Arcsine undoes the sine: if a ramp rises 1 m over a 4 m slope, arcsin(1/4) is its angle. Because many angles share each sine value, arcsin returns the principal value between −90° and 90°.
How to use the Arcsin Calculator
- x
Results update as you type, and everything is calculated in your browser.
How it works
The principal value comes from the inverse sine function. The other angle in [0°, 360°) with the same sine is 180° − y.
What each result means
- arcsin(x) = deg(asin([x]))
- In radians = asin([x])
- Other angle with the same sine = 180 – deg(asin([x]))
Example values
How the main result changes when x changes and everything else stays at the example values above:
| x | arcsin(x) (°) |
|---|---|
| 0.25 | 14.4775 |
| 0.375 | 22.0243 |
| 0.5 | 30 |
| 0.625 | 38.6822 |
| 0.75 | 48.5904 |
| 1 | 90 |
Formula
y = arcsin(x) ⇔ sin(y) = x, −1 ≤ x ≤ 1, −90° ≤ y ≤ 90°
Worked example
Inputs — x: 0.5.
Results — arcsin(x) = 30 °; In radians = 0.5235987756 rad; Other angle with the same sine = 150 °.
Key terms
- Principal value
- The single value an inverse function returns from its restricted range.
Frequently asked questions
What is arcsin(1/2)?
30°, or π/6 radians.
Why is arcsin(2) undefined?
Sine never exceeds 1, so no angle has sine 2.
Is arcsin the same as 1/sin?
No – 1/sin is the cosecant.
What is the range of arcsin?
−90° to 90° (−π/2 to π/2).