How Many Radians in a Right Angle?
Quick Answer
There are π/2 (approximately 1.5708) radians in a right angle.
90° = π/2 ≈ 1.5708 radians
Understanding the Conversion
A right angle of 90° equals exactly π/2 radians ≈ 1.5708 radians. The sine of a right angle is 1 and the cosine is 0. Right angles appear constantly in geometry, construction, and navigation.
Formula
90° = π/2 ≈ 1.5708 radians
Common Examples
| Description | Value |
|---|---|
| A square corner | 90° = π/2 rad |
| sin(π/2) | = 1 (maximum) |
| A 3-4-5 right triangle | Right angle opposite the 5 side |
Quick Reference Table
Use this table for quick conversions between right angle and radians:
| right angle | radians |
|---|---|
| 1 | 1.571 |
| 2 | 3.142 |
| 5 | 7.854 |
| 10 | 15.708 |
| 25 | 39.270 |
| 50 | 78.540 |
| 100 | 157.08 |
Frequently Asked Questions
How Many Radians in a Right Angle?
There are π/2 (approximately 1.5708) radians in a right angle. A right angle of 90° equals exactly π/2 radians ≈ 1.5708 radians. The sine of a right angle is 1 and the cosine is 0. Right angles appear constantly in geometry, construction, and navigation.
What is the formula to convert right angle to radians?
The formula is: 90° = π/2 ≈ 1.5708 radians. To convert, multiply the number of right angles by 1.571 to get the equivalent in radians.
How do I convert radians to right angle?
To convert radians to right angle, divide the number of radians by 1.571. For example, 7.854 radians equals 5 right angles.