Convert Radians to Degrees
Radians to degrees is the conversion you need when a calculator or a piece of code hands you an angle in radians and you want it in the degrees people actually picture. One radian is approximately 57.29578 degrees, so the degree number always comes out much larger.
Radians to Degrees conversion table
| Radians (rad) | Degrees (°) |
|---|---|
| 1 | 57.29578 |
| 2 | 114.591559 |
| 3 | 171.887339 |
| 5 | 286.478898 |
| 10 | 572.957795 |
| 20 | 1,145.91559 |
| 50 | 2,864.788976 |
| 100 | 5,729.577951 |
| 500 | 28,647.889757 |
| 1,000 | 57,295.779513 |
The formula
To convert radians to degrees, multiply the angle in radians by 57.29578 (which is 180 divided by pi):
degrees = radians × 57.29578
A worked example
Say a calculator gives you 1 radian and you want it in degrees:
1 × 57.29578 = 57.29578°
So 1 radian is about 57.29578 degrees.
Why it's an approximation
The factor 57.29578 is a rounded value. Here's where it comes from: a full circle is 2 pi radians and also 360 degrees, so one radian is 360 divided by 2 pi — that is, 180 divided by pi. Because pi is irrational and never ends, that division never resolves to a clean number, so any degree figure you write down is rounded. 57.29578 is precise enough for almost anything.
When you'll use it
Reading an angle out of a calculator or code — where sin, cos, and tan expect radians — and turning it into the degrees you'd use on a protractor, a map bearing, or a drawing.
Frequently asked questions
How many degrees are in a radian?
About 57.29578 degrees. It's a rounded figure — a radian equals 180 divided by pi, and pi never ends, so 57.29578 is the practical number to use.
What is a radian, exactly?
It's the natural angle unit used in math and physics — the angle you get when the arc length equals the radius. A full circle is 2 pi radians, which is why one radian works out to roughly 57.3 degrees.
Is the radians to degrees conversion exact?
No. The factor is 180 divided by pi, and pi is irrational, so 57.29578 is rounded for everyday use. More decimal places give you more precision if you need it.