Gradians to Degrees
Type a value in either box to convert between gradians and degrees. The factor is 0.9.
| Gradians | Degrees |
|---|---|
| 1 grad | 0.9 ° |
| 2 grad | 1.8 ° |
| 3 grad | 2.7 ° |
| 5 grad | 4.5 ° |
| 10 grad | 9 ° |
| 25 grad | 22.5 ° |
| 50 grad | 45 ° |
| 100 grad | 90 ° |
How to use
- Enter a value in the Gradians field.
- The Degrees figure appears immediately — no button to press.
- Typing in the Degrees field converts back to Gradians the same way.
- Use the reference table for the values that come up most often.
Gradians to Degrees formula
Converting gradians to degrees is a single multiplication by 0.9.
° = grad × 0.9
Put another way, one gradian is exactly 9/10 degrees.
Why this factor: the gradian and the degree are both defined against the degree, so dividing one definition by the other gives 0.9 directly. Both definitions are set out in full below.
To go the other way, divide by 0.9 — or use the Degrees to Gradians converter, which is the same calculation reversed.
Worked example
Take 45 grad and multiply by the factor 0.9: the result is 40.5 °.
45 grad × 0.9 = 40.5 °
The converter above does this for any value you type, in either direction.
What is a gradian?
A gradian, or gon, divides a right angle into 100 parts instead of 90.
Definition: A full turn is 400 gradians, so one gradian is exactly 0.9 degree.
Where it is used: European surveying and civil engineering, and still a mode on most scientific calculators.
What is a degree?
A degree is one 360th of a full turn, the everyday unit of angle.
Definition: Exactly 1/360 of a complete revolution. The choice of 360 comes from Babylonian base-60 arithmetic.
Where it is used: Geometry, navigation bearings, latitude and longitude, and CSS rotations.
Gradians vs Degrees
The gradian and the degree belong to the same family of units, so converting between them is usually a matter of shifting a decimal point or applying a small whole-number factor.
Frequently asked questions
How many degrees are in a gradian?
One gradian equals 0.9 degrees.
What is the formula to convert gradians to degrees?
Multiply the number of gradians by 0.9. To reverse it, divide by 0.9 instead.
How do I convert degrees back to gradians?
Divide by 0.9, which is the same as multiplying by 1.11111111.
How many degrees are in 10 gradians?
10 grad works out to 9 °.
How is the gradian defined?
A full turn is 400 gradians, so one gradian is exactly 0.9 degree.