^^^^^^
  // Error: Incompatible units px and s.
<% end %>

## Unary Operators

You can also write `+` and `-` as unary operators, which take only one value:

* `+<expression>` returns the expression's value without changing it.
* `-<expression>` returns the negative version of the expression's value.

<% example(autogen_css: false) do %>
  @debug +(5s + 7s); // 12s
  @debug -(50px + 30px); // -80px
  @debug -(10px - 15px); // 5px
  ===
  @debug +(5s + 7s)  // 12s
  @debug -(50px + 30px)  // -80px
  @debug -(10px - 15px)  // 5px
<% end %>

<% heads_up do %>
  Because `-` can refer to both subtraction and unary negation, it can be
  confusing which is which in a space-separated list. To be safe:

  * Always write spaces on both sides of `-` when subtracting.
  * Write a space before `-` but not after for a negative number or a unary
    negation.
  * Wrap unary negation in parentheses if it's in a space-separated list.

  The different meanings of `-` in Sass take precedence in the following order:

  1. `-` as part of an identifier. The only exception are units; Sass normally
     allows any valid identifier to be used as an identifier, but units may not
     contain a hyphen followed by a digit.
  2. `-` between an expression and a literal number with no whitespace, which is
     parsed as subtraction.
  3. `-` at the beginning of a literal number, which is parsed as a negative number.
  4. `-` between two numbers regardless of whitespace, which is parsed as subtraction.
  5. `-` before a value other than a literal number, which is parsed as unary negation.

  <% example(autogen_css: false) do %>
    @debug a-1; // a-1
    @debug 5px-3px; // 2px
    @debug 5-3; // 2
    @debug 1 -2 3; // 1 -2 3

    $number: 2;
    @debug 1 -$number 3; // -1 3
    @debug 1 (-$number) 3; // 1 -2 3
    ===
    @debug a-1  // a-1
    @debug 5px-3px  // 2px
    @debug 5-3  // 2
    @debug 1 -2 3  // 1 -2 3

    $number: 2
    @debug 1 -$number 3  // -1 3
    @debug 1 (-$number) 3  // 1 -2 3
  <% end %>
<% end %>

## Slash-Separated Values

A few CSS properties support `/` as a way of separating values. This means Sass
has to disambiguate between `/` as a property value and `/` as division. In
order to make this work, if two numbers are separated by `/`, Sass will print
the result as slash-separated instead of divided unless one of these conditions
is met:

* Either expression is anything other than a literal number.
* The result is stored in a variable or returned by a function.
* The operation is surrounded by parentheses, unless those parentheses are
  outside a list that contains the operation.
* The result is used as part of another operation (other than `/`).

If you want to force `/` to be used as a separator, you can write it as
`#{<expression>} / #{<expression>}`.

<% example do %>
  @debug 15px / 30px; // 15px/30px
  @debug (10px + 5px) / 30px; // 0.5
  @debug #{10px + 5px} / 30px; // 15px/30px

  $result: 15px / 30px;
  @debug $result; // 0.5

  @function fifteen-divided-by-thirty() {
    @return 15px / 30px;
  }
  @debug fifteen-divided-by-thirty(); // 0.5

  @debug (15px/30px); // 0.5
  @debug (bold 15px/30px sans-serif); // bold 15px/30px sans-serif
  @debug 15px/30px + 1; // 1.5
  ===
  @debug 15px / 30px  // 15px/30px
  @debug (10px + 5px) / 30px  // 0.5

  $result: 15px / 30px
  @debug $result  // 0.5

  @function fifteen-divided-by-thirty()
    @return 15px / 30px

  @debug fifteen-divided-by-thirty()  // 0.5

  @debug (15px/30px)  // 0.5
  @debug (bold 15px/30px sans-serif)  // bold 15px/30px sans-serif
  @debug 15px/30px + 1  // 1.5
<% end %>

<%= partial 'documentation/snippets/number-units' %>