Degree to Radian (° to rad)
Result
0.01745329252 Radian
Formula
rad = ° × 0.01745329252
1 ° = 0.01745329252 rad, and 1 rad = 57.29577951 °.
A full turn is 360°, 2π radians or 400 gradians, so 1 rad = 180/π ° (about 57.29578°) and 1 gradian = 0.9°.
Worked examples
- 1 ° × 0.01745329252 = 0.017453293 rad
- 10 ° × 0.01745329252 = 0.17453293 rad
- 100 ° × 0.01745329252 = 1.7453293 rad
Common mistakes
- Calculators and spreadsheet trigonometry functions usually expect radians: sin(30) in radian mode is −0.988, not 0.5.
- Compass bearings run clockwise from north; mathematical angles run anticlockwise from the positive x-axis.
Degree to Radian table
| Degree (°) | Radian (rad) |
|---|---|
| 1 | 0.017453293 |
| 2 | 0.034906585 |
| 5 | 0.087266463 |
| 10 | 0.17453293 |
| 20 | 0.34906585 |
| 50 | 0.87266463 |
| 100 | 1.7453293 |
| 1,000 | 17.453293 |
The units
- Degree (°)
- A unit of angle.
- Radian (rad)
- 1 Radian = 57.29577951 Degree.
Sources for these factors
- The International System of Units (SI Brochure), 9th edition — BIPM
- Guide for the Use of the International System of Units (SP 811), Appendix B: conversion factors — NIST
Last reviewed against these sources. An automated check recomputes every factor from its definition on each build. How we check accuracy