Milliradian to Microradian Converter
Angle · unit-converter
Convert Milliradian to Microradian 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 Microradian
A microradian is 1/1,000,000 radian. It is used for very small angular deviations in optics and precision metrology.
How to convert milliradians to microradians
1 milliradian equals 1000.0000000000001 microradian in this tool (via radian):
1 mrad = (0.001 rad ÷ 0.000001 rad) urad = 1000.0000000000001 urad
Each milliradian carries 0.001 rad and each microradian 0.000001 rad, so one mrad equals 0.001 ÷ 0.000001 urad.
Let θ(mrad) be the angle in Milliradian (mrad), and θ(urad) in Microradian (urad). Then:
θ(urad) = θ(mrad) × (0.001 / 0.000001)
Equivalently, divide by how many mrad fit into one urad (rad per urad divided by rad per mrad):
θ(urad) = θ(mrad) ÷ 0.001
Examples
Example #1: Convert 1 mrad to microradian
1 mrad = 1 mrad × (0.001/0.000001) urad = 1000 urad
1 mrad = 1 mrad ÷ 0.001 = 1000 urad
1 mrad × (0.001/0.000001) = 1,000.000000 urad
Example #2: Convert 10 mrad to microradian
10 mrad = 10 mrad × (0.001/0.000001) urad = 10000 urad
10 mrad = 10 mrad ÷ 0.001 = 10000 urad
10 mrad × (0.001/0.000001) = 10,000.000000 urad
Summary
To convert Milliradian to Microradian, multiply the value in mrad by (0.001 rad per mrad) / (0.000001 rad per urad). Equivalently: value_urad = value_mrad × (0.001 / 0.000001). Numerically, 1 mrad equals 1000.0000000000001 urad.
Relationship context
Both Milliradian and Microradian are converted by fixed multiples of the radian. Multiplying by (rad per mrad) ÷ (rad per urad) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Milliradian (mrad) | Microradian (urad) |
|---|---|
| 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 |
| Milliradian (mrad) | Microradian (urad) |
|---|---|
| 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 |