Radian to Microradian Converter
Angle · unit-converter
Convert Radian 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 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 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 radians to microradians
1 radian equals 1000000 microradian in this tool (via radian):
1 rad = (1 rad ÷ 0.000001 rad) urad = 1000000 urad
Each radian carries 1 rad and each microradian 0.000001 rad, so one rad equals 1 ÷ 0.000001 urad.
Let θ(rad) be the angle in Radian (rad), and θ(urad) in Microradian (urad). Then:
θ(urad) = θ(rad) × (1 / 0.000001)
Equivalently, divide by how many rad fit into one urad (rad per urad divided by rad per rad):
θ(urad) = θ(rad) ÷ 0.000001
Examples
Example #1: Convert 1 rad to microradian
1 rad = 1 rad × (1/0.000001) urad = 1000000 urad
1 rad = 1 rad ÷ 0.000001 = 1000000 urad
1 rad × (1/0.000001) = 1,000,000.000000 urad
Example #2: Convert 10 rad to microradian
10 rad = 10 rad × (1/0.000001) urad = 10000000 urad
10 rad = 10 rad ÷ 0.000001 = 10000000 urad
10 rad × (1/0.000001) = 10,000,000.000000 urad
Summary
To convert Radian to Microradian, multiply the value in rad by (1 rad per rad) / (0.000001 rad per urad). Equivalently: value_urad = value_rad × (1 / 0.000001). Numerically, 1 rad equals 1000000 urad.
Relationship context
Both Radian and Microradian are converted by fixed multiples of the radian. Multiplying by (rad per rad) ÷ (rad per urad) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Radian (rad) | Microradian (urad) |
|---|---|
| 0.1 | 100,000 |
| 1 | 1,000,000 |
| 2 | 2,000,000 |
| 3 | 3,000,000 |
| 4 | 4,000,000 |
| 5 | 5,000,000 |
| 6 | 6,000,000 |
| 7 | 7,000,000 |
| 8 | 8,000,000 |
| 9 | 9,000,000 |
| Radian (rad) | Microradian (urad) |
|---|---|
| 10 | 10,000,000 |
| 20 | 20,000,000 |
| 30 | 30,000,000 |
| 40 | 40,000,000 |
| 50 | 50,000,000 |
| 60 | 60,000,000 |
| 70 | 70,000,000 |
| 80 | 80,000,000 |
| 90 | 90,000,000 |
| 100 | 100,000,000 |