Radian to Milliradian Converter
Angle · unit-converter
Convert Radian 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 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 Milliradian
A milliradian is 1/1000 radian. Used in ballistics, long-range shooting, and engineering for small angles.
How to convert radians to milliradians
1 radian equals 1000 milliradian in this tool (via radian):
1 rad = (1 rad ÷ 0.001 rad) mrad = 1000 mrad
Each radian carries 1 rad and each milliradian 0.001 rad, so one rad equals 1 ÷ 0.001 mrad.
Let θ(rad) be the angle in Radian (rad), and θ(mrad) in Milliradian (mrad). Then:
θ(mrad) = θ(rad) × (1 / 0.001)
Equivalently, divide by how many rad fit into one mrad (rad per mrad divided by rad per rad):
θ(mrad) = θ(rad) ÷ 0.001
Examples
Example #1: Convert 1 rad to milliradian
1 rad = 1 rad × (1/0.001) mrad = 1000 mrad
1 rad = 1 rad ÷ 0.001 = 1000 mrad
1 rad × (1/0.001) = 1,000.000000 mrad
Example #2: Convert 10 rad to milliradian
10 rad = 10 rad × (1/0.001) mrad = 10000 mrad
10 rad = 10 rad ÷ 0.001 = 10000 mrad
10 rad × (1/0.001) = 10,000.000000 mrad
Summary
To convert Radian to Milliradian, multiply the value in rad by (1 rad per rad) / (0.001 rad per mrad). Equivalently: value_mrad = value_rad × (1 / 0.001). Numerically, 1 rad equals 1000 mrad.
Relationship context
Both Radian and Milliradian are converted by fixed multiples of the radian. Multiplying by (rad per rad) ÷ (rad per mrad) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Radian (rad) | Milliradian (mrad) |
|---|---|
| 0.1 | 100 |
| 1 | 1,000 |
| 2 | 2,000 |
| 3 | 3,000 |
| 4 | 4,000 |
| 5 | 5,000 |
| 6 | 6,000 |
| 7 | 7,000 |
| 8 | 8,000 |
| 9 | 9,000 |
| Radian (rad) | Milliradian (mrad) |
|---|---|
| 10 | 10,000 |
| 20 | 20,000 |
| 30 | 30,000 |
| 40 | 40,000 |
| 50 | 50,000 |
| 60 | 60,000 |
| 70 | 70,000 |
| 80 | 80,000 |
| 90 | 90,000 |
| 100 | 100,000 |