ArcSin Calculator
Find the angle whose sine equals a given value, with principal value in degrees or radians.
About ArcSin Calculator
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°]
Worked example
With the default values below, ArcSin Calculator returns arcsin(x) of 30.00000000. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Value (x)accepts -1–1
- 0.5
- Angle unitone of Degrees, Radians
- Degrees
Results
- arcsin(x)
- 30.00000000
- Result (degrees)
- 30.000000 °
- Result (radians)
- 0.52359878
Step by step
- 1Input value= 0.5
- 2Compute arcsin= 30° = 0.52359878 rad
- 3Principal range= [−90°, 90°]
Assumptions and limits
- The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
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.