Degrees to Radians Converter
1 degree = 0.0174533 radians.
Enter a value
Result
1 degree =
0.0174533 rad
1 ° × 0.0174533 = 0.0174533 rad
radians = degrees × π ÷ 180
The working
- 1. Convert 1 ° to degrees: 1 × 1 = 1.
- 2. Convert to rad: 1 ÷ 57.2958 = 0.0174533.
1 ° in every unit
Key angles
- Right angle
- 90° = π/2 rad
- Half turn
- 180° = π rad
- Full turn
- 360° = 2π rad
Conversion table
Degrees to Radians
| Degrees | Radians |
|---|---|
| 1 | 0.017453 |
| 15 | 0.2618 |
| 30 | 0.5236 |
| 45 | 0.7854 |
| 60 | 1.0472 |
| 90 | 1.5708 |
| 120 | 2.0944 |
| 180 | 3.1416 |
| 270 | 4.7124 |
| 360 | 6.2832 |
Radians to Degrees
| Radians | Degrees |
|---|---|
| 1 | 57.296 |
| 15 | 859.44 |
| 30 | 1,718.9 |
| 45 | 2,578.3 |
| 60 | 3,437.7 |
| 90 | 5,156.6 |
| 120 | 6,875.5 |
| 180 | 10,313 |
| 270 | 15,470 |
| 360 | 20,626 |
Formula and worked example
radians = degrees × 0.01745329252.
Convert 90 degrees to radians: 90 × 0.017453293 = 1.5708 rad.
When you need this
Trigonometry, programming and physics formulas expect angles in radians, while protractors and maps use degrees.
Questions people ask
How many radians are in a degree?
One degree is 0.017453293 radians.
How do I convert degrees to radians?
Multiply the number of degrees by 0.017453293, or divide by 57.29578.
What is 90 ° in rad?
90 degrees is 1.5708 radians.
How do I convert radians back to degrees?
Multiply by 57.29578: one radian is 57.29578 degrees.
Related conversions
How we calculate this
We use the standard published formula or definition for this calculation, and we show the working so you can check it. Source: NIST Special Publication 811, Guide for the Use of the International System of Units.
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