How to convert degrees to radians
Every degree is 0.01745 radians, so the conversion is a single multiplication:
Worked example: 25 ° → 25 × 0.0174533 = 0.4363 rad.
Quick mental estimate: Divide by 57: 25 ÷ 57 ≈ 0.4386 rad (exact: 0.4363).
Degrees to radians conversion table
| Degrees (°) | Radians (rad) |
|---|---|
| 1 ° | 0.01745 rad |
| 2 ° | 0.03491 rad |
| 3 ° | 0.05236 rad |
| 5 ° | 0.08727 rad |
| 10 ° | 0.1745 rad |
| 15 ° | 0.2618 rad |
| 20 ° | 0.3491 rad |
| 25 ° | 0.4363 rad |
| 50 ° | 0.8727 rad |
| 75 ° | 1.309 rad |
| 100 ° | 1.7453 rad |
| 200 ° | 3.4907 rad |
| 250 ° | 4.3633 rad |
| 500 ° | 8.7267 rad |
| 1,000 ° | 17.4533 rad |
Values rounded to four decimals. For a value that is not in the table, use the converter above — it accepts decimals and negative numbers.
When you need this conversion
- Programming and spreadsheets: trigonometric functions almost always expect radians, while the value you have is usually in degrees.
- Engineering, surveying and CAD work, where drawings are annotated in degrees but calculations run in radians.
- Physics and mathematics coursework, where the two appear side by side in the same problem.
Getting it right
Spreadsheets and programming languages expect radians in their trigonometric functions, so a value in degrees has to be converted before use — no error is raised if you forget.
Spreadsheets and programming languages expect radians in their trigonometric functions. Feeding them a value in degrees returns a wrong answer silently, with no error message.
Sanity-check the direction of the result before you use it. One degree is 0.01745 radians, so converting degrees to radians should make the number smaller. If it moved the other way, the conversion was applied backwards — the reverse converter is one click away.
About the units
Degree (°)
The degree is one 360th of a full turn. Compasses, protractors, geometry classes and everyday speech measure angles in degrees.
Radian (rad)
The radian is the angle at which the arc of a circle equals its radius. A full turn is 2π radians. Calculus, physics and most programming languages measure angles in radians.
Frequently asked questions
How many radians are in 1 degree?
1 degree equals 0.01745 radians. To convert any value, multiply the number of degrees by 0.0174533.
How do I convert degrees to radians in my head?
Divide by 57: 25 ÷ 57 ≈ 0.4386 rad (exact: 0.4363).
Is the ° to rad conversion exact?
180° equals π radians exactly, so one degree is π/180 ≈ 0.0174533 rad.
How do I convert degrees to radians in Excel or Google Sheets?
Put the value in A1 and use =A1*0.0174533. Multiplying by the factor works in every spreadsheet, in any programming language, and on a basic calculator.
How many decimal places should I keep?
For everyday use two decimals are plenty. Keep four if the result feeds another calculation, and round only at the very end — rounding intermediate steps is the most common reason a result comes out slightly wrong.