Arc Minute to Radian Converter
Angle · unit-converter
Convert Arc Minute 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 Arc Minute
An arc minute is 1/60 of a degree (π/10,800 rad). Used in astronomy, navigation, and precision optics (MOA).
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 arc minutes to radians
1 arc minute equals 0.0002908882086657216 radian in this tool (via radian):
1 arcmin = (0.0002908882086657216 rad ÷ 1 rad) rad = 0.0002908882086657216 rad
Each arc minute carries 0.0002908882086657216 rad and each radian 1 rad, so one arcmin equals 0.0002908882086657216 ÷ 1 rad.
Let θ(arcmin) be the angle in Arc Minute (arcmin), and θ(rad) in Radian (rad). Then:
θ(rad) = θ(arcmin) × (0.0002908882086657216 / 1)
Equivalently, divide by how many arcmin fit into one rad (rad per rad divided by rad per arcmin):
θ(rad) = θ(arcmin) ÷ 3437.7467707849396
Examples
Example #1: Convert 1 arcmin to radian
1 arcmin = 1 arcmin × (0.0002908882086657216/1) rad = 0.0002908882 rad
1 arcmin = 1 arcmin ÷ 3437.7467707849396 = 0.0002908882 rad
1 arcmin × (0.0002908882086657216/1) = 0.000291 rad
Example #2: Convert 10 arcmin to radian
10 arcmin = 10 arcmin × (0.0002908882086657216/1) rad = 0.0029088821 rad
10 arcmin = 10 arcmin ÷ 3437.7467707849396 = 0.0029088821 rad
10 arcmin × (0.0002908882086657216/1) = 0.002909 rad
Summary
To convert Arc Minute to Radian, multiply the value in arcmin by (0.0002908882086657216 rad per arcmin) / (1 rad per rad). Equivalently: value_rad = value_arcmin × (0.0002908882086657216 / 1). Numerically, 1 arcmin equals 0.0002908882086657216 rad.
Relationship context
Both Arc Minute and Radian are converted by fixed multiples of the radian. Multiplying by (rad per arcmin) ÷ (rad per rad) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Arc Minute (arcmin) | Radian (rad) |
|---|---|
| 0.1 | 0.0000290888 |
| 1 | 0.0002908882 |
| 2 | 0.0005817764 |
| 3 | 0.0008726646 |
| 4 | 0.0011635528 |
| 5 | 0.001454441 |
| 6 | 0.0017453293 |
| 7 | 0.0020362175 |
| 8 | 0.0023271057 |
| 9 | 0.0026179939 |
| Arc Minute (arcmin) | Radian (rad) |
|---|---|
| 10 | 0.0029088821 |
| 20 | 0.0058177642 |
| 30 | 0.0087266463 |
| 40 | 0.0116355283 |
| 50 | 0.0145444104 |
| 60 | 0.0174532925 |
| 70 | 0.0203621746 |
| 80 | 0.0232710567 |
| 90 | 0.0261799388 |
| 100 | 0.0290888209 |