Convert Gradians to Degrees
Gradians to degrees is the conversion you need when an angle comes to you in gradians — the surveyor's unit — but you think in the familiar degrees of a protractor. One gradian is exactly 0.9 degrees, so the degree number always comes out a little smaller.
Gradians to Degrees conversion table
| Gradians (grad) | Degrees (°) |
|---|---|
| 1 | 0.9 |
| 2 | 1.8 |
| 3 | 2.7 |
| 5 | 4.5 |
| 10 | 9 |
| 20 | 18 |
| 50 | 45 |
| 100 | 90 |
| 500 | 450 |
| 1,000 | 900 |
The formula
To convert gradians to degrees, multiply the number of gradians by 0.9:
degrees = gradians × 0.9
A worked example
Say you have 100 gradians — a right angle in the gradian system — and want it in degrees:
100 × 0.9 = 90°
So 100 gradians is exactly 90 degrees, a right angle.
Why the number is exact
The gradian (also called a "gon" or "grad") divides a right angle into 100 equal parts, which makes a full circle 400 gradians. That same full circle is 360 degrees. Since 360 divided by 400 lands cleanly on 0.9, one gradian is exactly 0.9 degrees — an exact figure, not a rounded one. Just don't confuse the gradian with the radian: they're different units, even though a calculator's "grad" mode is the gradian.
When you'll use it
Reading angles off surveying instruments or European engineering drawings, where gradians are common, and turning them back into the degrees you'd use on a protractor or in most everyday math.
Frequently asked questions
How many degrees are in a gradian?
Exactly 0.9 degrees. A gradian splits a right angle into 100 equal parts, so 100 gradians make 90 degrees — and each gradian is exactly 0.9 of a degree.
Is a gradian the same as a radian?
No, and it's an easy mix-up. A gradian divides a full circle into 400 parts (a right angle into 100), while a radian is a completely different unit tied to the circle's radius. The 'grad' button on a calculator means gradians, not radians.
Is the gradians to degrees conversion exact?
Yes. A full circle is exactly 400 gradians and exactly 360 degrees, so one gradian is exactly 0.9 degrees — nothing is rounded.