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Angle
Degrees to Radians
Convert degrees (°) to radians (rad). Type a value below to see the result update instantly. Reference table and formula included.
Calculator
1 ° = 0.017453 rad
Degrees to Radians Conversion Table
Common values, ready to copy:
| degrees | radians |
|---|---|
| 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 ° | 1.7453 rad |
| 1,000 ° | 17.4533 rad |
Formula
radians = degrees × 1.74532925e-2
Angles are ratios, not absolute quantities, so the conversion factors are exact. 1 full turn = 360° = 2π rad ≈ 6.2832 rad = 400 gon. 1° = 60 arcminutes = 3,600 arcseconds.
About Degrees and Radians
Degrees (°): 1/360 of a full turn; the 360-degree division comes from ancient Babylonian astronomy and the convenience of 360 being divisible by many small integers. Common uses: Navigation (compass headings), construction (angle cuts), geometry, geography (latitude and longitude), and almost any practical angle measurement.
Radians (rad): The natural SI unit for angle; one radian is the angle subtended by an arc equal in length to the radius (so a full circle is 2π radians ≈ 6.283). Common uses: Mathematics (calculus, trigonometry derivatives), physics, computer graphics, and any context where the formula simplifies in radians.
How the conversion works
Angles are ratios, not absolute quantities, so the conversion factors are exact. 1 full turn = 360° = 2π rad ≈ 6.2832 rad = 400 gon. 1° = 60 arcminutes = 3,600 arcseconds.
The exact relationship is radians = degrees × 1.74532925e-2, which the calculator at the top of this page applies in both directions. Type into either field and the other updates immediately.
When this conversion matters
Converting between degrees and radians comes up wherever angle measurements move between systems — from one country's conventions to another's, from a scientific reference to a practical specification, or from one industry's working unit to another's. The calculator and reference table above cover the everyday range; for unusual values you can type any number into either field.