degrees to radians | Exact Decimal + Formula
1 Degree = 0.017453 Radian
Degrees to radians is the fundamental angle conversion for trigonometry, programming, and engineering calculations.
About Degree and Radian
Degree (°)
A degree is 1/360 of a full rotation.
Where it's used: Geometry, navigation, roof pitches, and everyday angle measurement.
Radian (rad)
A radian is the angle subtended by an arc equal to the circle's radius; a full circle is 2π radians.
Where it's used: Calculus, physics, and programming trigonometry functions.
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Angle Converter
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Formula
rad = ° × 0.017453293
To convert Degree to Radian, use the formula displayed above.
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Degree to Radian: Quick Reference Table
| Degree | Radian (Decimal) | Fraction |
|---|---|---|
| 0.001 ° | 0.000017 rad | - |
| 0.01 ° | 0.000175 rad | - |
| 0.1 ° | 0.001745 rad | - |
| 0.5 ° | 0.008727 rad | - |
| 1 ° | 0.017453 rad | - |
| 2 ° | 0.034907 rad | - |
| 5 ° | 0.087266 rad | - |
| 10 ° | 0.174533 rad | - |
| 25 ° | 0.436332 rad | - |
| 50 ° | 0.872665 rad | - |
| 100 ° | 1.745329 rad | - |
| 250 ° | 4.363323 rad | - |
| 500 ° | 8.726646 rad | - |
| 1000 ° | 17.453293 rad | - |
° to rad Formula and Examples
Direct Formula
rad = ° × 0.017453293 Inverse Formula
° = rad × 57.29578 Mental Math Shortcut
Divide the value by roughly 57.3 to quickly estimate the converted result.
Common Degree to Radian Calculations
- 5 ° = 0.087266 rad
- 10 ° = 0.174533 rad
- 50 ° = 0.872665 rad
- 100 ° = 1.745329 rad
- 500 ° = 8.726646 rad
Precision & Practical Use
For example, 10 ° = 0.174533 rad — roughly fractional unit measurement.
Results are computed to up to 9 decimal places. Round to the precision of your measuring instrument — for most angle applications, 2–3 significant figures are plenty.
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How to Convert Degree to Radian
How many radians are in one degree?
One Degree (°) equals 0.017453 Radian (rad). To convert degrees to radians, multiply the degree value by 0.017453.
How do I convert Degree to Radian?
Multiply your degree value by 0.017453 to get the result in Radian: rad = ° × 0.017453. For example, 5 ° = 0.087266 rad.
What is the formula for converting ° to rad?
The conversion formula is rad = ° × 0.017453. Use the calculator above for any value, and see the reference table below for common inputs from 0.001 to 1000.
Is there a quick mental estimate for ° to rad?
Divide the value by roughly 57.3 to quickly estimate the converted result.
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