Arccos Calculator (Inverse Cosine)
The Arccos Calculator finds the inverse cosine of a value between -1 and 1, returning the angle in both radians and degrees. The formula used is: arccos(x) = the angle whose cosine is x.
Formula
arccos(x) = inverse cosine
- The Arccos Calculator updates instantly as you change the input value.
- Formula: arccos(x) = the angle whose cosine is x
- Input definitions: • Value (-1 to 1): the cosine value; arccos is only defined on this interval
- The result is the principal value, an angle from 0 to π radians (0° to 180°).
- Radians are converted to degrees by multiplying by 180/π.
- Values outside -1 to 1 have no real inverse cosine.
Example Calculation
Inputs
- Value (-1 to 1): 0.5
arccos(0.5) = π/3 ≈ 1.0472 radians, which equals 60°.
Frequently asked questions
What is arccos?
Arccos, or inverse cosine, returns the angle whose cosine equals the given value. It reverses the cosine function.
What input range is allowed?
Only values from -1 to 1, since cosine never produces results outside that range.
What is the output range?
The principal value runs from 0 to π radians (0° to 180°).
How do I convert the answer to degrees?
Multiply the radian result by 180/π. This calculator shows both radians and degrees automatically.
Why does arccos(0.5) equal 60°?
Because cos(60°) = 0.5, so the angle whose cosine is 0.5 is 60° (π/3 radians).