Gradian to Milliradian Converter
Angle · unit-converter
Convert Gradian to Milliradian 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 Milliradian
A milliradian is 1/1000 radian. Used in ballistics, long-range shooting, and engineering for small angles.
How to convert gradians to milliradians
1 gradian equals 15.707963267948967 milliradian in this tool (via radian):
1 grad = (0.015707963267948967 rad ÷ 0.001 rad) mrad = 15.707963267948967 mrad
Each gradian carries 0.015707963267948967 rad and each milliradian 0.001 rad, so one grad equals 0.015707963267948967 ÷ 0.001 mrad.
Let θ(grad) be the angle in Gradian (grad), and θ(mrad) in Milliradian (mrad). Then:
θ(mrad) = θ(grad) × (0.015707963267948967 / 0.001)
Equivalently, divide by how many grad fit into one mrad (rad per mrad divided by rad per grad):
θ(mrad) = θ(grad) ÷ 0.06366197723675814
Examples
Example #1: Convert 1 grad to milliradian
1 grad = 1 grad × (0.015707963267948967/0.001) mrad = 15.7079632679 mrad
1 grad = 1 grad ÷ 0.06366197723675814 = 15.7079632679 mrad
1 grad × (0.015707963267948967/0.001) = 15.707963 mrad
Example #2: Convert 10 grad to milliradian
10 grad = 10 grad × (0.015707963267948967/0.001) mrad = 157.079632679 mrad
10 grad = 10 grad ÷ 0.06366197723675814 = 157.079632679 mrad
10 grad × (0.015707963267948967/0.001) = 157.079633 mrad
Summary
To convert Gradian to Milliradian, multiply the value in grad by (0.015707963267948967 rad per grad) / (0.001 rad per mrad). Equivalently: value_mrad = value_grad × (0.015707963267948967 / 0.001). Numerically, 1 grad equals 15.707963267948967 mrad.
Relationship context
Both Gradian and Milliradian are converted by fixed multiples of the radian. Multiplying by (rad per grad) ÷ (rad per mrad) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Gradian (grad) | Milliradian (mrad) |
|---|---|
| 0.1 | 1.5707963268 |
| 1 | 15.7079632679 |
| 2 | 31.4159265359 |
| 3 | 47.1238898038 |
| 4 | 62.8318530718 |
| 5 | 78.5398163397 |
| 6 | 94.2477796077 |
| 7 | 109.955742876 |
| 8 | 125.663706144 |
| 9 | 141.371669412 |
| Gradian (grad) | Milliradian (mrad) |
|---|---|
| 10 | 157.079632679 |
| 20 | 314.159265359 |
| 30 | 471.238898038 |
| 40 | 628.318530718 |
| 50 | 785.398163397 |
| 60 | 942.477796077 |
| 70 | 1,099.55742876 |
| 80 | 1,256.63706144 |
| 90 | 1,413.71669412 |
| 100 | 1,570.79632679 |