Inverse Trig (Ratio to Angle)
This is the calculation for when you know a side ratio and want the angle. For the same 0.6, asin gives 36.87°, acos 53.13° and atan 30.96° — so decide which ratio you have first.
Your numbers
Angle (°)
36.87°
cos
53.13°
tan
30.964°
Radians
0.6435
Formula
Angle (°) = asin(Ratio)
asin and acos only accept values from −1 to 1. atan takes any real number but never quite reaches 90°.
What to enter
| Input | Default | Accepted range |
|---|---|---|
| RatioThe trigonometric ratio to invert, between −1 and 1. | 0.6 | -1 ~ 1 |
Step by step
Quick reference table
Results when only Ratio changes and everything else stays put.
| Ratio | Angle (°) (°) | cos (°) | tan (°) |
|---|---|---|---|
| 0.3 | 17.458 | 72.542 | 16.699 |
| 0.45 | 26.744 | 63.256 | 24.228 |
| 0.6 | 36.87 | 53.13 | 30.964 |
| 0.9 | 64.158 | 25.842 | 41.987 |
| 1 | 90 | 0 | 45 |
What each result means
| Result | At default values |
|---|---|
| Angle (°) (°)An angle in degrees; a full turn is 360°. | 36.87 |
| cos (°)The cosine of the angle — adjacent over hypotenuse. | 53.13 |
| tan (°)The tangent of the angle; it is undefined at 90°. | 30.964 |
| RadiansAn angle in radians; a full turn is 2π. | 0.6435 |
Common mistakes
asin and acos only accept values from −1 to 1. atan takes any real number but never quite reaches 90°.
Glossary
- Ratio
- The trigonometric ratio to invert, between −1 and 1.
- Angle (°)
- An angle in degrees; a full turn is 360°.
- cos
- The cosine of the angle — adjacent over hypotenuse.
- tan
- The tangent of the angle; it is undefined at 90°.
- Radians
- An angle in radians; a full turn is 2π.
Frequently asked questions
Q. How is Inverse Trig (Ratio to Angle) calculated?
Angle (°) = asin(Ratio) — This is the calculation for when you know a side ratio and want the angle. For the same 0.6, asin gives 36.87°, acos 53.13° and atan 30.96° — so decide which ratio you have first.
Q. Can you walk through an example?
With Ratio 0.6, the answer is Angle (°) 36.87°.
Q. What do I need to enter?
Enter Ratio. The result recalculates as you type, and an empty box counts as zero.
Q. How much does the answer move if I change a number?
Changing only Ratio moves the answer to Ratio 0.3 → Angle (°) (°) 17.458 and Ratio 1 → Angle (°) (°) 90. The table below lays out five steps.
Q. How are the numbers rounded?
Money is shown to the nearest whole unit, percentages to one decimal place and everything else to two. What you see is rounded; the calculation itself carries the unrounded value forward.
Q. Anything to watch out for?
asin and acos only accept values from −1 to 1. atan takes any real number but never quite reaches 90°.
Related calculators
Keep your length units consistent across inputs — mixing centimetres and metres throws results far off.