Arcsin Calculator
Calculate the inverse sine of a number and get the angle in degrees and radians.
arcsin(x) = sin⁻¹(x)Principal result range: -π/2 ≤ arcsin(x) ≤ π/2Online Arcsin Calculator
Arcsin, also written as sin⁻¹ or called arcsine, is the inverse function of sine. Enter a value from -1 to 1 to calculate its principal angle in both degrees and radians.
How to Use the Arcsin Calculator
Enter a value
Type a number between -1 and 1 into the x input.
Check the domain
Arcsin has real results only when -1 ≤ x ≤ 1.
Read both results
The angle is shown in degrees and radians in separate result cards.
Try a reference value
Select a sample value to compare common angles such as 30°, 45°, and 90°.
What Is Arcsin?
Arcsin is the inverse sine function. If sin(x) = y, then arcsin(y) returns the principal angle x. For real numbers, the input must be between -1 and 1, and the principal output is between -π/2 and π/2 radians, or -90° and 90°.
Arcsin Example
Because the sine of 30 degrees is 0.5, the inverse sine of 0.5 is 30 degrees, which is π/6 radians.
sin(30°) = 0.5arcsin(0.5) = 30° = π/6 rad
Common Arcsin Values
| x | arcsin(x) in degrees | arcsin(x) in radians |
|---|---|---|
-1 | -90° | -π/2 |
-0.8660254 | -60° | -π/3 |
-0.7071068 | -45° | -π/4 |
-0.5 | -30° | -π/6 |
0 | 0° | 0 |
0.5 | 30° | π/6 |
0.7071068 | 45° | π/4 |
0.8660254 | 60° | π/3 |
1 | 90° | π/2 |
Common Uses
- Trigonometry homework：Check inverse-trigonometric calculations and convert between angle units.
- Geometry：Recover an angle from a known sine ratio in a triangle or coordinate diagram.
- Engineering and science：Find angles from normalized measurements in signal processing, physics, and navigation.
- Programming：Verify Math.asin() results and remember that JavaScript returns radians by default.
Arcsin Calculator FAQ
What does arcsin calculate?
Arcsin calculates the principal angle whose sine equals the input value. It is the inverse of the sine function.
What is the valid range for arcsin?
For real-number results, the input x must be in the closed interval [-1, 1].
What is the range of the arcsin result?
The principal arcsin result is from -π/2 to π/2 radians, inclusive, equivalent to -90° to 90°.
Is arcsin the same as 1/sin(x)?
No. arcsin(x), or sin⁻¹(x), is the inverse function of sine. It is not the reciprocal 1/sin(x), which is called cosecant.
Does JavaScript Math.asin() return degrees?
No. Math.asin() returns radians. Multiply the result by 180/π to convert it to degrees.
Why is arcsin(0.5) equal to 30 degrees?
Because sin(30°) = 0.5, the principal inverse-sine result is arcsin(0.5) = 30°, or π/6 radians.