Authoritative definitions of the International System of Units and SI prefixes.
Dedicated unit pair
Degrees to Radians
Convert ° to rad instantly, then review the formula, assumptions, and rounding guidance.
AngleInstant result
Decimals
Formula result = input × 0.017453292519943295 ÷ 1. 1 ° = 0.0175 rad
Common examples
One value, several units
Radians0.0175 rad
Gradians1.1111 gon
Turns0.0028 turn
Arcminutes60 ′
Arcseconds3,600 ″
Conversion table
| ° | rad |
|---|---|
| 1 ° | 0.0175 rad |
| 2 ° | 0.0349 rad |
| 5 ° | 0.0873 rad |
| 10 ° | 0.1745 rad |
| 25 ° | 0.4363 rad |
| 50 ° | 0.8727 rad |
| 100 ° | 1.7453 rad |
Conversion chart
1 °0.0175 rad
5 °0.0873 rad
10 °0.1745 rad
25 °0.4363 rad
50 °0.8727 rad
Worked example
A full turn is 360 degrees or 2π radians.
Unit definition
Degrees (°) One degrees equals 0.0174532925199 radian.
Unit history
Degrees is represented here using its modern SI definition or an internationally accepted relationship to an SI base unit.
Step by step
1. Parse the value, including fractions.
2. Convert ° to radian.
3. Convert the base value to rad and apply your display precision.
Understand the result before using it
Degrees to Radians converts a value measured in Degrees (°) into the equivalent value in Radians (rad). The numerical value changes because the size and definition of the selected unit changes; the underlying quantity does not.
Calculated result
The conversion follows the displayed unit relationship. Display rounding can hide additional digits, and measured inputs cannot become more accurate merely by changing units.
Formula, assumptions, and example
Formula
result = input × 0.017453292519943295 ÷ 1
Assumptions
- Degrees and Radians represent the same angle quantity.
- The input is expressed in °; the output is expressed in rad.
- The unit definitions and conventional relationship shown on this page apply.
Worked example
1 ° = 0.0174532925199 rad. For another value, apply the same relationship and round only to the precision your source measurement supports.
When to use it
Good uses
- Read a ° measurement in a document that expects rad.
- Compare a degrees value with a value reported in radians.
- Check the °-to-rad arithmetic before copying the result into another calculation.
Limitations
Common mistakes to avoid
- Do not confuse ° with another unit that has a similar name or symbol.
- Round the output to a precision justified by the original measurement.
- Verify safety-critical, regulated, laboratory, and contractual conversions against the controlling standard.
Sources and further reading
These references explain the underlying standards or provide authoritative context. Your own contract, institution, clinician, product documentation, local code, or governing standard may be the controlling source.
Guidance on unit names, symbols, conversions, and numerical presentation.
Questions about this calculation
How do I convert Degrees to Radians?
result = input × 0.017453292519943295 ÷ 1 Using the displayed relationship, 1 ° equals 0.0174532925199 rad.
How many Radians are in one Degrees?
One Degrees is 0.0174532925199 Radians. The displayed digits may be rounded.
Can I reverse the ° to rad conversion?
Yes. Swap the source and target units in the converter. The reverse relationship converts rad back to °.
Is the Degrees to Radians result exact?
The conversion follows the displayed unit relationship. Display rounding can hide additional digits, and measured inputs cannot become more accurate merely by changing units.