Arcsin (inverse sine) calculator
Find an angle from its sine ratio. Choose degrees or radians and understand the answer.
Enter your values, then calculate.
Your calculation stays in your browser.
The formula, explained
arcsin(x)Arcsin returns the principal angle from −90° to 90° (−π/2 to π/2 radians). Its real input must be from −1 to 1.
Source and reference : NIST DLMF ↗
An example to check
Using the starting values below, the calculation gives:
What your result means — arcsin(0.5) ≈ 30°. This is the principal angle whose sine is 0.5.
In a right triangle, x = opposite ÷ hypotenuse. The unit selector changes the answer's unit, not the ratio you enter. Only ratios from −1 to 1 have a real answer.
How to use this tool
- Enter x as a decimal ratio. For a right triangle, use opposite ÷ hypotenuse.
- Choose the unit for the answer: degrees or radians.
- Read the principal angle and its explanation. Keep more digits for intermediate calculations.
A worked example
For opposite = 1 and hypotenuse = 2, x = 0.5 and arcsin(0.5) = 30° ≈ 0.523599 rad.
Is arcsin the same as 1/sin?
No. arcsin is the inverse function: it finds an angle from a ratio. 1/sin(θ) is the reciprocal of the ratio. The notation sin⁻¹(x) means the inverse function in this context.
Why does the calculator return one angle?
Trigonometric functions repeat, so a ratio can correspond to multiple angles. The calculator returns the principal angle in the range stated above.
Can I use a decimal comma?
Yes. Numeric fields accept 12.5 or 12,5 and spaces for thousands, such as 1 234.50. Do not mix a point and comma in one number.
Where are my inputs processed?
Calculations run in your browser. Form values are not sent to Analytics. Copying, printing, sharing or opening an external service is your choice.
Method and interface checked on 2026-10-15 · Report an error