Arccosine Calculator

About this calculator

The arccosine function, written cos⁻¹(x) or arccos(x), is the inverse of cosine: given a ratio between −1 and 1, it returns the angle (in the range 0° to 180°, or 0 to π radians) whose cosine produces that ratio. Because cosine itself repeats every 360°, arccos is defined only on this restricted range so that each input has exactly one output — this is the "principal value" convention used throughout mathematics and engineering.

Arccos shows up constantly wherever an angle needs to be recovered from a dot product or a ratio of sides. In physics and 3D graphics, the angle between two vectors is found by taking arccos of their normalized dot product; in surveying and navigation, it appears in bearing and triangulation formulas; in mechanical engineering, it is used to solve for joint angles in linkages and robotic arms from known link lengths. It is also the natural complement to arcsine — the two are related by arccos(x) = 90° − arcsin(x).

This calculator takes a cosine value between −1 and 1 and returns the corresponding angle in both degrees and radians, handling the domain restriction automatically so you don't have to consult a unit circle by hand.