The Excel ACOS Function


The Arccosine is the inverse of the cosine.

Therefore, for the simple right-angled triangle below, the arccosine of the adjacent side, a, divided by the hypotenuse, h, is equal to the angle θ.

Right-Angled Triangle

I.e. for the triangle above,

Arccosine Equation
The Inverse trig. functions are discussed further on the Wikipedia Inverse Trigonometric Functions Page

Basic Description

The Excel ACOS function calculates the arccosine (i.e. the inverse cosine) of a given number, and returns an angle, in radians, between 0 and π.

The syntax of the function is:

ACOS( number )

Where the number argument is the value, between -1 and +1, for which you want to calculate the arccosine.

Converting from Radians to Degrees

If you want the angle returned by the Acos function to be expressed in degrees, you can convert it, using the Excel Degrees function:

=DEGREES( radians )
An example of this is provided below.

Excel Acos Function Examples

Column A of the following spreadsheet the Excel Acos Function, used to calculate the arccosine of four different values.

1=ACOS( -1 )
2=ACOS( 0 )
3=ACOS( 1 / SQRT(2) )
4=DEGREES( ACOS( 1 / SQRT(2) ) )
13.141592654 - Result is π radians
21.570796327 - Result is π/2 radians
30.785398163 - Result is π/4 radians
445 - Result is 45 degrees

Note that in cell A4 of the above spreadsheet, the Excel Degrees function is used to convert the calculated angle from radians to degrees.

Further details and examples of the Excel Acos function can be found on the Microsoft Office website.

Acos Function Errors

If you get an error from the Excel Acos function, this is likely to be one of the following:

Common Errors
#NUM!-Occurs if the supplied number argument is outside the range -1 to +1.
#VALUE!-Occurs if the supplied number argument is non-numeric.