Arcsin Calculator
Find the angle whose sine is a given value, in degrees and radians. Results between −90° and 90°.
arcsin(0.5) = 30°
arcsin(0.5)
30°
In radians
0.5236 rad
Multiply degrees by π/180
Arcsin is the inverse of sine: it returns the angle whose sine is the given value. The result always lies between −90° and 90°.
Arcsin Calculator on True Calculator gives you an instant, accurate answer with no sign-up and no app install. Find the angle whose sine is a given value, in degrees and radians. Results between −90° and 90°. Every result shows the formula and a worked example so you can verify the calculation yourself, and all values are computed in your own browser — your numbers never leave your device.
Popular uses: arcsin calculator · inverse sine · sin inverse calculator
Reviewed by the True Calculator team · Last updated: August 2026
How We Calculate
This calculator uses standard mathematical formulas — the same ones taught in school and used in exams — verified by our team. All calculations are performed instantly in your browser using JavaScript, so no data is sent to any server.
The formulas follow standard mathematical definitions and conventions used in textbooks and by educational boards. Results are rounded transparently and shown with the exact formula on this page.
When to Use This Calculator
Arcsin recovers an angle from a measured ratio, which happens constantly in Indian engineering and physics labs. When a student knows the height an object rose and the length of the ramp it travelled, the ratio height ÷ ramp length fed into arcsin gives the ramp's angle of incline. Robotics hobbyists use it to find joint angles from displacement measurements, and smartphone apps use arcsin of accelerometer ratios to compute device tilt. Surveyors measure a distant tower's height ratio against the sight-line distance, then read the elevation angle directly. Pilots and drone operators compute climb angles from altitude gained and distance covered. Because the calculator returns both degrees and radians, it also supports physics work where angles must be expressed in radians for rotational equations, making it a regular companion during JEE and NEET preparation.
How to Use This Calculator
- Step 1: Enter a sine value between −1 and 1, such as 0.5.
- Step 2: Read the angle in degrees whose sine equals that value.
- Step 3: Read the same angle in radians alongside it.
- Step 4: Check that the result lies between −90° and 90°, which is always true for arcsin.
Worked Example
A student in Kolkata measures the ratio of a triangle's opposite side to its hypotenuse as 0.5 and needs the angle. arcsin(0.5) returns 30°, and in radians about 0.5236, since sin(30°) = 0.5. Entering 1 gives 90° — the steepest possible angle — while −1 gives −90°. For the ratio 0.7071, close to √2/2, the calculator returns 45°. This direct conversion from ratio to angle is the exact inverse operation of the sine calculator, so the two tools together cover every 'height and distance' board problem.
Tips and Common Mistakes
- •Tip 1: Values outside −1 and 1 are rejected because no real angle has a sine beyond that range.
- •Tip 2: Use arcsin when the opposite side and hypotenuse are known but the angle is not.
- •Tip 3: Multiply the degree result by π/180 to double-check the radians column by hand.
- ✗Mistake 1: Entering a side length instead of a ratio — arcsin needs opposite ÷ hypotenuse, not a raw measurement.
- ✗Mistake 2: Forgetting that a sine ratio can come from two angles between 0° and 360°, but arcsin always returns the one between −90° and 90°.
Frequently Asked Questions
What is arcsin?
Arcsin is the inverse of sine: it answers the question 'which angle has this sine value?' Since sin(30°) = 0.5, arcsin(0.5) = 30°. It is also written as sin⁻¹.
Why must the input be between −1 and 1?
Sine never produces values outside −1 to 1, so no angle has a sine of 2. The calculator rejects such inputs because arcsin(2) does not exist in real numbers.
What is the range of arcsin?
The result always lies between −90° and 90° (or −π/2 and π/2 radians). arcsin(1) = 90°, arcsin(−1) = −90°, and arcsin(0) = 0°.
When would I use arcsin in real life?
To recover an angle from a measured ratio — for example, finding the tilt of a phone from its accelerometer reading, or the elevation angle of a shadow when you know the height-to-length ratio.
How do I check an arcsin result?
Take the sine of the answer and you should get your original input. If arcsin(0.5) gives 30°, then sin(30°) = 0.5 confirms it — a quick sanity check for any trigonometry problem.
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