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Arcsin Calculator.

Calculate the principal inverse sine in radians and degrees.

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01

Set your values

Results update as you type.

Angle (rad): 0.523599 rad

Angle (rad)

0.523599rad
Angle: 30 °

Angle

30°

Results update automatically as you type.

Use Cases

Solve trigonometric equations

Find the angle when you know the sine value, useful in geometry, physics, and engineering problems.

Example: If sin(θ) = 0.5, arcsin(0.5) = 30° or π/6 rad.

Convert between sine and angle

Quickly convert a sine ratio back to an angle for calculations in surveying, navigation, or signal processing.

Example: arcsin(0.7071) ≈ 45° or 0.7854 rad.

Frequently Asked Questions

What is the principal value of arcsin?
The principal value of arcsin is the output in the range [-π/2, π/2] (or -90° to 90°). It is the unique angle whose sine equals the given value, within that restricted interval.
What is the domain of the arcsin function?
The domain is all real numbers between -1 and 1 inclusive. If you enter a value outside this range, the calculator will not return a real result because no real angle has a sine outside [-1, 1].
Can I get the result in both radians and degrees?
Yes, this calculator displays the principal inverse sine in both radians and degrees, so you can use the unit that fits your problem.

Tips & Common Mistakes

Tips

  • Ensure your sine value is between -1 and 1; otherwise, the result is undefined in real numbers.
  • Remember that arcsin returns the principal value, which is always between -90° and 90° (or -π/2 and π/2).
  • For angles outside the principal range, use the periodic nature of sine to find other solutions.
  • Check whether your problem expects radians or degrees; this calculator gives both.

Common Mistakes to Avoid

  • Entering a value outside -1 to 1, which yields no real result.
  • Confusing arcsin with the reciprocal of sine (cosecant). arcsin is the inverse function, not 1/sin.
  • Forgetting that arcsin gives only the principal angle, not all possible angles with that sine.

Last updated: August 13, 2026