Convert Radians to Degrees
1 radian is 57.3 °. One radian is exactly 57.2957795131 degrees.
One radian is 57.29578 degrees. To convert radians to degrees, multiply by 57.29578; to go the other way, divide by 57.29578 or multiply by 0.017453293. 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. The angle subtending an arc equal to the radius.
Factor checked against the defining standard · How we check
- Radians × 57.29578
1 * 57.2957857.296 °
1 radian in every angle unit
| Unit | Value | Exact factor |
|---|---|---|
| radians (as entered) | 1 rad | — |
| degrees | 57.29577951 ° | × 57.2957795131 |
| gradians | 63.66197724 gon | × 63.6619772368 |
| arcminutes | 3,437.746771 ′ | × 3,437.74677078 |
| arcseconds | 206,264.8062 ″ | × 206,264.806247 |
| turns | 0.1591549431 turn | × 0.159154943092 |
| milliradians | 1,000 mrad | × 1,000 |
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 radians to degrees? The converter and the working
- 1.Take the measurement in radians.
- 2.Multiply by 57.29578 — that is how many degrees fit in one radian.
- 3.To go back the other way, divide by 57.29578, or multiply by 0.017453293.
Worked example: 25 radians to degrees
- Formula
- rad × 57.29578 = °
- Arithmetic
- 25 × 57.29578 = 1,432.39 °
- Answer
- 25 rad = 1,432.39 °
The factor is rounded for display; the figure above is computed from the full value.
Radians to degrees conversion table
| Radians | Degrees |
|---|---|
| 1 rad | 57.3 ° |
| 2 rad | 114.59 ° |
| 3 rad | 171.89 ° |
| 4 rad | 229.18 ° |
| 5 rad | 286.48 ° |
| 6 rad | 343.77 ° |
| 7 rad | 401.07 ° |
| 8 rad | 458.37 ° |
| 9 rad | 515.66 ° |
| 10 rad | 572.96 ° |
| 12 rad | 687.55 ° |
| 15 rad | 859.44 ° |
| 20 rad | 1,145.92 ° |
| 25 rad | 1,432.39 ° |
| 50 rad | 2,864.79 ° |
| 100 rad | 5,729.58 ° |
| 200 rad | 11,459.16 ° |
| 300 rad | 17,188.73 ° |
| 500 rad | 28,647.89 ° |
| 1000 rad | 57,295.78 ° |
| 2000 rad | 114,591.56 ° |
| 5000 rad | 286,478.9 ° |
| 10000 rad | 572,957.8 ° |
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.
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.
How many degrees are in a radian?
One radian is 57.29578 degrees. Going the other way, one degree is 0.017453293 radians. 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 radian.
Source: NIST Special Publication 811 — the radian, and units accepted for use with the SI
Cite this page
- APA
- Rule Calculator. (2026). Convert Radians to degrees. Rule Calculator. https://rulecalculators.com/convert/radian-to-degree
- MLA
- "Convert Radians to degrees." Rule Calculator, August 16, 2026, https://rulecalculators.com/convert/radian-to-degree.
- Chicago
- Rule Calculator. "Convert Radians to degrees." Rule Calculator. Last reviewed August 16, 2026. https://rulecalculators.com/convert/radian-to-degree.
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Questions people actually ask
- How many degrees are in a radian?
- 57.29578. 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.
- How do I convert degrees back to radians?
- Divide by 57.29578, or multiply by 0.017453293 — they are the same operation.
Other angle conversions
Degrees to radians — the same conversion the other way.