Arccos Calculator
Find the angle whose cosine is a given value, returned in degrees or radians. Accepts any value from −1 to 1.
How to use it
- Enter a value between −1 and 1.
- Choose degrees or radians for the answer.
- The principal value runs from 0° to 180°.
Examples
| arccos(0.5) | 60° |
| arccos(−1) | 180° |
Arccos reverses cosine: given a ratio between −1 and 1, it returns the angle whose cosine is that value. It's the tool for finding an angle when the adjacent side and hypotenuse are known but the opposite side isn't — or, more generally, whenever the known ratio is a cosine rather than a sine.
Worked example — satellite dish tilt
A dish elevation calculation needs the angle between a mast (10 m) and the line to a satellite (12 m slant distance), with the horizontal separation known instead of the vertical. If the adjacent-to-hypotenuse ratio works out to 10 ÷ 12 ≈ 0.833, the angle is arccos(0.833) ≈ 33.6°.
Why the range is 0° to 180°
Cosine is symmetric about 0° — cos(30°) and cos(−30°) are the same value — so restricting arccos to a single unambiguous range requires half a turn rather than the ±90° range arcsin uses. 0° to 180° is the range over which cosine decreases smoothly and each output angle is unique, which is also the natural range for interior angles of a triangle.
Questions people ask
Why does arccos return 0° to 180° rather than −90° to 90°?
Cosine is symmetric about zero, so it has to be restricted to a half-turn to be invertible. The convention picks the range where cosine decreases smoothly from 1 to −1.
Is anything sent to a server?
No. Every calculation runs in your browser, so nothing you type is uploaded and the page keeps working offline once it has loaded.
Last updated 17 August 2026