This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.Find sources: "Unary operation" – news · newspapers · books · scholar · JSTOR (March 2010) (Learn how and when to remove this template message)
This article is written like a manual or guidebook. Please help rewrite this article from a descriptive, neutral point of view, and remove advice or instruction. (November 2020) (Learn how and when to remove this template message)

In mathematics, an unary operation is an operation with only one operand, i.e. a single input.[1] This is in contrast to binary operations, which use two operands.[2] An example is any function f : AA, where A is a set. The function f is a unary operation on A.

Common notations are prefix notation (e.g. ¬, ), postfix notation (e.g. factorial n!), functional notation (e.g. sinx or sin(x)), and superscripts (e.g. transpose AT). Other notations exist as well, for example, in the case of the square root, a horizontal bar extending the square root sign over the argument can indicate the extent of the argument.


Absolute Value

Obtaining the absolute value of a number is a unary operation. This function is defined as [3] where is the absolute value of .


This is used to find the negative value of a single number. This is technically not a unary operation as is just short form of .[4] Here are some examples:

Unary negative and positive

As unary operations have only one operand they are evaluated before other operations containing them. Here is an example using negation:

Here, the first '−' represents the binary subtraction operation, while the second '−' represents the unary negation of the 2 (or '−2' could be taken to mean the integer −2). Therefore, the expression is equal to:

Technically, there is also a unary + operation but it is not needed since we assume an unsigned value to be positive:

The unary + operation does not change the sign of a negative operation:

In this case, a unary negation is needed to change the sign:


In trigonometry, the trigonometric functions, such as , , and , can be seen as unary operations. This is because it is possible to provide only one term as input for these functions and retrieve a result. By contrast, binary operations, such as addition, require two different terms to compute a result.

Examples from programming languages


In JavaScript, these operators are unary:[5]

C family of languages

In the C family of languages, the following operators are unary:[6][7]

Unix Shell (Bash)

In the Unix/Linux shell (bash/sh), '$' is a unary operator when used for parameter expansion, replacing the name of a variable by its (sometimes modified) value. For example:

Windows PowerShell

See also


  1. ^ Weisstein, Eric W. "Unary Operation". Retrieved 2020-07-29.
  2. ^ Weisstein, Eric W. "Binary Operation". Retrieved 2020-07-29.
  3. ^ "Absolute value".
  4. ^ "Negative number".
  5. ^ "Unary Operators".
  6. ^ "Chapter 5. Expressions and Operators". C/C++ Language Reference. Version 6.0. p. 109. Archived from the original on 2012-10-16.
  7. ^ "Unary Operators - C Tutorials - Sanfoundry".