How to convert degrees to radians
One degree equals 0.017453 radians, so multiply the number of degrees by 0.017453:
rad = ° × 0.017453
° = rad ÷ 0.017453 (1 rad = 57.2958 °)
Example: 30 ° → 30 × 0.017453 = 0.523599 rad.
Going the other way, divide by 0.017453, or multiply by 57.2958; the radians to degrees converter does it for you.
Everyday values
| Degrees | Radians | For example |
|---|---|---|
| 30 ° | 0.523599 rad | 30° |
| 45 ° | 0.785398 rad | 45° |
| 90 ° | 1.5708 rad | a right angle |
| 180 ° | 3.1416 rad | a straight angle (π) |
| 360 ° | 6.2832 rad | a full turn (2π) |
When you need this conversion
Spreadsheets and programming languages (Excel's SIN, JavaScript's Math.sin) expect angles in radians. Multiply degrees by π/180 (0.017453) before using them in trigonometric functions.
Degree to radian conversion table
| ° | rad | ° | rad |
|---|---|---|---|
| 15 ° | 0.261799 rad | 195 ° | 3.4034 rad |
| 30 ° | 0.523599 rad | 210 ° | 3.6652 rad |
| 45 ° | 0.785398 rad | 225 ° | 3.927 rad |
| 60 ° | 1.0472 rad | 240 ° | 4.1888 rad |
| 75 ° | 1.309 rad | 255 ° | 4.4506 rad |
| 90 ° | 1.5708 rad | 270 ° | 4.7124 rad |
| 105 ° | 1.8326 rad | 285 ° | 4.9742 rad |
| 120 ° | 2.0944 rad | 300 ° | 5.236 rad |
| 135 ° | 2.3562 rad | 315 ° | 5.4978 rad |
| 150 ° | 2.618 rad | 330 ° | 5.7596 rad |
| 165 ° | 2.8798 rad | 345 ° | 6.0214 rad |
| 180 ° | 3.1416 rad | 360 ° | 6.2832 rad |
About the units
- Degree (°): 1/360 of a full turn.
- Radian (rad): the angle at which the arc equals the radius; a full turn is 2π radians.
Both are units of angle. The conversion factor comes from the exact definitions above, so the calculator is exact; results are only rounded for display (up to six significant digits).
Frequently asked questions
How many radians are in one degree?
One degree is 0.017453 radians. One radian is 57.2958 degrees.
How do I convert degrees to radians?
Multiply the value in degrees by 0.017453. To go back, divide by 0.017453.
What is 30 ° in radians?
30 ° = 0.523599 rad.
What is 45 ° in radians?
45 ° = 0.785398 rad.
Sources
- NIST Special Publication 811 (2008), Guide for the Use of the International System of Units (SI), Appendix B: conversion factors.
- NIST Handbook 44 (2024), Appendix C: General tables of units of measurement.
Last reviewed 5 October 2026. Results are estimates; see our disclaimer.