Degrees to Radians (deg to rad) Converter
1 degree equals 0.01745329 radians — multiply the number of degrees by π/180 (0.01745329) to convert. A full circle is 360 degrees or 2π radians, so one degree is π ÷ 180 = 0.01745329 radians. This is the standard bridge between degree-based geometry and radian-based trigonometry.
The formula
To convert degrees to radians, multiply by π/180 = 0.01745329:
radians = degrees × 0.01745329
Example: 180 × 0.01745329 = 3.14159265 (π)To reverse it, divide radians by 0.01745329 (or multiply by 57.29578) to get degrees.
Conversion table
| Degrees | Radians |
|---|---|
| 1 | 0.01745329 |
| 2 | 0.03490659 |
| 5 | 0.08726646 |
| 10 | 0.17453293 |
| 30 | 0.52359878 |
| 45 | 0.78539816 |
| 60 | 1.04719755 |
| 90 | 1.57079633 |
| 180 | 3.14159265 |
| 270 | 4.71238898 |
| 360 | 6.28318531 |
How to convert online
- Type the number of degrees into the first box.
- Read the radians value instantly in the second box.
- Or enter a radian value to convert back to degrees — it works both ways.
Use the Degree to Radian Converter — free and instant in your browser.
Where this conversion is used
Radians are the native angle unit in calculus, physics, and virtually every programming language's trig functions (sin, cos, tan in JavaScript, Python and C all expect radians). Converting degrees to radians is a constant need in game development, graphics, robotics, and any math where angles feed into trigonometric functions.
FAQ
How many radians are in a degree?
One degree equals 0.01745329 radians. Multiply degrees by 0.01745329 — for example, 90 degrees = 1.57079633 radians (π/2).
What is the formula to convert degrees to radians?
radians = degrees × π/180, where π/180 ≈ 0.01745329.
How do I convert radians back to degrees?
Multiply radians by 180/π ≈ 57.29578. For example, π radians × 57.29578 = 180 degrees.
What is 180 degrees in radians?
Exactly π, which is approximately 3.14159265 radians.
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