Minute of Angle (MOA) to Gradian Converter
Angle · unit-converter
Convert Minute of Angle (MOA) 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 Minute of Angle (MOA)
Minute of angle (MOA) equals one arc minute (1/60 degree). It is widely used in firearms optics and precision aiming.
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 minutes of angle (moa) to gradians
1 minute of angle (moa) equals 0.018518518518518517 gradian in this tool (via radian):
1 moa = (0.0002908882086657216 rad ÷ 0.015707963267948967 rad) grad = 0.018518518518518517 grad
Each minute of angle (moa) carries 0.0002908882086657216 rad and each gradian 0.015707963267948967 rad, so one moa equals 0.0002908882086657216 ÷ 0.015707963267948967 grad.
Let θ(moa) be the angle in Minute of Angle (MOA) (moa), and θ(grad) in Gradian (grad). Then:
θ(grad) = θ(moa) × (0.0002908882086657216 / 0.015707963267948967)
Equivalently, divide by how many moa fit into one grad (rad per grad divided by rad per moa):
θ(grad) = θ(moa) ÷ 54.00000000000001
Examples
Example #1: Convert 1 moa to gradian
1 moa = 1 moa × (0.0002908882086657216/0.015707963267948967) grad = 0.0185185185 grad
1 moa = 1 moa ÷ 54.00000000000001 = 0.0185185185 grad
1 moa × (0.0002908882086657216/0.015707963267948967) = 0.018519 grad
Example #2: Convert 10 moa to gradian
10 moa = 10 moa × (0.0002908882086657216/0.015707963267948967) grad = 0.1851851852 grad
10 moa = 10 moa ÷ 54.00000000000001 = 0.1851851852 grad
10 moa × (0.0002908882086657216/0.015707963267948967) = 0.185185 grad
Summary
To convert Minute of Angle (MOA) to Gradian, multiply the value in moa by (0.0002908882086657216 rad per moa) / (0.015707963267948967 rad per grad). Equivalently: value_grad = value_moa × (0.0002908882086657216 / 0.015707963267948967). Numerically, 1 moa equals 0.018518518518518517 grad.
Relationship context
Both Minute of Angle (MOA) and Gradian are converted by fixed multiples of the radian. Multiplying by (rad per moa) ÷ (rad per grad) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Minute of Angle (MOA) (moa) | 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 |
| Minute of Angle (MOA) (moa) | 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 |