Arc Second to Gradian Converter
Angle · unit-converter
Convert Arc Second 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 Second
An arc second is 1/60 of an arc minute or 1/3600 of a degree. Common in astronomy and very fine angular resolution.
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 seconds to gradians
1 arc second equals 0.00030864197530864197 gradian in this tool (via radian):
1 arcsec = (0.00000484813681109536 rad ÷ 0.015707963267948967 rad) grad = 0.00030864197530864197 grad
Each arc second carries 0.00000484813681109536 rad and each gradian 0.015707963267948967 rad, so one arcsec equals 0.00000484813681109536 ÷ 0.015707963267948967 grad.
Let θ(arcsec) be the angle in Arc Second (arcsec), and θ(grad) in Gradian (grad). Then:
θ(grad) = θ(arcsec) × (0.00000484813681109536 / 0.015707963267948967)
Equivalently, divide by how many arcsec fit into one grad (rad per grad divided by rad per arcsec):
θ(grad) = θ(arcsec) ÷ 3240
Examples
Example #1: Convert 1 arcsec to gradian
1 arcsec = 1 arcsec × (0.00000484813681109536/0.015707963267948967) grad = 0.000308642 grad
1 arcsec = 1 arcsec ÷ 3240 = 0.000308642 grad
1 arcsec × (0.00000484813681109536/0.015707963267948967) = 0.000309 grad
Example #2: Convert 10 arcsec to gradian
10 arcsec = 10 arcsec × (0.00000484813681109536/0.015707963267948967) grad = 0.0030864198 grad
10 arcsec = 10 arcsec ÷ 3240 = 0.0030864198 grad
10 arcsec × (0.00000484813681109536/0.015707963267948967) = 0.003086 grad
Summary
To convert Arc Second to Gradian, multiply the value in arcsec by (0.00000484813681109536 rad per arcsec) / (0.015707963267948967 rad per grad). Equivalently: value_grad = value_arcsec × (0.00000484813681109536 / 0.015707963267948967). Numerically, 1 arcsec equals 0.00030864197530864197 grad.
Relationship context
Both Arc Second and Gradian are converted by fixed multiples of the radian. Multiplying by (rad per arcsec) ÷ (rad per grad) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Arc Second (arcsec) | Gradian (grad) |
|---|---|
| 0.1 | 0.0000308642 |
| 1 | 0.000308642 |
| 2 | 0.000617284 |
| 3 | 0.0009259259 |
| 4 | 0.0012345679 |
| 5 | 0.0015432099 |
| 6 | 0.0018518519 |
| 7 | 0.0021604938 |
| 8 | 0.0024691358 |
| 9 | 0.0027777778 |
| Arc Second (arcsec) | Gradian (grad) |
|---|---|
| 10 | 0.0030864198 |
| 20 | 0.0061728395 |
| 30 | 0.0092592593 |
| 40 | 0.012345679 |
| 50 | 0.0154320988 |
| 60 | 0.0185185185 |
| 70 | 0.0216049383 |
| 80 | 0.024691358 |
| 90 | 0.0277777778 |
| 100 | 0.0308641975 |