Find the angle whose sine equals a given value — the inverse of the sine function, commonly written arcsin or sin⁻¹.
How it works
For any x between −1 and 1, arcsin(x) returns the angle (in this calculator, in degrees) whose sine is x. Arcsin only ever returns an answer between −90° and 90°, even though many other angles share the same sine value.
What this does not include
This returns only the principal value in the −90° to 90° range. Sine is periodic, so infinitely many other angles share the same sine value — this calculator doesn’t list them all.
How to use this calculator
- Enter a value between −1 and 1.
A worked example
arcsin(0.5) = 30°, since sin(30°) = 0.5.
arcsin(1) = 90°, the maximum input sine can ever produce.
What the variables mean
| Variable | Meaning |
|---|---|
| x | A sine value, between −1 and 1 |
| Result | The angle (in degrees) whose sine equals x |
Edge cases worth knowing
Inputs outside −1 to 1 have no valid answer. Sine itself never exceeds that range, so there’s no angle whose sine equals 1.5 — the calculator correctly declines to show a result.
arcsin always returns a value between −90° and 90° — its defined range — even though sine repeats infinitely, since arcsin picks one consistent angle per input.
Why is arcsin only defined between −1 and 1?
Because sine itself never produces a value outside that range — there’s no angle whose sine is, say, 2, so arcsin has no valid input there.
Why does arcsin only return values between −90° and 90°?
Sine repeats the same values at many different angles, so arcsin is defined to return just one consistent answer — the one in that range — rather than an ambiguous list.
How is this different from inverse cosine?
They’re different functions with different output ranges — arcsin spans −90° to 90°, while arccos spans 0° to 180° — so the same input value generally returns a different angle from each.
