Gradian to Radian Converter
Angle · unit-converter
Convert Gradian to Radian 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 Gradian
Gradians (gon) divide a right angle into 100 parts; 400 gradians make a full turn. Used in some surveying and European contexts.
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.
How to convert gradians to radians
1 gradian equals 0.015707963267948967 radian in this tool (via radian):
1 grad = (0.015707963267948967 rad ÷ 1 rad) rad = 0.015707963267948967 rad
Each gradian carries 0.015707963267948967 rad and each radian 1 rad, so one grad equals 0.015707963267948967 ÷ 1 rad.
Let θ(grad) be the angle in Gradian (grad), and θ(rad) in Radian (rad). Then:
θ(rad) = θ(grad) × (0.015707963267948967 / 1)
Equivalently, divide by how many grad fit into one rad (rad per rad divided by rad per grad):
θ(rad) = θ(grad) ÷ 63.66197723675813
Examples
Example #1: Convert 1 grad to radian
1 grad = 1 grad × (0.015707963267948967/1) rad = 0.0157079633 rad
1 grad = 1 grad ÷ 63.66197723675813 = 0.0157079633 rad
1 grad × (0.015707963267948967/1) = 0.015708 rad
Example #2: Convert 10 grad to radian
10 grad = 10 grad × (0.015707963267948967/1) rad = 0.1570796327 rad
10 grad = 10 grad ÷ 63.66197723675813 = 0.1570796327 rad
10 grad × (0.015707963267948967/1) = 0.157080 rad
Summary
To convert Gradian to Radian, multiply the value in grad by (0.015707963267948967 rad per grad) / (1 rad per rad). Equivalently: value_rad = value_grad × (0.015707963267948967 / 1). Numerically, 1 grad equals 0.015707963267948967 rad.
Relationship context
Both Gradian and Radian are converted by fixed multiples of the radian. Multiplying by (rad per grad) ÷ (rad per rad) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Gradian (grad) | Radian (rad) |
|---|---|
| 0.1 | 0.0015707963 |
| 1 | 0.0157079633 |
| 2 | 0.0314159265 |
| 3 | 0.0471238898 |
| 4 | 0.0628318531 |
| 5 | 0.0785398163 |
| 6 | 0.0942477796 |
| 7 | 0.1099557429 |
| 8 | 0.1256637061 |
| 9 | 0.1413716694 |
| Gradian (grad) | Radian (rad) |
|---|---|
| 10 | 0.1570796327 |
| 20 | 0.3141592654 |
| 30 | 0.471238898 |
| 40 | 0.6283185307 |
| 50 | 0.7853981634 |
| 60 | 0.9424777961 |
| 70 | 1.0995574288 |
| 80 | 1.2566370614 |
| 90 | 1.4137166941 |
| 100 | 1.5707963268 |