Radian to Gradian Converter
Angle · unit-converter
Convert Radian to Gradian with a fixed input and output unit, step-by-step formula line, and reference tables. All calculations bridge through radians with fixed definitions (360° per turn, 400 grad per turn, 60′ per degree, 60″ per minute, plus practical units like MOA, urad, and NATO 6400 mils per turn).
About Radian
The radian is the SI unit of plane angle. One radian is the angle subtended by an arc equal to the radius; 2π rad = one full circle.
About Gradian
Gradians (gon) divide a right angle into 100 parts; 400 gradians make a full turn. Used in some surveying and European contexts.
How to convert radians to gradians
1 radian equals 63.66197723675813 gradian in this tool (via radian):
1 rad = (1 rad ÷ 0.015707963267948967 rad) grad = 63.66197723675813 grad
Each radian carries 1 rad and each gradian 0.015707963267948967 rad, so one rad equals 1 ÷ 0.015707963267948967 grad.
Let θ(rad) be the angle in Radian (rad), and θ(grad) in Gradian (grad). Then:
θ(grad) = θ(rad) × (1 / 0.015707963267948967)
Equivalently, divide by how many rad fit into one grad (rad per grad divided by rad per rad):
θ(grad) = θ(rad) ÷ 0.015707963267948967
Examples
Example #1: Convert 1 rad to gradian
1 rad = 1 rad × (1/0.015707963267948967) grad = 63.6619772368 grad
1 rad = 1 rad ÷ 0.015707963267948967 = 63.6619772368 grad
1 rad × (1/0.015707963267948967) = 63.661977 grad
Example #2: Convert 10 rad to gradian
10 rad = 10 rad × (1/0.015707963267948967) grad = 636.619772368 grad
10 rad = 10 rad ÷ 0.015707963267948967 = 636.619772368 grad
10 rad × (1/0.015707963267948967) = 636.619772 grad
Summary
To convert Radian to Gradian, multiply the value in rad by (1 rad per rad) / (0.015707963267948967 rad per grad). Equivalently: value_grad = value_rad × (1 / 0.015707963267948967). Numerically, 1 rad equals 63.66197723675813 grad.
Relationship context
Both Radian and Gradian are converted by fixed multiples of the radian. Multiplying by (rad per rad) ÷ (rad per grad) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Radian (rad) | Gradian (grad) |
|---|---|
| 0.1 | 6.3661977237 |
| 1 | 63.6619772368 |
| 2 | 127.323954474 |
| 3 | 190.98593171 |
| 4 | 254.647908947 |
| 5 | 318.309886184 |
| 6 | 381.971863421 |
| 7 | 445.633840657 |
| 8 | 509.295817894 |
| 9 | 572.957795131 |
| Radian (rad) | Gradian (grad) |
|---|---|
| 10 | 636.619772368 |
| 20 | 1,273.23954474 |
| 30 | 1,909.8593171 |
| 40 | 2,546.47908947 |
| 50 | 3,183.09886184 |
| 60 | 3,819.71863421 |
| 70 | 4,456.33840657 |
| 80 | 5,092.95817894 |
| 90 | 5,729.57795131 |
| 100 | 6,366.19772368 |