Gradian to Arc Second Converter
Angle · unit-converter
Convert Gradian to Arc Second 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 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.
How to convert gradians to arc seconds
1 gradian equals 3240 arc second in this tool (via radian):
1 grad = (0.015707963267948967 rad ÷ 0.00000484813681109536 rad) arcsec = 3240 arcsec
Each gradian carries 0.015707963267948967 rad and each arc second 0.00000484813681109536 rad, so one grad equals 0.015707963267948967 ÷ 0.00000484813681109536 arcsec.
Let θ(grad) be the angle in Gradian (grad), and θ(arcsec) in Arc Second (arcsec). Then:
θ(arcsec) = θ(grad) × (0.015707963267948967 / 0.00000484813681109536)
Equivalently, divide by how many grad fit into one arcsec (rad per arcsec divided by rad per grad):
θ(arcsec) = θ(grad) ÷ 0.00030864197530864197
Examples
Example #1: Convert 1 grad to arc second
1 grad = 1 grad × (0.015707963267948967/0.00000484813681109536) arcsec = 3240 arcsec
1 grad = 1 grad ÷ 0.00030864197530864197 = 3240 arcsec
1 grad × (0.015707963267948967/0.00000484813681109536) = 3,240.000000 arcsec
Example #2: Convert 10 grad to arc second
10 grad = 10 grad × (0.015707963267948967/0.00000484813681109536) arcsec = 32400 arcsec
10 grad = 10 grad ÷ 0.00030864197530864197 = 32400 arcsec
10 grad × (0.015707963267948967/0.00000484813681109536) = 32,400.000000 arcsec
Summary
To convert Gradian to Arc Second, multiply the value in grad by (0.015707963267948967 rad per grad) / (0.00000484813681109536 rad per arcsec). Equivalently: value_arcsec = value_grad × (0.015707963267948967 / 0.00000484813681109536). Numerically, 1 grad equals 3240 arcsec.
Relationship context
Both Gradian and Arc Second are converted by fixed multiples of the radian. Multiplying by (rad per grad) ÷ (rad per arcsec) matches passing through radians, keeping degrees, gradians, arc minutes, NATO mils, and revolutions consistent on the hub.
Conversion tables
| Gradian (grad) | Arc Second (arcsec) |
|---|---|
| 0.1 | 324 |
| 1 | 3,240 |
| 2 | 6,480 |
| 3 | 9,720 |
| 4 | 12,960 |
| 5 | 16,200 |
| 6 | 19,440 |
| 7 | 22,680 |
| 8 | 25,920 |
| 9 | 29,160 |
| Gradian (grad) | Arc Second (arcsec) |
|---|---|
| 10 | 32,400 |
| 20 | 64,800 |
| 30 | 97,200 |
| 40 | 129,600 |
| 50 | 162,000 |
| 60 | 194,400 |
| 70 | 226,800 |
| 80 | 259,200 |
| 90 | 291,600 |
| 100 | 324,000 |