Arcsin Calculator
Online arcsin(y) calculator — the inverse sine function. Enter a sine value y between -1 and 1 and press Calculate to get every angle whose sine is y, in degrees and in radians, with the full general solution. Everything runs locally in your browser.
Enter the sine value y
Type the value y whose arcsine you want — any number from -1 to 1, such as 0.5, -0.2 or 1. The sine of any real angle never leaves this range, so values outside it are rejected with an in-app message.
Press Calculate
Two solutions per rotation appear: the principal angle and its supplement. For y = 0.5 you get 30° and 150° in degrees, 0.52359878 and 2.61799387 radians, plus a calculation panel with degrees-minutes-seconds and the k·360° / k·2π general solution.
Read the result or reset
Select any read-only output field to copy the value yourself. Press Reset to clear the input and all three outputs and start over. Invalid input clears the previous result and shows exactly what is wrong.
Arcsine definition
- What is arcsin?
- The arcsine function is the inverse function of y = sin(x): if sin(30°) = 0.5 then arcsin(0.5) = sin⁻¹(0.5) = 30°. Because sine repeats every 360°, every valid y has infinitely many angles — the calculator shows the two solution families x = arcsin(y) + k·360° and x = 180° - arcsin(y) + k·360° for k = …-1, 0, 1, …
- Common arcsin values
- arcsin(0) = 0° = 0 rad; arcsin(0.5) = 30° = π/6; arcsin(√2/2 ≈ 0.7071) = 45° = π/4; arcsin(√3/2 ≈ 0.8660254) = 60° = π/3; arcsin(1) = 90° = π/2; arcsin(-0.5) = -30° = -π/6. The calculation panel also prints each result as a multiple of π (for example 0.166667π rad = π/6).
- Degrees, radians, DMS and π multiples
- The degrees field lists the principal angle and its supplement (180° - principal); the radians field does the same (π - principal). The calculation panel decomposes the principal angle into degrees / minutes / seconds — e.g. arcsin(0.2) = 11° 32′ 13.053″ — and states each family in radians and in multiples of π.
- How are results rounded?
- Degrees and radians are rounded to 8 decimal places, seconds to 3, and π coefficients to 6 — matching the reference tables. That is why the 7-decimal table entry 0.8660254 returns 59.99999957°, not exactly 60°: the shortfall is in the input itself, and the calculator reports it honestly.
- What inputs does the calculator reject?
- Empty input, non-numeric text (including comma decimals like 0,5 and scientific notation like 1e-3), and any y greater than 1 or less than -1, where arcsin is undefined over the real numbers. The previous result is cleared and an in-app message states the reason.
More trigonometry tools are listed in Math & Statistics.
Privacy: every calculation runs in your browser tab — no value you type is sent anywhere. Results are rounded as described above; verify safety- or exam-critical trigonometry against authoritative tables.