Milliradian to Revolution Converter
Angle · unit-converter
Convert Milliradian 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 Milliradian
A milliradian is 1/1000 radian. Used in ballistics, long-range shooting, and engineering for small angles.
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 milliradians to revolutions
1 milliradian equals 0.00015915494309189535 revolution in this tool (via radian):
1 mrad = (0.001 rad ÷ 6.283185307179586 rad) turn = 0.00015915494309189535 turn
Each milliradian carries 0.001 rad and each revolution 6.283185307179586 rad, so one mrad equals 0.001 ÷ 6.283185307179586 turn.
Let θ(mrad) be the angle in Milliradian (mrad), and θ(turn) in Revolution (turn). Then:
θ(turn) = θ(mrad) × (0.001 / 6.283185307179586)
Equivalently, divide by how many mrad fit into one turn (rad per turn divided by rad per mrad):
θ(turn) = θ(mrad) ÷ 6283.185307179586
Examples
Example #1: Convert 1 mrad to revolution
1 mrad = 1 mrad × (0.001/6.283185307179586) turn = 0.0001591549 turn
1 mrad = 1 mrad ÷ 6283.185307179586 = 0.0001591549 turn
1 mrad × (0.001/6.283185307179586) = 0.000159 turn
Example #2: Convert 10 mrad to revolution
10 mrad = 10 mrad × (0.001/6.283185307179586) turn = 0.0015915494 turn
10 mrad = 10 mrad ÷ 6283.185307179586 = 0.0015915494 turn
10 mrad × (0.001/6.283185307179586) = 0.001592 turn
Summary
To convert Milliradian to Revolution, multiply the value in mrad by (0.001 rad per mrad) / (6.283185307179586 rad per turn). Equivalently: value_turn = value_mrad × (0.001 / 6.283185307179586). Numerically, 1 mrad equals 0.00015915494309189535 turn.
Relationship context
Both Milliradian and Revolution are converted by fixed multiples of the radian. Multiplying by (rad per mrad) ÷ (rad per turn) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Milliradian (mrad) | Revolution (turn) |
|---|---|
| 0.1 | 0.0000159155 |
| 1 | 0.0001591549 |
| 2 | 0.0003183099 |
| 3 | 0.0004774648 |
| 4 | 0.0006366198 |
| 5 | 0.0007957747 |
| 6 | 0.0009549297 |
| 7 | 0.0011140846 |
| 8 | 0.0012732395 |
| 9 | 0.0014323945 |
| Milliradian (mrad) | Revolution (turn) |
|---|---|
| 10 | 0.0015915494 |
| 20 | 0.0031830989 |
| 30 | 0.0047746483 |
| 40 | 0.0063661977 |
| 50 | 0.0079577472 |
| 60 | 0.0095492966 |
| 70 | 0.011140846 |
| 80 | 0.0127323954 |
| 90 | 0.0143239449 |
| 100 | 0.0159154943 |