Inverse Sine (arcsin) Calculator
Calculate arcsin(x) in degrees and radians from a decimal, fraction or surd like √3/2, with exact angles and every solution from 0° to 360°.
Inverse sine, written arcsin or sin⁻¹, answers the question “which angle has this sine?” Enter a value between −1 and 1, as a decimal, a fraction like 1/2 or a surd like √3/2, and get the angle in degrees and radians, its exact form for standard values, and both solutions between 0° and 360°.
How to use this tool
- Type the sine value: 0.5, 1/2, √3/2 and sqrt(2)/2 all work.
- Read the principal angle in degrees and radians; it is always between −90° and 90°.
- Use the table and the note for every angle from 0° to 360°, or for the general solution.
Formula
θ = arcsin(x), where sin θ = x and −90° ≤ θ ≤ 90°
Because sine repeats, many angles share the same sine, and arcsin returns the principal one. The full solution is θ = arcsin(x) + 360°k or θ = 180° − arcsin(x) + 360°k for any whole number k. To convert, radians = degrees × π / 180.
Example
For x = 0.5, arcsin(0.5) = 30°, which is π/6 ≈ 0.5236 rad, and the other angle between 0° and 360° with the same sine is 180° − 30° = 150°. For x = 0.3 there is no neat exact form: arcsin(0.3) ≈ 17.4576°, or 0.3047 rad.
Frequently asked questions
Why does arcsin of 2 give an error?
The sine of a real angle is always between −1 and 1, so no angle has a sine of 2. In a right triangle, check that you did not swap the opposite side and the hypotenuse.
Is sin⁻¹(x) the same as 1/sin(x)?
No. sin⁻¹ is the inverse function and returns an angle; 1/sin x is the cosecant, a different ratio.
How do I find an angle in a right triangle with arcsin?
Divide the side opposite the angle by the hypotenuse and take the arcsin. With an opposite side of 3 and a hypotenuse of 6, arcsin(0.5) = 30°.
Why is my answer negative?
For negative inputs the principal angle lies between −90° and 0°. Add 360° for the equivalent positive angle: −45° points the same way as 315°.
Last updated: 2026-10-30