Arcsin Calculator
Find the angle whose sine 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.
- Pick whether you want the answer in degrees or radians.
- The principal value is returned — the angle between −90° and 90°.
Examples
| arcsin(0.5) | 30° |
| arcsin(1) | 90° |
Arcsin reverses sine: given a ratio between −1 and 1, it returns the angle whose sine is that value. Where sine takes an angle and gives a ratio, arcsin takes the ratio and gives the angle back — the tool you reach for once you already know the sides of a triangle and need the angle itself.
Worked example — angle of elevation
A zip line drops 18 m over a cable length of 45 m. The angle of descent is arcsin(18 ÷ 45) = arcsin(0.4) ≈ 23.6°. Arcsin is the right choice here specifically because both the opposite side (drop) and the hypotenuse (cable length) are known, rather than the adjacent side.
The principal value
Sine repeats every 360°, so infinitely many angles share the same sine. Arcsin always returns the principal value, between −90° and 90°, which is the conventional single answer — if a problem needs an angle outside that range (like an obtuse triangle angle), it has to be derived separately using the triangle's other known angles.
Questions people ask
Why is the input limited to −1 and 1?
Because sine never leaves that range, so no angle has a sine of 1.5. Values outside the range have no real inverse.
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