Degrees to Gradians
Convert degrees to gradians instantly — one degree is 1.11111 gradians.
| Degrees | Gradians |
|---|---|
| 1 ° | 1.111111 grad |
| 2 ° | 2.222222 grad |
| 3 ° | 3.333333 grad |
| 5 ° | 5.555556 grad |
| 10 ° | 11.111111 grad |
| 25 ° | 27.777778 grad |
| 50 ° | 55.555556 grad |
| 100 ° | 111.111111 grad |
How to use
- Enter a value in the Degrees field.
- The Gradians figure appears immediately — no button to press.
- Typing in the Gradians field converts back to Degrees the same way.
- Use the reference table for the values that come up most often.
Degrees to Gradians formula
To convert degrees to gradians, multiply by 1.11111111.
grad = ° × 1.11111111
Put another way, one degree is exactly 10/9 gradians.
Why this factor: the degree and the gradian are both defined against the degree, so dividing one definition by the other gives 1.11111111 directly. Both definitions are set out in full below.
To go the other way, divide by 1.11111111 — or use the Gradians to Degrees converter, which is the same calculation reversed.
Worked example
Take 45 ° and multiply by the factor 1.11111111: the result is 50 grad.
45 ° × 1.11111111 = 50 grad
The converter above does this for any value you type, in either direction.
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.
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.
Degrees vs Gradians
The degree and the gradian 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 gradians are in a degree?
One degree equals 1.11111111 gradians.
What is the formula to convert degrees to gradians?
Multiply the number of degrees by 1.11111111. To reverse it, divide by 1.11111111 instead.
How do I convert gradians back to degrees?
Divide by 1.11111111, which is the same as multiplying by 0.9.
How many gradians are in 10 degrees?
10 ° works out to 11.111111 grad.
How is the degree defined?
Exactly 1/360 of a complete revolution. The choice of 360 comes from Babylonian base-60 arithmetic.