Gradians to Radians
An instant gradians-to-radians converter, with the formula and a reference table below.
| Gradians | Radians |
|---|---|
| 1 grad | 0.015708 rad |
| 2 grad | 0.031416 rad |
| 3 grad | 0.047124 rad |
| 5 grad | 0.07854 rad |
| 10 grad | 0.15708 rad |
| 25 grad | 0.392699 rad |
| 50 grad | 0.785398 rad |
| 100 grad | 1.570796 rad |
How to use
- Enter a value in the Gradians field.
- The Radians figure appears immediately — no button to press.
- Typing in the Radians field converts back to Gradians the same way.
- Use the reference table for the values that come up most often.
Gradians to Radians formula
The factor from gradians to radians is 0.0157079633.
rad = grad × 0.0157079633
Why this factor: the gradian and the radian are both defined against the degree, so dividing one definition by the other gives 0.0157079633 directly. Both definitions are set out in full below.
To go the other way, divide by 0.0157079633 — or use the Radians to Gradians converter, which is the same calculation reversed.
Worked example
Given 90 grad, multiplying by 0.0157079633 yields 1.413717 rad.
90 grad × 0.0157079633 = 1.413717 rad
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 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.
Gradians vs Radians
The gradian is a specialized unit while the radian is an SI 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 radians are in a gradian?
One gradian equals 0.0157079633 radians.
What is the formula to convert gradians to radians?
Multiply the number of gradians by 0.0157079633. To reverse it, divide by 0.0157079633 instead.
How do I convert radians back to gradians?
Divide by 0.0157079633, which is the same as multiplying by 63.6619772.
How many radians are in 10 gradians?
10 grad works out to 0.15708 rad.
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 gradian defined?
A full turn is 400 gradians, so one gradian is exactly 0.9 degree.