Revolution to Milliradian Converter
Angle · unit-converter
Convert Revolution to Milliradian 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 Revolution
One revolution (turn) is a full circle: 2π radians or 360°. Used in rotation rates, motors, and astronomy (e.g. revolutions per minute).
About Milliradian
A milliradian is 1/1000 radian. Used in ballistics, long-range shooting, and engineering for small angles.
How to convert revolutions to milliradians
1 revolution equals 6283.185307179586 milliradian in this tool (via radian):
1 turn = (6.283185307179586 rad ÷ 0.001 rad) mrad = 6283.185307179586 mrad
Each revolution carries 6.283185307179586 rad and each milliradian 0.001 rad, so one turn equals 6.283185307179586 ÷ 0.001 mrad.
Let θ(turn) be the angle in Revolution (turn), and θ(mrad) in Milliradian (mrad). Then:
θ(mrad) = θ(turn) × (6.283185307179586 / 0.001)
Equivalently, divide by how many turn fit into one mrad (rad per mrad divided by rad per turn):
θ(mrad) = θ(turn) ÷ 0.00015915494309189535
Examples
Example #1: Convert 1 turn to milliradian
1 turn = 1 turn × (6.283185307179586/0.001) mrad = 6283.18530718 mrad
1 turn = 1 turn ÷ 0.00015915494309189535 = 6283.18530718 mrad
1 turn × (6.283185307179586/0.001) = 6,283.185307 mrad
Example #2: Convert 10 turn to milliradian
10 turn = 10 turn × (6.283185307179586/0.001) mrad = 62831.8530718 mrad
10 turn = 10 turn ÷ 0.00015915494309189535 = 62831.8530718 mrad
10 turn × (6.283185307179586/0.001) = 62,831.853072 mrad
Summary
To convert Revolution to Milliradian, multiply the value in turn by (6.283185307179586 rad per turn) / (0.001 rad per mrad). Equivalently: value_mrad = value_turn × (6.283185307179586 / 0.001). Numerically, 1 turn equals 6283.185307179586 mrad.
Relationship context
Both Revolution and Milliradian are converted by fixed multiples of the radian. Multiplying by (rad per turn) ÷ (rad per mrad) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Revolution (turn) | Milliradian (mrad) |
|---|---|
| 0.1 | 628.318530718 |
| 1 | 6,283.18530718 |
| 2 | 12,566.3706144 |
| 3 | 18,849.5559215 |
| 4 | 25,132.7412287 |
| 5 | 31,415.9265359 |
| 6 | 37,699.1118431 |
| 7 | 43,982.2971503 |
| 8 | 50,265.4824574 |
| 9 | 56,548.6677646 |
| Revolution (turn) | Milliradian (mrad) |
|---|---|
| 10 | 62,831.8530718 |
| 20 | 125,663.706144 |
| 30 | 188,495.559215 |
| 40 | 251,327.412287 |
| 50 | 314,159.265359 |
| 60 | 376,991.118431 |
| 70 | 439,822.971503 |
| 80 | 502,654.824574 |
| 90 | 565,486.6776460001 |
| 100 | 628,318.530718 |