Degrees ↔ Radians
Convert between degrees and radians
Degrees ↔ Radians
Quick Facts
- •π radians = 180°
- •1 radian ≈ 57.296°
- •90° = π/2 ≈ 1.5708 rad
- •360° = 2π ≈ 6.2832 rad
Degrees and Radians
Degrees and radians are two ways to measure angles. A full circle is 360 degrees or 2π radians. Degrees are used in everyday life, navigation, and geography. Radians are the standard in mathematics, physics, and engineering because they simplify many formulas (e.g., arc length = radius × angle in radians).
Key Angle Values
90° = π/2 radians (right angle), 180° = π radians (straight line), 360° = 2π radians (full circle), 45° = π/4 radians, 60° = π/3 radians. The conversion formula is: radians = degrees × π/180, and degrees = radians × 180/π.
How to convert Degrees to Radians
To convert degrees to radians, multiply the number of degrees by the conversion factor. The exact factor is 0.017453.
Formula
Radians = Degrees × 0.017453
Worked example
Convert 10 ° to rad: 10 ° = 0.174533 rad.
Degrees to Radians reference table
Use this quick lookup for common degrees to radians values.
| Degrees (°) | Radians (rad) |
|---|---|
| 1 ° | 0.017453 rad |
| 2 ° | 0.034907 rad |
| 5 ° | 0.087266 rad |
| 10 ° | 0.174533 rad |
| 20 ° | 0.349066 rad |
| 25 ° | 0.436332 rad |
| 50 ° | 0.872665 rad |
| 75 ° | 1.308997 rad |
| 100 ° | 1.745329 rad |
| 250 ° | 4.363323 rad |
Frequently asked questions
What is the formula to convert Degrees to Radians?
Multiply the number of degrees by 0.017453 to get radians. For example, 10 ° equals 0.174533 rad.
How many radians are in 1 degree?
1 ° equals 0.017453 rad.
How do I convert radians back to degrees?
Reverse the formula: Degrees = Radians ÷ 0.017453. For example, 100 rad equals 5,729.577951 °.
Is this Degrees to Radians converter accurate?
Yes. Conversions use the internationally accepted ratio for degrees and radians and are calculated to 6 decimal places in your browser.
What is 10 ° in rad?
10 ° equals 0.174533 rad.
This calculator is for educational and reference purposes only. Always verify critical calculations independently.