# Documentation/Calc Functions/ACOS

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ACOS

Mathematical

## Summary:

Returns the inverse trigonometric cosine (the arccosine) of a number. This function calculates the principal value.

ACOS(Number)

## Returns:

This function returns the inverse trigonometric cosine of Number, that is the angle (in radians) whose cosine is Number. The angle returned is between 0 and PI, i.e. [0,π].

## Arguments:

Number is the real number, or a reference to a cell containing that number, between -1 and +1, whose inverse trigonometric cosine value is to be calculated.

If the value of Number is outside this range, the function returns an invalid numeric value (#NUM!) error.

• To return the angle in degrees, use the DEGREES function.
• Alternatively multiply by 180/PI() to convert the result from radians to degrees.

The GIF below illustrates the function ACOS.

## Examples:

Formula Description Returns
=ACOS(-1) Inverse trigonometric cosine of -1 3.14159265358979 (PI radians or π)
=ACOS(0.5) Inverse trigonometric cosine of 0.5 1.0471975511966 (radians)
=DEGREES(ACOS(0.5)) Inverse trigonometric cosine of 0.5. Further, converting angle in radians to degrees. 60° (degrees)
=ACOS(-0.5)*180/PI() Inverse trigonometric cosine of -0.5. Further, converting angle in radians to degrees by multiplying by 180/PI(). 120° (degrees)
=ACOS(2) Inverse trigonometric cosine of 2 will return an invalid numeric value (#NUM!) error because 2 is out of its domain. #NUM!

COS

DEGREES

ACOS