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Convert degrees to radians
Instant, accurate ° → rad conversion with a live converter, table and formula.
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1 degree = 0.0174533 radians
1 radian = 57.2958 degrees
degrees to radians table
| degrees (°) | radians (rad) |
|---|---|
| 0.5 | 0.00872665 |
| 1 | 0.0174533 |
| 2 | 0.0349066 |
| 5 | 0.0872665 |
| 10 | 0.174533 |
| 20 | 0.349066 |
| 50 | 0.872665 |
| 100 | 1.74533 |
| 500 | 8.72665 |
| 1000 | 17.4533 |
Formula
radians = degrees × 0.0174533.
Example
10 degrees = 0.174533 radians.
What is a degree?
A degree (°) is 1/360 of a full circle.
What is a radian?
A radian (rad) is the SI angle unit; a full circle is 2π radians.
Real-world reference points
A right angle is 90° (π/2 rad); a full turn 360° (2π); one minute on a clock face is 6°.
| Reference | degrees | radians |
|---|---|---|
| Clock minute tick | 6 ° | 0.105 rad |
| 45° ramp | 45 ° | 0.785 rad |
| Right angle | 90 ° | 1.57 rad |
| Full circle | 360 ° | 6.28 rad |
Mistakes to avoid with angle conversions
- Calling Math.sin() with degrees — programming languages default to radians.
- Confusing slope percent with degrees: a 100% grade is 45°, not 90°.
- Mixing gradians (400/turn) from surveying tools with degrees (360/turn).
Frequently asked questions
How many radians in a degrees?+
1 degree = 0.0174533 radians.
How do I convert degrees to radians?+
Enter the value in the degrees box above and the radians value appears instantly. You can also type in the radians box to convert the other way.
Is this ° to rad converter free?+
Yes — it is 100% free, needs no sign-up, and runs entirely in your browser.