Arcsine Calculator

About this calculator

The arcsine function (sin⁻¹) is the inverse of sine: given a ratio between −1 and 1, it returns the angle whose sine equals that ratio. Because sine repeats endlessly around the unit circle, arcsin is defined only over a restricted principal range of −90° to 90° (−π/2 to π/2 radians), so every input maps to exactly one output angle rather than infinitely many.

Arcsin shows up whenever you know a ratio of sides and need the angle that produced it — surveyors and structural engineers use it to recover an incline angle from a rise-over-hypotenuse measurement, physicists back-calculate a projectile’s launch angle from its velocity components, and game and graphics programmers use it to rotate objects to match a known direction vector. It is distinct from arccos and arctan, which solve the same kind of problem for cosine and tangent ratios and therefore return different angles for the same numeric input.

This calculator takes your sine value, checks that it falls in the valid −1 to 1 domain, and returns the corresponding angle in both degrees and radians.