Convert Gradians to Turns
Gradians to turns is the conversion you need when an angle comes in gradians — the surveyor's unit — but you want it as a fraction of a full circle. One gradian is exactly 0.0025 turn, which is exactly one 400th, so the turn number comes out very small.
Gradians to Turns conversion table
| Gradians (grad) | Turns (turn) |
|---|---|
| 1 | 0.0025 |
| 2 | 0.005 |
| 3 | 0.0075 |
| 5 | 0.0125 |
| 10 | 0.025 |
| 20 | 0.05 |
| 50 | 0.125 |
| 100 | 0.25 |
| 500 | 1.25 |
| 1,000 | 2.5 |
The formula
To convert gradians to turns, multiply the number of gradians by 0.0025 (which is exactly 1/400):
turns = gradians × 0.0025
A worked example
Say you have 400 gradians and want it in turns:
400 × 0.0025 = 1 turn
So 400 gradians is exactly 1 turn, a full circle.
Why the number is exact
The gradian (also called a "gon" or "grad") divides a right angle into 100 equal parts, so a full circle is 400 gradians. A turn is simply one full circle. That makes one gradian exactly 1/400 of a turn, or 0.0025 — an exact fraction, not an approximation. Just don't confuse the gradian with the radian: a calculator's "grad" mode is the gradian, which is a different unit.
When you'll use it
Working with survey or European engineering angles measured in gradians and expressing them as a share of a full circle, which is handy in rotational math, animation, and anywhere a "turn" is the natural unit.
Frequently asked questions
How many turns are in a gradian?
Exactly 0.0025 turn, which is exactly 1/400. A full circle is 400 gradians, so one gradian is one 400th of a complete turn.
How many gradians make one full turn?
Exactly 400 gradians. A gradian divides a right angle into 100 parts, so four right angles — a full circle — come to 400 gradians, which is one turn.
Is the gradians to turns conversion exact?
Yes. A full circle is exactly 400 gradians and exactly 1 turn, so one gradian is exactly 1/400 of a turn — 0.0025 — with nothing rounded away.