Convert Radians to Gradians
Radians to gradians is the conversion you need when an angle comes out of math or code in radians and you want it in gradians — the surveying unit where a right angle is 100. One radian is approximately 63.66198 gradians, so the gradian number always comes out much larger.
Radians to Gradians conversion table
| Radians (rad) | Gradians (grad) |
|---|---|
| 1 | 63.661977 |
| 2 | 127.323954 |
| 3 | 190.985932 |
| 5 | 318.309886 |
| 10 | 636.619772 |
| 20 | 1,273.239545 |
| 50 | 3,183.098862 |
| 100 | 6,366.197724 |
| 500 | 31,830.988618 |
| 1,000 | 63,661.977237 |
The formula
To convert radians to gradians, multiply the angle in radians by 63.66198 (which is 200 divided by pi):
gradians = radians × 63.66198
A worked example
Say you have 1 radian and want it in gradians:
1 × 63.66198 = 63.66198 grad
So 1 radian is about 63.66198 gradians.
Why it's an approximation
The factor 63.66198 is a rounded value. Here's where it comes from: a full circle is 2 pi radians and also 400 gradians, so one radian is 400 divided by 2 pi — that is, 200 divided by pi. Because pi is irrational and never ends, that division never resolves to a clean number, so any gradian figure you write down is rounded. 63.66198 is precise enough for almost anything.
When you'll use it
Moving an angle from math or code, where sin, cos, and tan expect radians, into the gradians used in surveying and some engineering — where a right angle is a round 100.
Frequently asked questions
How many gradians are in a radian?
About 63.66198 gradians. It's a rounded figure — a radian equals 200 divided by pi, and pi never ends, so 63.66198 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 63.66 gradians.
Is the radians to gradians conversion exact?
No. The factor is 200 divided by pi, and pi is irrational, so 63.66198 is rounded for everyday use. More decimal places give you more precision if you need it.