Microradian to Revolution Converter
Angle · unit-converter
Convert Microradian to Revolution 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 Revolution
One revolution (turn) is a full circle: 2π radians or 360°. Used in rotation rates, motors, and astronomy (e.g. revolutions per minute).
How to convert microradians to revolutions
1 microradian equals 1.5915494309189532e-7 revolution in this tool (via radian):
1 urad = (0.000001 rad ÷ 6.283185307179586 rad) turn = 1.5915494309189532e-7 turn
Each microradian carries 0.000001 rad and each revolution 6.283185307179586 rad, so one urad equals 0.000001 ÷ 6.283185307179586 turn.
Let θ(urad) be the angle in Microradian (urad), and θ(turn) in Revolution (turn). Then:
θ(turn) = θ(urad) × (0.000001 / 6.283185307179586)
Equivalently, divide by how many urad fit into one turn (rad per turn divided by rad per urad):
θ(turn) = θ(urad) ÷ 6283185.307179587
Examples
Example #1: Convert 1 urad to revolution
1 urad = 1 urad × (0.000001/6.283185307179586) turn = 0.0000001592 turn
1 urad = 1 urad ÷ 6283185.307179587 = 0.0000001592 turn
1 urad × (0.000001/6.283185307179586) = 0.000000 turn
Example #2: Convert 10 urad to revolution
10 urad = 10 urad × (0.000001/6.283185307179586) turn = 0.0000015915 turn
10 urad = 10 urad ÷ 6283185.307179587 = 0.0000015915 turn
10 urad × (0.000001/6.283185307179586) = 0.000002 turn
Summary
To convert Microradian to Revolution, multiply the value in urad by (0.000001 rad per urad) / (6.283185307179586 rad per turn). Equivalently: value_turn = value_urad × (0.000001 / 6.283185307179586). Numerically, 1 urad equals 1.5915494309189532e-7 turn.
Relationship context
Both Microradian and Revolution are converted by fixed multiples of the radian. Multiplying by (rad per urad) ÷ (rad per turn) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Microradian (urad) | Revolution (turn) |
|---|---|
| 0.1 | 0.0000000159 |
| 1 | 0.0000001592 |
| 2 | 0.0000003183 |
| 3 | 0.0000004775 |
| 4 | 0.0000006366 |
| 5 | 0.0000007958 |
| 6 | 0.0000009549 |
| 7 | 0.0000011141 |
| 8 | 0.0000012732 |
| 9 | 0.0000014324 |
| Microradian (urad) | Revolution (turn) |
|---|---|
| 10 | 0.0000015915 |
| 20 | 0.0000031831 |
| 30 | 0.0000047746 |
| 40 | 0.0000063662 |
| 50 | 0.0000079577 |
| 60 | 0.0000095493 |
| 70 | 0.0000111408 |
| 80 | 0.0000127324 |
| 90 | 0.0000143239 |
| 100 | 0.0000159155 |