Radians to Degrees Converter
Convert Radians to Degrees
Quick Conversions
How to Convert Radians to Degrees
To convert from radians to degrees, you multiply the angle in radians by 180/π. For more information about radians as a unit of measurement, visit our radians page.
Formula
Degrees = Radians × (180 / π)
or
° = rad × 57.2958
Step-by-step process
- Take the angle in radians.
- Multiply it by 57.2958 (or 180/π).
- The result is the equivalent angle in degrees.
Examples
- 1 rad = 1 × (180 / π) = 57.2958°
- π/2 rad = (π/2) × (180 / π) = 90°
- π rad = π × (180 / π) = 180°
- 2π rad = 2π × (180 / π) = 360°
When to Convert Radians to Degrees
This conversion is useful for visualizing angles in a more familiar unit.
General Use
Most people are more familiar with degrees, so converting radians to degrees can make angles easier to understand.
Construction and Engineering
In some practical applications, degrees are preferred for specifying angles.
Common Radians to Degrees Conversions
Here is a table of common conversions for quick reference:
| Radians (rad) | Degrees (°) | Radians (rad) | Degrees (°) |
|---|---|---|---|
| 0.2618 (π/12) | 15 | 2.618 (5π/6) | 150 |
| 0.5236 (π/6) | 30 | 3.1416 (π) | 180 |
| 0.7854 (π/4) | 45 | 3.6652 (7π/6) | 210 |
| 1.0472 (π/3) | 60 | 4.1888 (4π/3) | 240 |
| 1.309 (5π/12) | 75 | 4.7124 (3π/2) | 270 |
| 1.5708 (π/2) | 90 | 5.236 (5π/3) | 300 |
| 1.8326 (7π/12) | 105 | 5.7596 (11π/6) | 330 |
| 2.0944 (2π/3) | 120 | 6.2832 (2π) | 360 |
| 2.3562 (3π/4) | 135 |
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 degrees to radians?
To convert from degrees to radians, you multiply the angle in degrees by π/180. For example, 90° is equal to 90 * (π/180) = π/2 radians.