Radians to Gradians
Convert radians to gradians instantly — one radian is 63.662 gradians.
| Radians | Gradians |
|---|---|
| 1 rad | 63.661977 grad |
| 2 rad | 127.323954 grad |
| 3 rad | 190.985932 grad |
| 5 rad | 318.309886 grad |
| 10 rad | 636.619772 grad |
| 25 rad | 1591.549431 grad |
| 50 rad | 3183.098862 grad |
| 100 rad | 6366.197724 grad |
How to use
- Enter a value in the Radians field.
- The Gradians figure appears immediately — no button to press.
- Typing in the Gradians field converts back to Radians the same way.
- Use the reference table for the values that come up most often.
Radians to Gradians formula
The factor from radians to gradians is 63.6619772.
grad = rad × 63.6619772
Why this factor: the radian and the gradian are both defined against the degree, so dividing one definition by the other gives 63.6619772 directly. Both definitions are set out in full below.
To go the other way, divide by 63.6619772 — or use the Gradians to Radians converter, which is the same calculation reversed.
Worked example
Given 90 rad, multiplying by 63.6619772 yields 5729.577951 grad.
90 rad × 63.6619772 = 5729.577951 grad
The converter above does this for any value you type, in either direction.
What is a radian?
A radian is the angle that subtends an arc equal in length to the circle's radius — the natural unit of angle.
Definition: A full turn is exactly 2π radians, so one radian is 180/π degrees, about 57.29578°.
Where it is used: Calculus and trigonometry, physics, and every standard programming library's sin, cos and tan.
Worth knowing: Programming maths functions almost always expect radians. Passing degrees to Math.sin() is one of the most common numerical bugs.
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.
Radians vs Gradians
The radian is an SI unit while the gradian is a specialized unit. That is why the factor between them is not a round number: the two systems were defined independently and only later tied together by exact agreement.
Frequently asked questions
How many gradians are in a radian?
One radian equals 63.6619772 gradians.
What is the formula to convert radians to gradians?
Multiply the number of radians by 63.6619772. To reverse it, divide by 63.6619772 instead.
How do I convert gradians back to radians?
Divide by 63.6619772, which is the same as multiplying by 0.0157079633.
How many gradians are in 10 radians?
10 rad works out to 636.619772 grad.
Is there anything to watch out for with radians?
Programming maths functions almost always expect radians. Passing degrees to Math.sin() is one of the most common numerical bugs.
How is the radian defined?
A full turn is exactly 2π radians, so one radian is 180/π degrees, about 57.29578°.