How to convert degrees to radians
- Take the value in degrees.
- Use the formula radians = degrees × 0.01745329252.
- For example, 1 ° is 0.0175 rad.
About degrees and radians
A full circle is 360 degrees or 2π radians, so multiply degrees by π/180 to get radians. That makes 1° equal to 0.0174533 rad. Dividing by 57.3 gets you within 0.01%.
You need radians whenever you do trigonometry in code or a spreadsheet. JavaScript’s Math.sin, Python’s math.sin and Excel’s SIN all expect radians, so an angle in degrees has to be converted first.
Examples
- 1 ° (one degree) is 0.0175 rad
- 90 ° (a right angle) is 1.57 rad
- 180 ° (a straight line, or π radians) is 3.14 rad
- 360 ° (a full circle, or 2π radians) is 6.28 rad
Degrees to radians chart
| Degrees (°) | Radians |
|---|---|
| 0 | 0 |
| 1 | 0.0175 |
| 5 | 0.0873 |
| 10 | 0.175 |
| 15 | 0.262 |
| 20 | 0.349 |
| 30 | 0.524 |
| 45 | 0.785 |
| 60 | 1.05 |
| 75 | 1.31 |
| 90 | 1.57 |
| Degrees (°) | Radians |
|---|---|
| 120 | 2.09 |
| 135 | 2.36 |
| 150 | 2.62 |
| 180 | 3.14 |
| 210 | 3.67 |
| 225 | 3.93 |
| 240 | 4.19 |
| 270 | 4.71 |
| 300 | 5.24 |
| 315 | 5.5 |
| 360 | 6.28 |