Find the angle whose cosine equals a given value — the inverse of the cosine function, commonly written arccos or cos⁻¹.
How it works
For any x between −1 and 1, arccos(x) returns the angle (in this calculator, in degrees) whose cosine is x. Arccos always returns an answer between 0° and 180°.
What this does not include
This returns only the principal value in the 0° to 180° range. Cosine is periodic, so other angles share the same cosine value — this calculator doesn’t list them all.
How to use this calculator
- Enter a value between −1 and 1.
A worked example
cos⁻¹(0.5) = 60°, since cos(60°) = 0.5.
cos⁻¹(−1) = 180°, the angle where cosine reaches its minimum value.
What the variables mean
| Variable | Meaning |
|---|---|
| x | A cosine value, between −1 and 1 |
| Result | The angle (in degrees) whose cosine equals x |
Edge cases worth knowing
Inputs outside −1 to 1 have no valid answer. Cosine itself never produces a value beyond that range, so there’s no angle to find for an input like 1.5 — the calculator correctly declines to show a result.
cos⁻¹ always returns a value between 0° and 180° — its defined range — even though cosine repeats infinitely, since inverse cosine picks one consistent angle per input.
Why is arccos only defined between −1 and 1?
Because cosine itself never produces a value outside that range, so there’s no angle to return for an input beyond it.
Why does arccos(−1) equal 180°?
Cosine of 180° is −1, since that angle points in exactly the opposite direction along the unit circle from 0° — arccos simply reverses that relationship.
How is this different from inverse sine?
They’re different functions with different output ranges — arccos spans 0° to 180°, while arcsin spans −90° to 90° — so the same input generally returns a different angle from each.
