Arcsin calculator
Enter a number between −1 and 1 and get the angle whose sine it is, in degrees or radians. For example sin⁻¹(0.5) = 30°.
Fill in the fields; the answer appears here straight away.
How it's worked out
How it works
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Enter the values
Type the numbers or the formula. Decimals may use a point or a comma. No idea? Click Fill in an example.
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Instant answer
The answer appears as you type, with the most important intermediate values.
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See the working
Under "How it's worked out" you see the steps, handy for checking your own calculation.
What does arcsin do?
Arcsin (also written sin⁻¹ or asin) works backwards: you know the sine and want the angle. Because many angles share the same sine (sin 30° = sin 150°), the calculator gives the principal value, which lies between −90° and 90°.
Why only between −1 and 1?
A sine is never smaller than −1 or larger than 1, so arcsin(2) doesn't exist. You get a message instead of a strange answer. For the other inverse functions, use the arccos and arctan calculators.
Examples
| Input | arcsin in degrees |
|---|---|
| −1 | −90° |
| 0 | 0° |
| 0.5 | 30° |
| 0.7071 | 45° |
| 0.8 | 53.13° |
| 1 | 90° |
Finding the angle of a ramp
A ramp of 6 m in length rises 0.5 m. The sine of its angle is the rise divided by the length, 0.5 ÷ 6 ≈ 0.0833, so the angle is arcsin(0.0833) ≈ 4.78°. If you know the horizontal run instead of the length, use the arctan calculator.
A useful identity
arcsin(x) + arccos(x) = 90° for every x from −1 to 1. If you know one of the two angles, the other is the difference from a right angle. The arccos calculator gives the second.
Frequently asked questions
Why does arcsin give only one angle when two angles share a sine?
Arcsin is defined to return the principal value, between −90° and 90°. The other angle with the same sine is 180° minus that value: sin(30°) = sin(150°) = 0.5.
Is arcsin the same as 1/sin?
No. sin⁻¹ and arcsin mean the inverse function, which gives an angle. 1/sin is the cosecant, a different thing.
What happens with a number outside −1 to 1?
You get a message that there is no such angle. No real angle has a sine larger than 1 or smaller than −1.
How do I convert the result between degrees and radians?
Multiply degrees by π/180 for radians, or radians by 180/π for degrees. The calculator shows both.