The Excel ACOS Function


Arccosine

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 (ie. the inverse cosine) of a given number, and returns an angle, in radians, between 0 and π.

The format 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 given below.


Excel Acos Function Examples

Column A of the spreadsheet below, shows examples of the Excel Acos Function, used to calculate the arccosine of different values. In the example in cell A4, the result is converted from radians, into degrees.

 Formulas:
  A
1 =ACOS( -1 )
2 =ACOS( 0 )
3 =ACOS( 1 / SQRT(2) )
4 =DEGREES( ACOS( 1 / SQRT(2) ) )
 Results:
  A B
1 3.141592654 - Result is π radians
2 1.570796327 - Result is π/2 radians
3 0.785398163 - Result is π/4 radians
4 45 - Result is 45 degrees

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


Acos Function Error

If you get an error from the Excel Acos function, this is likely to be the #NUM! error:

Common Error
#NUM! - Occurs if the supplied number argument is outside of the range -1 to +1.
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