Radians to Degrees
Convert radians to degrees instantly, with a reference table.
Radians to Degrees at a glance
Radians to Degrees is a free online converter you can use right now to convert radians to degrees instantly, with a reference table โ no account, no install and no usage limit. It runs entirely inside your browser, so whatever you enter stays on your own device.
- Price
- Free โ no trial, no paid tier, no watermark
- Sign-up
- Not required
- Where it runs
- In your browser โ nothing is uploaded to a server
- Works on
- Chrome, Safari, Firefox and Edge โ desktop, tablet and phone
- Category
- Unit Conversions
Radians to Degrees conversion table
| Radians (rad) | Degrees (ยฐ) |
|---|---|
| 1 rad | 57.29578 ยฐ |
| 2 rad | 114.59156 ยฐ |
| 3 rad | 171.88734 ยฐ |
| 5 rad | 286.4789 ยฐ |
| 10 rad | 572.9578 ยฐ |
| 25 rad | 1,432.3945 ยฐ |
| 50 rad | 2,864.789 ยฐ |
| 100 rad | 5,729.578 ยฐ |
| 500 rad | 28,647.89 ยฐ |
| 1000 rad | 57,295.78 ยฐ |
About Radians to Degrees
Convert radians to degrees instantly, with a reference table of common values. The factor is exact: 1 rad = 57.29577951 ยฐ.
Needed to make a calculated angle intelligible, since design software, navigation and construction all work in degrees rather than radians.
The radian is defined by the circle itself: it is the angle subtended by an arc equal in length to the radius. That makes it the natural angular unit โ calculus formulas for sine and cosine only work cleanly in radians. It is the standard in mathematics, physics and programming. Most languages' trigonometric functions expect radians, which is a frequent source of wrong results. A full turn is 2ฯ radians, so one radian is about 57.3ยฐ.
Worked through with real numbers: 1 rad is 57.296 ยฐ, 45 rad is 2578.31 ยฐ, 90 rad is 5156.62 ยฐ.
As for the other side of the conversion: A right angle is 90ยฐ, a full turn 360ยฐ, and one degree is 60 arcminutes.
Degrees are convenient for humans and radians are natural to mathematics, since a radian is defined by the circle's own radius. Most programming languages' trigonometric functions expect radians, which is a frequent cause of wrong results in geometry code.
How to use Radians to Degrees
- Enter the number of radians you want to convert.
- The equivalent in degrees appears instantly โ there is no button to press.
- Check the reference table for common Radians to Degrees values.
Frequently asked questions
How do I convert radians to degrees?
Multiply your radians figure by 57.29577951 to get degrees โ or type a value above and read the answer straight off.
How many degrees are in one radian?
1 rad = 57.29577951 ยฐ.
When would I need to convert radians to degrees?
Needed to make a calculated angle intelligible, since design software, navigation and construction all work in degrees rather than radians.
What is a radian, exactly?
The radian is defined by the circle itself: it is the angle subtended by an arc equal in length to the radius. That makes it the natural angular unit โ calculus formulas for sine and cosine only work cleanly in radians. A full turn is 2ฯ radians, so one radian is about 57.3ยฐ.
Where is the degree actually used?
It is the everyday unit for angles in navigation, construction, geometry teaching and design software. A right angle is 90ยฐ, a full turn 360ยฐ, and one degree is 60 arcminutes.
Is there anything tricky about angle conversions?
Degrees are convenient for humans and radians are natural to mathematics, since a radian is defined by the circle's own radius. Most programming languages' trigonometric functions expect radians, which is a frequent cause of wrong results in geometry code.
Is this converter accurate?
Yes. It uses the exact standard factor of 1 rad = 57.29577951 ยฐ, and the conversion runs in your browser so nothing is uploaded.