Degrees vs Radians
Compare degrees and radians side by side, convert in both directions, and see the exact factor - Angle units.
= 0.017453 rad
= 57.2958 °
1 degree = 0.017453 rad · 1 radian = 57.2958 °
The Degrees is the smaller unit - the same amount has a smaller number when measured in it.
| Degrees (°) | Radians (rad) | Radians (rad) | Degrees (°) |
|---|---|---|---|
| 1 | 0.017453 | 1 | 57.2958 |
| 2 | 0.034907 | 2 | 114.6 |
| 5 | 0.087266 | 5 | 286.5 |
| 10 | 0.174533 | 10 | 573 |
| 25 | 0.436332 | 25 | 1,432 |
| 50 | 0.872665 | 50 | 2,865 |
| 100 | 1.7453 | 100 | 5,730 |
| 250 | 4.3633 | 250 | 14,324 |
| 500 | 8.7266 | 500 | 28,648 |
| 1000 | 17.4533 | 1000 | 57,296 |
Quick Answer
1 degree (°) = 0.017453 radians (rad), and 1 radian = 57.2958 degrees. Radians is the larger unit, so the same physical amount needs a bigger number when measured in degrees. Convert either way with the live tool below or the dedicated converter pages.
Key Facts
- 1 degree (°) = 0.017453 rad
- 1 radian (rad) = 57.2958 °
- Conversion is exact multiplication - no rounding in the factor
- Table below covers common values in both directions
- Dedicated converters: °→rad and rad→° pages with live tools
Frequently Asked Questions
Which is bigger, a degree or a radian?
One degree equals 0.017453 rad, and one radian equals 57.2958 °. The unit with the larger factor is the physically bigger one.
How do I convert degrees to radians?
Multiply by the factor: value in rad = value in ° × 0.017453. Example: 5 ° = 0.087266 rad. Reverse: divide by 0.017453 (or multiply by 57.2958).
Why are degrees and radians different?
They come from different measurement systems - Degrees belongs to the metric (SI) world, Radians to the US customary world (or another convention). The conversion is exact: 0.017453 rad per degree, no rounding needed for the factor itself.
Is there a quick way to convert without a calculator?
Memorize the 1-to factor: 1 degree ≈ 0.017453 rad. Then multiply. For 2 ° that's ≈ 0.034907 rad.
Frequently Asked Questions
One degree equals 0.017453 rad, and one radian equals 57.2958 °. The unit with the larger factor is the physically bigger one.
Multiply by the factor: value in rad = value in ° × 0.017453. Example: 5 ° = 0.087266 rad. Reverse: divide by 0.017453 (or multiply by 57.2958).
They come from different measurement systems - Degrees belongs to the metric (SI) world, Radians to the US customary world (or another convention). The conversion is exact: 0.017453 rad per degree, no rounding needed for the factor itself.
Memorize the 1-to factor: 1 degree ≈ 0.017453 rad. Then multiply. For 2 ° that's ≈ 0.034907 rad.