Milliradian to Arc Minute Converter
Angle · unit-converter
Convert Milliradian to Arc Minute 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 Arc Minute
An arc minute is 1/60 of a degree (π/10,800 rad). Used in astronomy, navigation, and precision optics (MOA).
How to convert milliradians to arc minutes
1 milliradian equals 3.4377467707849396 arc minute in this tool (via radian):
1 mrad = (0.001 rad ÷ 0.0002908882086657216 rad) arcmin = 3.4377467707849396 arcmin
Each milliradian carries 0.001 rad and each arc minute 0.0002908882086657216 rad, so one mrad equals 0.001 ÷ 0.0002908882086657216 arcmin.
Let θ(mrad) be the angle in Milliradian (mrad), and θ(arcmin) in Arc Minute (arcmin). Then:
θ(arcmin) = θ(mrad) × (0.001 / 0.0002908882086657216)
Equivalently, divide by how many mrad fit into one arcmin (rad per arcmin divided by rad per mrad):
θ(arcmin) = θ(mrad) ÷ 0.29088820866572157
Examples
Example #1: Convert 1 mrad to arc minute
1 mrad = 1 mrad × (0.001/0.0002908882086657216) arcmin = 3.4377467708 arcmin
1 mrad = 1 mrad ÷ 0.29088820866572157 = 3.4377467708 arcmin
1 mrad × (0.001/0.0002908882086657216) = 3.437747 arcmin
Example #2: Convert 10 mrad to arc minute
10 mrad = 10 mrad × (0.001/0.0002908882086657216) arcmin = 34.3774677078 arcmin
10 mrad = 10 mrad ÷ 0.29088820866572157 = 34.3774677078 arcmin
10 mrad × (0.001/0.0002908882086657216) = 34.377468 arcmin
Summary
To convert Milliradian to Arc Minute, multiply the value in mrad by (0.001 rad per mrad) / (0.0002908882086657216 rad per arcmin). Equivalently: value_arcmin = value_mrad × (0.001 / 0.0002908882086657216). Numerically, 1 mrad equals 3.4377467707849396 arcmin.
Relationship context
Both Milliradian and Arc Minute are converted by fixed multiples of the radian. Multiplying by (rad per mrad) ÷ (rad per arcmin) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Milliradian (mrad) | Arc Minute (arcmin) |
|---|---|
| 0.1 | 0.3437746771 |
| 1 | 3.4377467708 |
| 2 | 6.8754935416 |
| 3 | 10.3132403124 |
| 4 | 13.7509870831 |
| 5 | 17.1887338539 |
| 6 | 20.6264806247 |
| 7 | 24.0642273955 |
| 8 | 27.5019741663 |
| 9 | 30.9397209371 |
| Milliradian (mrad) | Arc Minute (arcmin) |
|---|---|
| 10 | 34.3774677078 |
| 20 | 68.7549354157 |
| 30 | 103.132403124 |
| 40 | 137.509870831 |
| 50 | 171.887338539 |
| 60 | 206.264806247 |
| 70 | 240.642273955 |
| 80 | 275.019741663 |
| 90 | 309.397209371 |
| 100 | 343.774677078 |