Arcsin Calculator
Find the inverse sine of any value between −1 and 1 in degrees and radians, with a quick reference table of common arcsine results.
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°.
Common arcsin values
| x | arcsin(x) degrees | arcsin(x) radians |
|---|---|---|
| -1 | -90° | -π/2 |
| -√3/2 | -60° | -π/3 |
| -√2/2 | -45° | -π/4 |
| -1/2 | -30° | -π/6 |
| 0 | 0° | 0 |
| 1/2 | 30° | π/6 |
| √2/2 | 45° | π/4 |
| √3/2 | 60° | π/3 |
| 1 | 90° | π/2 |
Last updated: January 2026
How this calculator is verified
Checked by True Calculator automated test suite on
- Formula verified against a published worked example in the automated test suite
- Edge cases (zero, negative, boundary and unit-mismatch inputs) covered by unit tests
The full verification method is on our how we verify page. Found an error? Tell us and we will re-check it.
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 0.6.
- Step 2: Read the angle in degrees whose sine equals that value.
- Step 3: Read the same angle in radians alongside it.
- Step 4: Use the common-values table to check standard ratios such as 0.5 → 30° and √2/2 → 45°.
Worked Example
In a right triangle with the opposite side 6 and the hypotenuse 10, the sine ratio is 6/10 = 0.6. arcsin(0.6) returns 36.87°, or about 0.6435 radians, since sin(36.87°) = 0.6. Entering 0.5 gives 30° (π/6 radians), and 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 function, so the two tools together cover every 'find the angle' trigonometry 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.
Compare these tools
- Percentage Calculator — Calculate percentages, percentage difference and percentage change instantly
- Rounding Calculator — Round any number to the nearest value, or up and down, to any decimal places
- Standard Form Calculator — Convert numbers to and from standard form (scientific notation) with one click
You might also need
Related calculators from other categories
Date
Add Days Calculator
Add or subtract days from any date and get the new date, its weekday and the equivalent span in weeks and months instantly.
Date
Age Calculator
Find your exact age in years, months and days from your date of birth — plus total days, weeks, hours, minutes and your next birthday countdown.
Health & Fitness
Bra Size Calculator
Find your bra size from underbust and bust measurements in cm — band, cup and full size, plus sister sizes that fit.
Health & Fitness
Conception Calculator
Estimate when conception happened and your fertile window from your cycle or due date. Understand your pregnancy timeline.