# Arcsin Calculator

URL: https://speedycalculator.com/calculators/math/arcsin/
Last updated: 2026-10-30

> The arcsin calculator finds the angle whose sine is x (the inverse sine) for any x between −1 and 1, in degrees and radians, plus the second angle with the same sine.

## Inputs

- x

## Results

- arcsin(x)
- In radians
- Other angle with the same sine

## Formula

```
y = arcsin(x) ⇔ sin(y) = x,  −1 ≤ x ≤ 1,  −90° ≤ y ≤ 90°
```

## Explanation

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:

xarcsin(x) (°)0.2514.47750.37522.02430.5300.62538.68220.7548.5904190

## 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.

## FAQ

**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).


## Sources

- [OpenStax – Algebra and Trigonometry 2e](https://openstax.org/details/books/algebra-and-trigonometry-2e)
- [OpenStax – Precalculus 2e](https://openstax.org/details/books/precalculus-2e)
- [Wolfram MathWorld – Inverse sine](https://mathworld.wolfram.com/InverseSine.html)