Degrees to Radians
Convert degrees to radians instantly, with a reference table.
Degrees to Radians at a glance
Degrees to Radians is a free online converter you can use right now to convert degrees to radians 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
Degrees to Radians conversion table
| Degrees (ยฐ) | Radians (rad) |
|---|---|
| 1 ยฐ | 0.017453 rad |
| 2 ยฐ | 0.034907 rad |
| 3 ยฐ | 0.05236 rad |
| 5 ยฐ | 0.087266 rad |
| 10 ยฐ | 0.174533 rad |
| 25 ยฐ | 0.436332 rad |
| 50 ยฐ | 0.872665 rad |
| 100 ยฐ | 1.745329 rad |
| 500 ยฐ | 8.726646 rad |
| 1000 ยฐ | 17.453293 rad |
About Degrees to Radians
Convert degrees to radians instantly, with a reference table of common values. The factor is exact: 1 ยฐ = 0.017453293 rad.
Essential in programming and physics, because almost every language's trigonometric functions expect radians. Passing degrees to them is one of the most common causes of wrong geometry results.
The 360-degree circle comes from Babylonian astronomy and their base-60 number system. The number survives because 360 divides evenly by a great many integers, making fractions of a circle convenient to express. 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.
Worked through with real numbers: 1 ยฐ is 0.017453 rad, 45 ยฐ is 0.785398 rad, 90 ยฐ is 1.571 rad.
As for the other side of the conversion: A full turn is 2ฯ radians, so one radian is about 57.3ยฐ.
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 Degrees to Radians
- Enter the number of degrees you want to convert.
- The equivalent in radians appears instantly โ there is no button to press.
- Check the reference table for common Degrees to Radians values.
Frequently asked questions
How do I convert degrees to radians?
Multiply your degrees figure by 0.017453293 to get radians โ or type a value above and read the answer straight off.
How many radians are in one degree?
1 ยฐ = 0.017453293 rad.
When would I need to convert degrees to radians?
Essential in programming and physics, because almost every language's trigonometric functions expect radians. Passing degrees to them is one of the most common causes of wrong geometry results.
What is a degree, exactly?
The 360-degree circle comes from Babylonian astronomy and their base-60 number system. The number survives because 360 divides evenly by a great many integers, making fractions of a circle convenient to express. A right angle is 90ยฐ, a full turn 360ยฐ, and one degree is 60 arcminutes.
Where is the radian actually used?
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.
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 ยฐ = 0.017453293 rad, and the conversion runs in your browser so nothing is uploaded.