How to use the Excel ACOS function

Summary

The ACOS function returns the inverse cosine of a number. The function is the inverse of COS and expects input in the range from -1 to 1.

Purpose

Get the inverse cosine of a value, in radians.

Return value

Angle in radians.

Syntax

=ACOS (number)

Arguments

number - The value to get the inverse cosine of. The number must be between -1 and 1 inclusive.

Usage notes

The ACOS function returns the inverse cosine of a value. Input to the arc-cosine function must be between -1 and 1, inclusive. Geometrically, given the ratio of a triangle's adjacent side over its hypotenuse, the function returns the angle of the triangle. For example, given a ratio of 0.5 the function returns the angle of 1.047 radians.

=ACOS(0.5) // Returns 1.047 radians

Convert Result to Degrees

To convert the result from radians to degrees, multiply the result by 180/PI() or use the DEGREES function. For example, the convert the result of ACOS(0.5) to degrees, you can use either formula below:

=ACOS(0.5)*180/PI() // Returns 60 degrees
=DEGREES(ACOS(0.5)) // Returns 60 degrees

Explanation

Graph of ACOS Function

The graph of ACOS visualizes the output of the function in the range from -1 to 1. ACOS is the inverse of the COS function. However, because COS is a periodic function, the output of ACOS is limited to the range from 0 to π.

Graph courtesy of wumbo.net.

Related functions

Excel COS Function

The Excel COS function returns the cosine of an angle given in radians. To supply an angle to COS in degrees, use the RADIANS function to convert to radians.

Excel ASIN Function

The Excel ASIN function returns the inverse sine of a number.

Excel ATAN Function

The Excel ATAN function returns the inverse tangent of a number. The function is the inverse of TAN.

Excel ATAN2 Function

The Excel ATAN2 function returns the arctangent from x- and y-coordinates. In geometric terms, the function returns the radian angle corresponding to the input point.