Convert Degrees to Gradians
Degrees to gradians is the conversion you need when you meet the surveyor's angle unit — the gradian, also called the gon — where a full circle is split into 400 parts instead of 360. One degree is about 1.1111111111111112 gradians, so the gradian number comes out a little larger than the degree number.
Degrees to Gradians conversion table
| Degrees (°) | Gradians (grad) |
|---|---|
| 1 | 1.111111 |
| 2 | 2.222222 |
| 3 | 3.333333 |
| 5 | 5.555556 |
| 10 | 11.111111 |
| 20 | 22.222222 |
| 50 | 55.555556 |
| 100 | 111.111111 |
| 500 | 555.555556 |
| 1,000 | 1,111.111111 |
The formula
To convert degrees to gradians, multiply the number of degrees by 1.1111111111111112 (which is 10/9):
gradians = degrees × 1.1111111111111112
A worked example
Say you have 45 degrees — half a right angle — and want it in gradians:
45 × 1.1111111111111112 = 50 grad
So 45 degrees is exactly 50 gradians.
Why it's an approximation
The clean number lives on the other side: one gradian is defined as exactly 0.9 degrees. Flip that around to go from degrees to gradians and you get 10 divided by 9 — a decimal that repeats forever as 1.1111…, never settling. So the multiply factor you use, 1.1111111111111112, is rounded off at some point. In practice round angles still come out tidy — a right angle is exactly 100 gradians and 45 degrees is exactly 50 — because those divide evenly; it's only the general-purpose factor that has to be trimmed.
When you'll use it
Reading survey and civil-engineering measurements in continental Europe, where the gradian is common, and working with instruments or calculators set to "gon" mode where a right angle reads as 100.
Frequently asked questions
How many gradians are in a degree?
About 1.1111111111111112 gradians. The clean fact runs the other way: one gradian is exactly 0.9 degrees, which makes a degree 10/9 of a gradian — a repeating 1.1111 that never quite ends.
What is 45 degrees in gradians?
Exactly 50 gradians. Round angles land on clean gradian values because a right angle (90 degrees) is exactly 100 gradians, so half of it is 50.
Is the degrees to gradians conversion exact?
The reverse direction is: one gradian is exactly 0.9 degrees. Going from degrees to gradians you multiply by 10/9, which is a repeating decimal (1.1111…), so the factor itself is rounded even though round angles still come out clean.