Milliradian to Gradian Converter
Angle · unit-converter
Convert Milliradian 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 Milliradian
A milliradian is 1/1000 radian. Used in ballistics, long-range shooting, and engineering for small angles.
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 milliradians to gradians
1 milliradian equals 0.06366197723675814 gradian in this tool (via radian):
1 mrad = (0.001 rad ÷ 0.015707963267948967 rad) grad = 0.06366197723675814 grad
Each milliradian carries 0.001 rad and each gradian 0.015707963267948967 rad, so one mrad equals 0.001 ÷ 0.015707963267948967 grad.
Let θ(mrad) be the angle in Milliradian (mrad), and θ(grad) in Gradian (grad). Then:
θ(grad) = θ(mrad) × (0.001 / 0.015707963267948967)
Equivalently, divide by how many mrad fit into one grad (rad per grad divided by rad per mrad):
θ(grad) = θ(mrad) ÷ 15.707963267948967
Examples
Example #1: Convert 1 mrad to gradian
1 mrad = 1 mrad × (0.001/0.015707963267948967) grad = 0.0636619772 grad
1 mrad = 1 mrad ÷ 15.707963267948967 = 0.0636619772 grad
1 mrad × (0.001/0.015707963267948967) = 0.063662 grad
Example #2: Convert 10 mrad to gradian
10 mrad = 10 mrad × (0.001/0.015707963267948967) grad = 0.6366197724 grad
10 mrad = 10 mrad ÷ 15.707963267948967 = 0.6366197724 grad
10 mrad × (0.001/0.015707963267948967) = 0.636620 grad
Summary
To convert Milliradian to Gradian, multiply the value in mrad by (0.001 rad per mrad) / (0.015707963267948967 rad per grad). Equivalently: value_grad = value_mrad × (0.001 / 0.015707963267948967). Numerically, 1 mrad equals 0.06366197723675814 grad.
Relationship context
Both Milliradian and Gradian are converted by fixed multiples of the radian. Multiplying by (rad per mrad) ÷ (rad per grad) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Milliradian (mrad) | Gradian (grad) |
|---|---|
| 0.1 | 0.0063661977 |
| 1 | 0.0636619772 |
| 2 | 0.1273239545 |
| 3 | 0.1909859317 |
| 4 | 0.2546479089 |
| 5 | 0.3183098862 |
| 6 | 0.3819718634 |
| 7 | 0.4456338407 |
| 8 | 0.5092958179 |
| 9 | 0.5729577951 |
| Milliradian (mrad) | Gradian (grad) |
|---|---|
| 10 | 0.6366197724 |
| 20 | 1.2732395447 |
| 30 | 1.9098593171 |
| 40 | 2.5464790895 |
| 50 | 3.1830988618 |
| 60 | 3.8197186342 |
| 70 | 4.4563384066 |
| 80 | 5.0929581789 |
| 90 | 5.7295779513 |
| 100 | 6.3661977237 |