Gradian to Arc Minute Converter
Angle · unit-converter
Convert Gradian 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 Gradian
Gradians (gon) divide a right angle into 100 parts; 400 gradians make a full turn. Used in some surveying and European contexts.
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 gradians to arc minutes
1 gradian equals 54.00000000000001 arc minute in this tool (via radian):
1 grad = (0.015707963267948967 rad ÷ 0.0002908882086657216 rad) arcmin = 54.00000000000001 arcmin
Each gradian carries 0.015707963267948967 rad and each arc minute 0.0002908882086657216 rad, so one grad equals 0.015707963267948967 ÷ 0.0002908882086657216 arcmin.
Let θ(grad) be the angle in Gradian (grad), and θ(arcmin) in Arc Minute (arcmin). Then:
θ(arcmin) = θ(grad) × (0.015707963267948967 / 0.0002908882086657216)
Equivalently, divide by how many grad fit into one arcmin (rad per arcmin divided by rad per grad):
θ(arcmin) = θ(grad) ÷ 0.018518518518518517
Examples
Example #1: Convert 1 grad to arc minute
1 grad = 1 grad × (0.015707963267948967/0.0002908882086657216) arcmin = 54 arcmin
1 grad = 1 grad ÷ 0.018518518518518517 = 54 arcmin
1 grad × (0.015707963267948967/0.0002908882086657216) = 54.000000 arcmin
Example #2: Convert 10 grad to arc minute
10 grad = 10 grad × (0.015707963267948967/0.0002908882086657216) arcmin = 540 arcmin
10 grad = 10 grad ÷ 0.018518518518518517 = 540 arcmin
10 grad × (0.015707963267948967/0.0002908882086657216) = 540.000000 arcmin
Summary
To convert Gradian to Arc Minute, multiply the value in grad by (0.015707963267948967 rad per grad) / (0.0002908882086657216 rad per arcmin). Equivalently: value_arcmin = value_grad × (0.015707963267948967 / 0.0002908882086657216). Numerically, 1 grad equals 54.00000000000001 arcmin.
Relationship context
Both Gradian and Arc Minute are converted by fixed multiples of the radian. Multiplying by (rad per grad) ÷ (rad per arcmin) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Gradian (grad) | Arc Minute (arcmin) |
|---|---|
| 0.1 | 5.4 |
| 1 | 54 |
| 2 | 108 |
| 3 | 162 |
| 4 | 216 |
| 5 | 270 |
| 6 | 324 |
| 7 | 378 |
| 8 | 432 |
| 9 | 486 |
| Gradian (grad) | Arc Minute (arcmin) |
|---|---|
| 10 | 540 |
| 20 | 1,080 |
| 30 | 1,620 |
| 40 | 2,160 |
| 50 | 2,700 |
| 60 | 3,240 |
| 70 | 3,780 |
| 80 | 4,320 |
| 90 | 4,860 |
| 100 | 5,400 |