Easily convert radians to degrees with our free calculator. Includes the rad to deg formula (180/π), a quick reference conversion table, and an explanation of the radian unit.
Radians to Degrees
How to Convert Radians to Degrees
While degrees are commonly used for navigation and basic geometry, radians are the preferred unit in advanced mathematics and physics. One 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.
The Conversion Formula
To convert from radians to degrees, you multiply the value by 180 divided by π (Pi). The formula is:
Degrees = Radians × (180 / π)
Common Radians to Degrees Table
Use this reference table for quick conversions of common trigonometric angles:
| Radians (rad) | Degrees (°) | π Equivalent |
|---|---|---|
| 0.5236 | 30° | π / 6 |
| 0.7854 | 45° | π / 4 |
| 1.0472 | 60° | π / 3 |
| 1.5708 | 90° | π / 2 |
| 3.1416 | 180° | π |
| 6.2832 | 360° | 2π |
Why is π (Pi) used in Radians?
The circumference of a circle is calculated as 2πr. Since a full rotation around a circle corresponds to its entire circumference, a full circle in radians is equal to 2π (approximately 6.28318 radians). Consequently, a half-circle (180 degrees) is equal to π radians.
Applications of Radians
- Physics: Measuring rotational speed (angular velocity) in radians per second.
- Calculus: The derivatives of sine and cosine are only simple (sin’ = cos) when using radians.
- Engineering: Used in the analysis of wave cycles, oscillations, and alternating current (AC) circuits.
Why Use This Converter?
In school or technical fields, you often encounter radian values as decimals rather than clean fractions of π. This tool provides an instant, high-precision conversion to degrees, helping you visualize the angle or verify your manual calculations for complex trigonometry problems.