Arcsin Calculator

Enter a value between −1 and 1 to find the angle (in degrees or radians) whose sine equals it.

How to Use the Arcsin Calculator

Enter a sine value between −1 and 1, choose degrees or radians for the answer, and the angle updates immediately.

Arcsin's principal-value range sits centered on zero — anywhere from −90° to 90° (−π/2 to π/2 radians) — which is worth noticing if you've also used the Arccos calculator, since that one returns values from 0° to 180° instead. Both functions have to pick one answer out of infinitely many angles sharing the same sine or cosine, and where that answer falls depends on which function it is: arcsin centers its range on zero, arccos doesn't.

if sin(θ) = x, then arcsin(x) = θ, where −90° ≤ θ ≤ 90°

That range choice explains a result that looks odd at first: sin(30°) and sin(150°) are both exactly 0.5, but arcsin(0.5) only ever returns 30°. 150° is a perfectly real angle with that same sine — it's just outside the range arcsin is allowed to return, so the function settles on the one inside it instead of the other.

The Domain Restriction Comes From Sine Itself

Values outside −1 to 1 get rejected here rather than calculated, because sine itself is physically incapable of producing them — the ratio it represents (opposite over hypotenuse, in a right triangle) can never exceed 1 or drop below −1 no matter the angle. There's no real angle whose sine is 2, so asking arcsin(2) isn't a hard question with a hidden answer — it's a question with no answer to find at all.