Arcseconds to Gradians
An instant arcseconds-to-gradians converter, with the formula and a reference table below.
| Arcseconds | Gradians |
|---|---|
| 1 ″ | 0.000309 grad |
| 2 ″ | 0.000617 grad |
| 3 ″ | 0.000926 grad |
| 5 ″ | 0.001543 grad |
| 10 ″ | 0.003086 grad |
| 25 ″ | 0.007716 grad |
| 50 ″ | 0.015432 grad |
| 100 ″ | 0.030864 grad |
How to use
- Enter a value in the Arcseconds field.
- The Gradians figure appears immediately — no button to press.
- Typing in the Gradians field converts back to Arcseconds the same way.
- Use the reference table for the values that come up most often.
Arcseconds to Gradians formula
The factor from arcseconds to gradians is 0.000308641975.
grad = ″ × 0.000308641975
Put another way, one arcsecond is exactly 1/3,240 of a gradian.
Why this factor: the arcsecond and the gradian are both defined against the degree, so dividing one definition by the other gives 0.000308641975 directly. Both definitions are set out in full below.
To go the other way, divide by 0.000308641975 — or use the Gradians to Arcseconds converter, which is the same calculation reversed.
Worked example
Take 30 ″ and multiply by the factor 0.000308641975: the result is 0.009259 grad.
30 ″ × 0.000308641975 = 0.009259 grad
The converter above does this for any value you type, in either direction.
What is an arcsecond?
An arcsecond is one 3,600th of a degree — the precision unit of astronomy.
Definition: Exactly 1/3600 degree, or 1/60 arcminute. Symbol is the double prime (″).
Where it is used: Telescope resolution and seeing, stellar parallax (the basis of the parsec), and precision surveying.
What is a gradian?
A gradian, or gon, divides a right angle into 100 parts instead of 90.
Definition: A full turn is 400 gradians, so one gradian is exactly 0.9 degree.
Where it is used: European surveying and civil engineering, and still a mode on most scientific calculators.
Arcseconds vs Gradians
The arcsecond and the gradian belong to the same family of units, so converting between them is usually a matter of shifting a decimal point or applying a small whole-number factor.
Frequently asked questions
How many gradians are in an arcsecond?
One arcsecond equals 0.000308641975 gradians.
What is the formula to convert arcseconds to gradians?
Multiply the number of arcseconds by 0.000308641975. To reverse it, divide by 0.000308641975 instead.
How do I convert gradians back to arcseconds?
Divide by 0.000308641975, which is the same as multiplying by 3240.
How many gradians are in 10 arcseconds?
10 ″ works out to 0.003086 grad.
How is the arcsecond defined?
Exactly 1/3600 degree, or 1/60 arcminute. Symbol is the double prime (″).