Arcsin Calculator (Inverse Sine)
The Arcsin Calculator finds the inverse sine of a value between -1 and 1, returning the angle in radians and degrees. The formula used is: arcsin(x) = the angle whose sine is x, in the range [-90°, 90°].
Formula
arcsin(x) = inverse sine
- The Arcsin Calculator updates instantly as you change the input value.
- Formula: arcsin(x) = the angle whose sine is x
- Input definitions: • Value (-1 to 1): the sine value; arcsin is only defined on this interval
- The result is the principal value, an angle from -90° to 90° (-π/2 to π/2 radians).
- Radians are converted to degrees by multiplying by 180/π.
- Values outside -1 to 1 have no real inverse sine.
Example Calculation
Inputs
- Value (-1 to 1): 0.5
arcsin(0.5) = π/6 ≈ 0.5236 radians, which equals 30°, because sin(30°) = 0.5.
Frequently asked questions
What is arcsin?
Arcsin, the inverse sine, returns the angle whose sine equals the value you enter. It reverses the sine function.
What input range is allowed?
Only values from -1 to 1, since sine never produces a result outside that range.
What is the output range?
The principal value runs from -90° to 90° (-π/2 to π/2 radians).
How do I convert the answer to degrees?
Multiply the radian result by 180/π. This calculator shows both radians and degrees.
Why does arcsin(0.5) equal 30°?
Because sin(30°) = 0.5, so the angle whose sine is 0.5 is 30°.