Convert Radians to Gradians
Convert Radians (rad) to Gradians (grad) instantly and accurately.
Conversion Formula
grad = rad × 63.66197724
About Radians
The radian (rad) is the SI unit of plane angle, defined as the angle subtended at the centre of a circle by an arc equal in length to the radius. A full circle = 2π rad; a right angle = π/2 rad. The radian is dimensionless (arc length / radius), so it can be omitted in equations. All calculus and physics formulas are simplest in radians: d/dx(sin x) = cos x holds only in radians; Taylor series sin x = x − x³/6 + x⁵/120 hold only for x in radians; angular frequency ω = 2πf gives energy E = ħω. 1 rad = 180°/π ≈ 57.2958° ≈ 206,264.8″.
About Gradians
A gradian (grad), also called a gon (ISO 31/DIN), equals 1/400 of a full circle - π/200 rad = 0.9°. Its main advantage: a right angle = exactly 100 grad, simplifying complementary and supplementary angle arithmetic. Introduced during the French Revolution as part of decimal angle reform. Surveying in France, the Netherlands, Switzerland, and Scandinavia uses gradians; professional total stations display both degrees and gons. A 1% slope ≈ 0.6366 grad. 1 grad = 0.9° = 54′ = π/200 rad; 400 grad = 360° = one full circle.
Quick Reference Table
| Radians (rad) | Gradians (grad) |
|---|---|
| 1 rad | 63.662 grad |
| 2 rad | 127.324 grad |
| 5 rad | 318.31 grad |
| 10 rad | 636.62 grad |
| 25 rad | 1591.55 grad |
| 50 rad | 3183.1 grad |
| 100 rad | 6366.2 grad |