Microradian to Milliradian Converter
Angle · unit-converter
Convert Microradian 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 Microradian
A microradian is 1/1,000,000 radian. It is used for very small angular deviations in optics and precision metrology.
About Milliradian
A milliradian is 1/1000 radian. Used in ballistics, long-range shooting, and engineering for small angles.
How to convert microradians to milliradians
1 microradian equals 0.001 milliradian in this tool (via radian):
1 urad = (0.000001 rad ÷ 0.001 rad) mrad = 0.001 mrad
Each microradian carries 0.000001 rad and each milliradian 0.001 rad, so one urad equals 0.000001 ÷ 0.001 mrad.
Let θ(urad) be the angle in Microradian (urad), and θ(mrad) in Milliradian (mrad). Then:
θ(mrad) = θ(urad) × (0.000001 / 0.001)
Equivalently, divide by how many urad fit into one mrad (rad per mrad divided by rad per urad):
θ(mrad) = θ(urad) ÷ 1000.0000000000001
Examples
Example #1: Convert 1 urad to milliradian
1 urad = 1 urad × (0.000001/0.001) mrad = 0.001 mrad
1 urad = 1 urad ÷ 1000.0000000000001 = 0.001 mrad
1 urad × (0.000001/0.001) = 0.001000 mrad
Example #2: Convert 10 urad to milliradian
10 urad = 10 urad × (0.000001/0.001) mrad = 0.01 mrad
10 urad = 10 urad ÷ 1000.0000000000001 = 0.01 mrad
10 urad × (0.000001/0.001) = 0.010000 mrad
Summary
To convert Microradian to Milliradian, multiply the value in urad by (0.000001 rad per urad) / (0.001 rad per mrad). Equivalently: value_mrad = value_urad × (0.000001 / 0.001). Numerically, 1 urad equals 0.001 mrad.
Relationship context
Both Microradian and Milliradian are converted by fixed multiples of the radian. Multiplying by (rad per urad) ÷ (rad per mrad) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Microradian (urad) | Milliradian (mrad) |
|---|---|
| 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 |
| Microradian (urad) | Milliradian (mrad) |
|---|---|
| 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 |