ArcSin Calculator
Find the angle whose sine equals a given value, with principal value in degrees or radians.
Inputs
Must be between −1 and 1.
arcsin(x)
30.00000000
Result (degrees)
30.000000°
Result (radians)
0.52359878
Step by step
Input value
= 0.5
Compute arcsin
arcsin(0.5)
= 30° = 0.52359878 rad
Principal range
= [−90°, 90°]
How it works
The inverse sine (arcsin) returns the angle whose sine equals x. The principal value is in [−90°, 90°] or [−π/2, π/2]. The domain is [−1, 1].
Formula
Inverse sine
θ = arcsin(x), where −1 ≤ x ≤ 1
- x
- The sine value
- θ
- The resulting angle in [−90°, 90°]
Frequently Asked Questions
What is arcsin(0.5)?
arcsin(0.5) = 30°, because sin(30°) = 0.5.
Why is the domain limited to [−1, 1]?
Sine never exceeds 1 or drops below −1, so no angle exists whose sine is outside that range.