Degree to Radian Converter
Converts degree (°) to radian (rad) and back. The conversion factor is shown below every result.
How to Convert Degree to Radian
What Is a Degree?
The degree (°) divides a full circle into 360 equal parts.
What Is a Radian?
The radian (rad) is the SI unit of angle, defined so that a full circle equals exactly 2π radians.
Common Degree to Radian Reference Points
Real-world reference values for quick sanity checks.
| Item | Degree (°) | Radian (approx.) |
|---|---|---|
| A right angle | 90 ° | 1.5708 rad |
| A full circle | 360 ° | 6.2832 rad |
| Reference values are illustrative approximations for common items, not measured specifications. | ||
Degree to Radian Conversion Table
| Degree (°) | Radian (rad) |
|---|---|
| 15 ° | 0.261799 rad |
| 30 ° | 0.523599 rad |
| 45 ° | 0.785398 rad |
| 60 ° | 1.047198 rad |
| 90 ° | 1.570796 rad |
| 180 ° | 3.141593 rad |
| 270 ° | 4.712389 rad |
| 360 ° | 6.283185 rad |
| Source: NIST SP 811, Appendix B (2π radians = 360 degrees, by definition) | |
Frequently Asked Questions
How do I convert degrees to radians?
Multiply the degree value by π/180 (approximately 0.0174532925). For example, 45° × 0.0174532925 = 0.7854 rad.
Why do radians use π instead of a simple round number?
The radian is defined geometrically: one full circle equals exactly 2π radians, tying the unit directly to the ratio of a circle's circumference to its radius. That definition doesn't produce a round conversion factor against degrees, which instead divide a circle into 360 arbitrary parts.
Why does math and physics prefer radians over degrees?
Radians make calculus involving trigonometric functions simpler because derivatives and series expansions of sine and cosine only take their simplest form when the angle is measured in radians. Degrees remain more common in everyday and engineering contexts.
Related Angle Converters
A good measuring tool marked in both ° and rad removes the guesswork at the point of use.