Degrees to Radians Converter
Convert Degrees to Radians
Quick Conversions
How to Convert Degrees to Radians
To convert from degrees to radians, you multiply the angle in degrees by π/180. For more information about degrees as a unit of measurement, visit our degrees page.
Formula
Radians = Degrees × (π / 180)
or
rad = ° × 0.0174533
Step-by-step process
- Take the angle in degrees.
- Multiply it by 0.0174533 (or π/180).
- The result is the equivalent angle in radians.
Examples
- 30° = 30 × (π / 180) = 0.5236 rad
- 45° = 45 × (π / 180) = 0.7854 rad
- 90° = 90 × (π / 180) = 1.5708 rad
- 180° = 180 × (π / 180) = 3.14159 rad (π)
When to Convert Degrees to Radians
This conversion is fundamental in mathematics, physics, and engineering, especially in calculus and trigonometry.
Mathematics
Radians are the standard unit of angular measure in calculus and other higher mathematics.
Physics and Engineering
Many formulas in physics and engineering, particularly those involving rotational motion, require angles to be in radians.
Common Degrees to Radians Conversions
Here is a table of common conversions for quick reference:
| Degrees (°) | Radians (rad) | Degrees (°) | Radians (rad) |
|---|---|---|---|
| 15 | 0.2618 | 150 | 2.618 |
| 30 | 0.5236 | 180 | 3.1416 |
| 45 | 0.7854 | 210 | 3.6652 |
| 60 | 1.0472 | 240 | 4.1888 |
| 75 | 1.309 | 270 | 4.7124 |
| 90 | 1.5708 | 300 | 5.236 |
| 105 | 1.8326 | 330 | 5.7596 |
| 120 | 2.0944 | 360 | 6.2832 |
| 135 | 2.3562 |
Frequently Asked Questions
What is a radian?
A radian is the angle subtended at the center of a circle by an arc that is equal in length to the radius of the circle. There are 2π radians in a full circle.
How do I convert radians to degrees?
To convert from radians to degrees, you multiply the angle in radians by 180/π. For example, π/2 radians is equal to (π/2) * (180/π) = 90°.