Math
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Arcsine Calculator.
Calculate the principal arcsine of a ratio.
On-device calculationNo signup
01
Set your values
Results update as you type.
02 / ANSWER
Value: 0.5
Angle (radians): 0.523599
angleDegrees: 30
Results update automatically as you type.
Use Cases
Solve trigonometric equations
When you know the sine of an angle but not the angle itself, use the arcsine to find the principal angle. This is common in physics, engineering, and geometry problems.
Example: If sin(θ) = 0.5, then θ = arcsine(0.5) = 30° or π/6 radians.
Convert sine ratios to angles in real-world measurements
In fields like surveying, navigation, or construction, you often measure a ratio (like opposite/hypotenuse) and need to find the corresponding angle. This calculator gives you that angle quickly.
Example: If a ramp has a sine ratio of 0.3, the angle of inclination is arcsine(0.3) ≈ 17.46°.
Frequently Asked Questions
- What is the arcsine of a ratio?
- The arcsine (or inverse sine) of a ratio is the angle whose sine equals that ratio. For a ratio r, arcsine(r) returns the angle θ such that sin(θ) = r, with θ in the principal range from -π/2 to π/2 radians (or -90° to 90°).
- What is the valid range for the ratio input?
- The ratio must be between -1 and 1 inclusive. Since the sine of any angle is always between -1 and 1, ratios outside this range do not have a real arcsine. If you enter a value outside this range, the calculator will not produce a valid result.
- In what units does the calculator output the angle?
- The calculator outputs the principal arcsine in both radians and degrees. Radians are the standard mathematical unit, while degrees are often used in practical applications. The principal value is always between -π/2 and π/2 radians (or -90° and 90°).
Tips & Common Mistakes
Tips
- Ensure your ratio is between -1 and 1. If you get an error, check your input for values outside this range.
- Remember that arcsine returns the principal value. For angles outside the principal range, you may need to adjust using the periodic nature of sine.
- If you need the angle in degrees, use the degree output; for most mathematical calculations, radians are preferred.
- Double-check your ratio: it should be the sine of the angle, which is the opposite side divided by the hypotenuse in a right triangle.
Common Mistakes to Avoid
- Entering a ratio greater than 1 or less than -1, which is invalid because sine values are always within that range.
- Confusing arcsine with sine: arcsine takes a ratio and gives an angle, not the other way around.
- Forgetting that the output is the principal angle, so if you expect an angle outside -90° to 90°, you need to add or subtract multiples of 180°.
Last updated: August 13, 2026