Inverse Cosine Calculator
Find the angle whose cosine is a given value. Returns degrees and radians for any input in [−1, 1].
How it works
- 1Enter a value in [−1, 1] — for example 0.5. Values outside this range have no real arccos.
- 2The calculator applies arccos (cos⁻¹), finding the unique angle in [0°, 180°] whose cosine equals your input.
- 3Results appear instantly in both degrees and radians.
Use cases
- Determining the angle between two vectors from their dot product in physics and 3-D graphics.
- Solving triangles in navigation and surveying when a side ratio (cosine) is known.
- Checking or inverting cosine values produced by signal-processing or machine-learning models.
Frequently asked questions
Why is arccos only defined between −1 and 1?
The cosine of any angle always lies in [−1, 1], so no real angle has a cosine outside that range. Inputs beyond it yield no real solution.
Why does arccos return an angle between 0° and 180°?
Infinitely many angles share the same cosine. By convention arccos returns the principal value — the unique angle in [0°, 180°] — making it single-valued.
How do I convert the radian result to degrees?
Multiply radians by 180 ÷ π (≈ 57.2958). For example, π ÷ 3 rad × (180 ÷ π) = 60°.
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