Arc Minute to Gradian Converter
Angle · unit-converter
Convert Arc Minute to Gradian 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 Gradian
Gradians (gon) divide a right angle into 100 parts; 400 gradians make a full turn. Used in some surveying and European contexts.
How to convert arc minutes to gradians
1 arc minute equals 0.018518518518518517 gradian in this tool (via radian):
1 arcmin = (0.0002908882086657216 rad ÷ 0.015707963267948967 rad) grad = 0.018518518518518517 grad
Each arc minute carries 0.0002908882086657216 rad and each gradian 0.015707963267948967 rad, so one arcmin equals 0.0002908882086657216 ÷ 0.015707963267948967 grad.
Let θ(arcmin) be the angle in Arc Minute (arcmin), and θ(grad) in Gradian (grad). Then:
θ(grad) = θ(arcmin) × (0.0002908882086657216 / 0.015707963267948967)
Equivalently, divide by how many arcmin fit into one grad (rad per grad divided by rad per arcmin):
θ(grad) = θ(arcmin) ÷ 54.00000000000001
Examples
Example #1: Convert 1 arcmin to gradian
1 arcmin = 1 arcmin × (0.0002908882086657216/0.015707963267948967) grad = 0.0185185185 grad
1 arcmin = 1 arcmin ÷ 54.00000000000001 = 0.0185185185 grad
1 arcmin × (0.0002908882086657216/0.015707963267948967) = 0.018519 grad
Example #2: Convert 10 arcmin to gradian
10 arcmin = 10 arcmin × (0.0002908882086657216/0.015707963267948967) grad = 0.1851851852 grad
10 arcmin = 10 arcmin ÷ 54.00000000000001 = 0.1851851852 grad
10 arcmin × (0.0002908882086657216/0.015707963267948967) = 0.185185 grad
Summary
To convert Arc Minute to Gradian, multiply the value in arcmin by (0.0002908882086657216 rad per arcmin) / (0.015707963267948967 rad per grad). Equivalently: value_grad = value_arcmin × (0.0002908882086657216 / 0.015707963267948967). Numerically, 1 arcmin equals 0.018518518518518517 grad.
Relationship context
Both Arc Minute and Gradian are converted by fixed multiples of the radian. Multiplying by (rad per arcmin) ÷ (rad per grad) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Arc Minute (arcmin) | Gradian (grad) |
|---|---|
| 0.1 | 0.0018518519 |
| 1 | 0.0185185185 |
| 2 | 0.037037037 |
| 3 | 0.0555555556 |
| 4 | 0.0740740741 |
| 5 | 0.0925925926 |
| 6 | 0.1111111111 |
| 7 | 0.1296296296 |
| 8 | 0.1481481481 |
| 9 | 0.1666666667 |
| Arc Minute (arcmin) | Gradian (grad) |
|---|---|
| 10 | 0.1851851852 |
| 20 | 0.3703703704 |
| 30 | 0.5555555556 |
| 40 | 0.7407407407 |
| 50 | 0.9259259259 |
| 60 | 1.1111111111 |
| 70 | 1.2962962963 |
| 80 | 1.4814814815 |
| 90 | 1.6666666667 |
| 100 | 1.8518518519 |