Inverse Sine (asin) Calculator
Enter a value between -1 and 1 to find its arcsine.
Tip: asin(x) returns the principal angle in the range [-π/2, π/2].
What is asin?
The asin function, also written as arcsin or sin-1(x), is the inverse of the sine function. If sin(θ) = x, then asin(x) = θ for the principal angle. It is widely used in geometry, trigonometry, physics, graphics, and engineering whenever you need to recover an angle from a sine ratio.
Domain and range
Because sine outputs only values between -1 and 1, the inverse sine accepts inputs only in that interval.
- Domain of asin(x): [-1, 1]
- Range of asin(x): [-π/2, π/2] in radians, or [-90°, 90°] in degrees
If your input is less than -1 or greater than 1, there is no real-angle result. This calculator validates that for you and shows a clear error message.
How to use this asin calculator
- Type a number for x between -1 and 1.
- Select whether you want radians, degrees, or both.
- Choose decimal precision.
- Click Calculate asin(x).
You can also press Enter inside the form. The result section shows the angle and a quick check by taking sine of the output angle again.
Common values to remember
Reference angles
- asin(0) = 0
- asin(1/2) = π/6 = 30°
- asin(√2/2) = π/4 = 45°
- asin(√3/2) = π/3 = 60°
- asin(1) = π/2 = 90°
Negative inputs
Arcsine is an odd function in the principal branch: asin(-x) = -asin(x). So if asin(0.5) = 30°, then asin(-0.5) = -30°.
Practical applications
- Right-triangle problems: find an angle from opposite/hypotenuse ratio.
- Navigation and robotics: estimate orientation and motion angles.
- Computer graphics: convert directional vectors into pitch/tilt angles.
- Signal processing: recover phase information from normalized values.
- Physics: work with projectile motion, wave equations, and oscillations.
Radians vs degrees
Most programming languages (including JavaScript) return arcsine in radians. If you need degrees, convert with:
degrees = radians × (180 / π)
This calculator automatically handles that conversion and can show either unit or both.
Frequently asked questions
Is asin the same as 1/sin?
No. asin(x) means inverse sine (angle output), while 1/sin(x) is csc(x), the reciprocal trig function.
Why do I only get one angle?
Many angles can have the same sine value, but inverse sine returns the principal value in the range [-π/2, π/2].
What happens for x = 1.2?
There is no real solution because sine cannot exceed 1. You would need complex numbers to extend beyond the real domain.
Final thoughts
A reliable asin calculator is useful for students, developers, and professionals who need quick, accurate angle recovery. Keep the domain rules in mind, choose the correct unit, and you will avoid most trigonometry mistakes.