Milliradian to Radian Converter
Angle · unit-converter
Convert Milliradian 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 Milliradian
A milliradian is 1/1000 radian. Used in ballistics, long-range shooting, and engineering for small angles.
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 milliradians to radians
1 milliradian equals 0.001 radian in this tool (via radian):
1 mrad = (0.001 rad ÷ 1 rad) rad = 0.001 rad
Each milliradian carries 0.001 rad and each radian 1 rad, so one mrad equals 0.001 ÷ 1 rad.
Let θ(mrad) be the angle in Milliradian (mrad), and θ(rad) in Radian (rad). Then:
θ(rad) = θ(mrad) × (0.001 / 1)
Equivalently, divide by how many mrad fit into one rad (rad per rad divided by rad per mrad):
θ(rad) = θ(mrad) ÷ 1000
Examples
Example #1: Convert 1 mrad to radian
1 mrad = 1 mrad × (0.001/1) rad = 0.001 rad
1 mrad = 1 mrad ÷ 1000 = 0.001 rad
1 mrad × (0.001/1) = 0.001000 rad
Example #2: Convert 10 mrad to radian
10 mrad = 10 mrad × (0.001/1) rad = 0.01 rad
10 mrad = 10 mrad ÷ 1000 = 0.01 rad
10 mrad × (0.001/1) = 0.010000 rad
Summary
To convert Milliradian to Radian, multiply the value in mrad by (0.001 rad per mrad) / (1 rad per rad). Equivalently: value_rad = value_mrad × (0.001 / 1). Numerically, 1 mrad equals 0.001 rad.
Relationship context
Both Milliradian and Radian are converted by fixed multiples of the radian. Multiplying by (rad per mrad) ÷ (rad per rad) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Milliradian (mrad) | Radian (rad) |
|---|---|
| 0.1 | 0.0001 |
| 1 | 0.001 |
| 2 | 0.002 |
| 3 | 0.003 |
| 4 | 0.004 |
| 5 | 0.005 |
| 6 | 0.006 |
| 7 | 0.007 |
| 8 | 0.008 |
| 9 | 0.009 |
| Milliradian (mrad) | Radian (rad) |
|---|---|
| 10 | 0.01 |
| 20 | 0.02 |
| 30 | 0.03 |
| 40 | 0.04 |
| 50 | 0.05 |
| 60 | 0.06 |
| 70 | 0.07 |
| 80 | 0.08 |
| 90 | 0.09 |
| 100 | 0.1 |