Microradian to Radian Converter
Angle · unit-converter
Convert Microradian 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 Microradian
A microradian is 1/1,000,000 radian. It is used for very small angular deviations in optics and precision metrology.
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 microradians to radians
1 microradian equals 0.000001 radian in this tool (via radian):
1 urad = (0.000001 rad ÷ 1 rad) rad = 0.000001 rad
Each microradian carries 0.000001 rad and each radian 1 rad, so one urad equals 0.000001 ÷ 1 rad.
Let θ(urad) be the angle in Microradian (urad), and θ(rad) in Radian (rad). Then:
θ(rad) = θ(urad) × (0.000001 / 1)
Equivalently, divide by how many urad fit into one rad (rad per rad divided by rad per urad):
θ(rad) = θ(urad) ÷ 1000000
Examples
Example #1: Convert 1 urad to radian
1 urad = 1 urad × (0.000001/1) rad = 0.000001 rad
1 urad = 1 urad ÷ 1000000 = 0.000001 rad
1 urad × (0.000001/1) = 0.000001 rad
Example #2: Convert 10 urad to radian
10 urad = 10 urad × (0.000001/1) rad = 0.00001 rad
10 urad = 10 urad ÷ 1000000 = 0.00001 rad
10 urad × (0.000001/1) = 0.000010 rad
Summary
To convert Microradian to Radian, multiply the value in urad by (0.000001 rad per urad) / (1 rad per rad). Equivalently: value_rad = value_urad × (0.000001 / 1). Numerically, 1 urad equals 0.000001 rad.
Relationship context
Both Microradian and Radian are converted by fixed multiples of the radian. Multiplying by (rad per urad) ÷ (rad per rad) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Microradian (urad) | Radian (rad) |
|---|---|
| 0.1 | 0.0000001 |
| 1 | 0.000001 |
| 2 | 0.000002 |
| 3 | 0.000003 |
| 4 | 0.000004 |
| 5 | 0.000005 |
| 6 | 0.000006 |
| 7 | 0.000007 |
| 8 | 0.000008 |
| 9 | 0.000009 |
| Microradian (urad) | Radian (rad) |
|---|---|
| 10 | 0.00001 |
| 20 | 0.00002 |
| 30 | 0.00003 |
| 40 | 0.00004 |
| 50 | 0.00005 |
| 60 | 0.00006 |
| 70 | 0.00007 |
| 80 | 0.00008 |
| 90 | 0.00009 |
| 100 | 0.0001 |