Syntax
ACOS(number)
| Parameter | Description |
|---|---|
| number | Parameter of the ACOS function. |
Examples
Arccosine of 0.5
Formula
=ACOS(0.5)
Returns ~1.0472 radians (π/3 or 60°). The angle whose cosine is 0.5 is 60 degrees.
Angle between vectors
Formula
=DEGREES(ACOS(SUMPRODUCT(A1:A3,B1:B3)/(SQRT(SUMSQ(A1:A3))*SQRT(SUMSQ(B1:B3)))))
Returns the angle in degrees between two 3D vectors. The formula uses the dot product divided by the product of magnitudes.
Right triangle angle
Formula
=DEGREES(ACOS(4/5))
Returns ~36.87°. In a right triangle with adjacent=4 and hypotenuse=5, the angle is about 36.87 degrees.
Common Errors
#NUM!
Input must be between -1 and 1. =ACOS(2) returns #NUM! because no angle has a cosine of 2.
#VALUE!
Non-numeric input returns #VALUE!.
Tips
Angle between vectors
The angle between two vectors = ACOS(dot_product / (magnitude1 × magnitude2)). This is one of the most common uses of ACOS.
Range is 0 to π
ACOS always returns a value between 0 and π (0° to 180°). It never returns negative angles.
Complementary to ASIN
ASIN(x) + ACOS(x) = π/2 (90°). If you know the arcsine, you can get the arccosine by subtracting from π/2.
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