Convert Degrees to Radians
One degree equals 0.0174533 radians. Type any value to convert degrees to radians instantly — with a full reference table below.
Convert Degrees to Radians
Converted in your browser — nothing you enter is sent anywhere.
How to convert Degrees to Radians
To convert degrees to radians, multiply by 0.0174533. One degree equals 0.0174533 rad, and one radian equals 57.29578 °.
- Take the value in degrees — for example 7.5 °.
- Multiply by 0.0174533 (the number of radians in one degree).
- 7.5 × 0.0174533 = 0.1309 rad.
Quick mental estimate: Divide the number of degrees by 57 (within 0.5% of the exact answer).
Degrees to Radians conversion table
| Degrees | Radians |
|---|---|
| 1 ° | 0.0174533 rad |
| 5 ° | 0.0872665 rad |
| 10 ° | 0.174533 rad |
| 15 ° | 0.261799 rad |
| 30 ° | 0.523599 rad |
| 45 ° | 0.785398 rad |
| 60 ° | 1.047198 rad |
| 90 ° | 1.570796 rad |
| 120 ° | 2.094395 rad |
| 180 ° | 3.141593 rad |
| 270 ° | 4.712389 rad |
| 360 ° | 6.283185 rad |
| Radians | Degrees |
|---|---|
| 1 rad | 57.29578 ° |
| 5 rad | 286.4789 ° |
| 10 rad | 572.9578 ° |
| 15 rad | 859.4367 ° |
| 30 rad | 1,718.873 ° |
| 45 rad | 2,578.31 ° |
| 60 rad | 3,437.747 ° |
| 90 rad | 5,156.62 ° |
| 120 rad | 6,875.494 ° |
| 180 rad | 10,313.24 ° |
| 270 rad | 15,469.86 ° |
| 360 rad | 20,626.48 ° |
About converting Degrees to Radians
Degrees (°) and Radians (rad) are both units of angle. The exact factor is 1 ° = 0.0174533 rad, so multiply by 0.0174533 to go from degrees to radians (or divide to go back).
The conversion runs entirely in your browser. Need the reverse? Use the Radians to Degrees converter, or the full unit converter for every unit at once.
Real-world angle in degrees and radians
| Example | Degrees | Radians |
|---|---|---|
| A 1:12 wheelchair ramp (ADA) | 4.763641 ° | 0.0831412 rad |
| A 4/12 roof pitch | 18.43495 ° | 0.321751 rad |
| Earth's axial tilt | ≈ 23.44 ° | ≈ 0.409105 rad |
| A right angle | 90 ° | 1.570796 rad |
| A straight angle | 180 ° | 3.141593 rad |
| A full turn | 360 ° | 6.283185 rad |
“≈” marks typical values; the rest are defined or measured figures.
The units
1/360 of a full turn.
Used for: Geometry, navigation and construction.
The SI unit of angle: the angle whose arc equals the radius; a full turn is 2π.
Used for: Maths, physics and programming (Math.sin uses radians).
A full turn is 360°, 2π radians or 400 gradians; the radian factor is irrational, so it is shown rounded.