Convert Degrees to Radians
1 degree is 0.02 rad. One degree is exactly 0.0174532925199 radians.
One degree is 0.017453293 radians. To convert degrees to radians, multiply by 0.017453293; to go the other way, divide by 0.017453293 or multiply by 57.29578. The relation is exact but the figure is not: it is a rounding of a number that does not terminate, and it follows from NIST Special Publication 811. A 360th of a full turn, inherited from Babylonian astronomy and its base-60 arithmetic.
Factor checked against the defining standard · How we check
- Degrees × 0.017453293
1 * 0.01745330.017 rad
1 degree in every angle unit
| Unit | Value | Exact factor |
|---|---|---|
| radians | 0.01745329252 rad | × 0.0174532925199 |
| degrees (as entered) | 1 ° | — |
| gradians | 1.111111111 gon | × 1.11111111111 |
| arcminutes | 60 ′ | × 60 |
| arcseconds | 3,600 ″ | × 3,600 |
| turns | 0.002777777778 turn | × 0.00277777777778 |
| milliradians | 17.45329252 mrad | × 17.4532925199 |
Factors are entered by hand from NIST Special Publication 811 rather than derived from a units library, so the ones that terminate are exact rather than rounded.
How do you convert degrees to radians? The converter and the working
- 1.Take the measurement in degrees.
- 2.Multiply by 0.017453293 — that is how many radians fit in one degree.
- 3.To go back the other way, divide by 0.017453293, or multiply by 57.29578.
Worked example: 25 degrees to radians
- Formula
- ° × 0.017453293 = rad
- Arithmetic
- 25 × 0.017453293 = 0.44 rad
- Answer
- 25 ° = 0.44 rad
The factor is rounded for display; the figure above is computed from the full value.
Degrees to radians conversion table
| Degrees | Radians |
|---|---|
| 1 ° | 0.02 rad |
| 2 ° | 0.03 rad |
| 3 ° | 0.05 rad |
| 4 ° | 0.07 rad |
| 5 ° | 0.09 rad |
| 6 ° | 0.1 rad |
| 7 ° | 0.12 rad |
| 8 ° | 0.14 rad |
| 9 ° | 0.16 rad |
| 10 ° | 0.17 rad |
| 12 ° | 0.21 rad |
| 15 ° | 0.26 rad |
| 20 ° | 0.35 rad |
| 25 ° | 0.44 rad |
| 50 ° | 0.87 rad |
| 100 ° | 1.75 rad |
| 200 ° | 3.49 rad |
| 300 ° | 5.24 rad |
| 500 ° | 8.73 rad |
| 1000 ° | 17.45 rad |
| 2000 ° | 34.91 rad |
| 5000 ° | 87.27 rad |
| 10000 ° | 174.53 rad |
What is a degree?
A 360th of a full turn, inherited from Babylonian astronomy and its base-60 arithmetic. 360 survives because it divides evenly by everything from 2 to 12 except 7.
What is a radian?
The angle subtending an arc equal to the radius. It is the unit every trigonometric function in every programming language actually takes, which is why a sine computed in degrees comes out wrong.
How many radians are in a degree?
One degree is 0.017453293 radians. Going the other way, one radian is 57.29578 degrees. Both figures come from the same defined relation rather than from a measurement, which is why they are the same today as they were in 1959.
Every angle unit here
The whole group — 7 units with their symbols and the size of each one in radians — is on the conversion index, along with every pair it makes. The table above already gives each of them relative to a degree.
Source: NIST Special Publication 811 — the radian, and units accepted for use with the SI
Cite this page
- APA
- Rule Calculator. (2026). Convert Degrees to radians. Rule Calculator. https://rulecalculators.com/convert/degree-to-radian
- MLA
- "Convert Degrees to radians." Rule Calculator, August 16, 2026, https://rulecalculators.com/convert/degree-to-radian.
- Chicago
- Rule Calculator. "Convert Degrees to radians." Rule Calculator. Last reviewed August 16, 2026. https://rulecalculators.com/convert/degree-to-radian.
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Questions people actually ask
- How many radians are in a degree?
- 0.017453293. The angle subtending an arc equal to the radius. It is the unit every trigonometric function in every programming language actually takes, which is why a sine computed in degrees comes out wrong.
- How do I convert radians back to degrees?
- Divide by 0.017453293, or multiply by 57.29578 — they are the same operation.
Other angle conversions
Radians to degrees — the same conversion the other way.