Degrees to Radians Converter
Convert degrees (°) to radians (rad) with the calculator below. Enter a value in either field for an instant result.
10 ° equals 0.1745329252 rad.
Degrees to Radians Conversion Table
Use these common values as a quick reference.
| Degrees (°) | Radians (rad) |
|---|---|
| 0.01 ° | 0.0001745329252 rad |
| 0.1 ° | 0.001745329252 rad |
| 1 ° | 0.01745329252 rad |
| 2 ° | 0.03490658504 rad |
| 5 ° | 0.0872664626 rad |
| 10 ° | 0.1745329252 rad |
| 20 ° | 0.3490658504 rad |
| 50 ° | 0.872664626 rad |
| 100 ° | 1.745329252 rad |
| 1000 ° | 17.45329252 rad |
How to Convert Degree to Radian
Conversion: 1 ° = 0.01745329252 rad.
Formula: radians = degrees × 0.01745329252
- Enter the degree value.
- Apply the conversion formula shown above.
- Round the result only as much as your use requires.
Example: 10 ° = 0.1745329252 rad.
Understanding the Degree to Radian Conversion
One degree equals 0.01745329252 rad. Because this factor is less than one, the numerical value usually becomes smaller when converting from ° to rad, even though the measured quantity does not change.
Angle units describe rotation or separation between directions. Degrees are familiar in everyday use, radians are standard in mathematics, and arcminutes and arcseconds support very precise measurement.
Degree is commonly used for navigation, geometry and everyday angles, while Radian is commonly used for mathematics, physics and engineering. Converting between them makes measurements easier to compare without changing the quantity being described.
Worked Degree to Radian Examples
These examples show how the conversion works for several practical values.
- 0.5 °: 0.5 × 0.01745329252 = 0.00872664626 rad.
- 3 °: 3 × 0.01745329252 = 0.05235987756 rad.
- 25 °: 25 × 0.01745329252 = 0.436332313 rad.
Accuracy, Precision and Rounding
Everyday Units stores each unit as a factor relative to a shared base unit—Radian. The entered value is converted to that base and then to radian.
The calculator normally shows up to ten significant digits and removes unnecessary trailing zeros. This balances accuracy with readability. If the result will be used in engineering, science, medicine, trade or another precision-sensitive setting, follow the rounding and tolerance rules required for that specific use.
Common mistakes to avoid
- Check that the selected symbols match the units shown in the source measurement.
- Do not round the conversion factor before completing the calculation.
- Keep the unit symbol beside the number so the result cannot be mistaken for another measurement.
About the Units
Degree (°)
Definition: One degree is equal to 0.01745329252 rad in the converter’s base system.
History and origin: A full circle is divided into 360 degrees.
Current use: This unit is commonly used for navigation, geometry and everyday angles.
Radian (rad)
Definition: The radian is the base unit used by this angle converter.
History and origin: The radian relates arc length directly to radius.
Current use: This unit is commonly used for mathematics, physics and engineering.
Frequently Asked Questions
How many radians are in one degree?
One degree is 0.01745329252 rad. The calculator uses this relationship for every value entered.
What is the reverse radian to degree conversion?
One radian equals 57.29577951 °. Use the reverse-conversion link below to open that calculator directly.
Can I convert decimal and very small values?
Yes. Enter integers, decimals, or very small values in either field. Results use sensible precision, with scientific notation only when it improves readability.
How should I round the result?
Keep the full calculator result during intermediate work, then round once at the end. Everyday estimates may need only two or three decimal places, while technical work may require more significant digits.
Is the degree to radian conversion accurate?
The calculation uses the centralized conversion constant shown on this page. Everyday Units converts through the category’s base unit and keeps more precision internally than is normally needed for display.
How This Calculator Works
All calculations happen locally in your browser. No conversion request is sent to an external service. The same centralized unit definitions power the calculator, formula, examples and tables, which helps keep the figures consistent across every related page. Read our conversion methodology and sources for standards, assumptions and rounding details.
For a quick check, compare the forward and reverse relationships above: converting a value to rad and back to ° should return the original measurement, apart from normal display rounding.