″ to gon — convert arcseconds to gradians
Exact 1 ÷ 3,240 = 0.000308641975
1 arcsecond in other units
| Degrees | 0.000277777778 | ° |
|---|---|---|
| Radians | 0.000004848137 | rad |
| Milliradians | 0.004848136811 | mrad |
| Gradians | 0.000308641975 | gon |
| Arcminutes | 0.01666667 | ′ |
| Turns | 7.716e-7 | turn |
″ to gon at a glance
| Arcseconds | Gradians |
|---|---|
| 1 ″ | 0.000308641975 gon |
| 2 ″ | 0.000617283951 gon |
| 3 ″ | 0.000925925926 gon |
| 5 ″ | 0.001543209877 gon |
| 10 ″ | 0.003086419753 gon |
| 20 ″ | 0.006172839506 gon |
| 25 ″ | 0.007716049383 gon |
| 50 ″ | 0.0154321 gon |
| 100 ″ | 0.0308642 gon |
| 250 ″ | 0.07716049 gon |
| 500 ″ | 0.15432099 gon |
| 1,000 ″ | 0.30864198 gon |
How to convert arcseconds to gradians
Multiply by 0.000308641975 — one arcsecond is 0.000308641975 gradians. That factor is exact: it comes from the definition of the units rather than from a measurement, so it will not change and does not need rounding.
Working 1 ÷ 3,240 = 0.000308641975
What these units are
The arcsecond and the gradian are covered in the angle unit guide, along with every other unit on this page.
Questions
How many gradians are in a arcsecond?
One arcsecond is 0.000308641975 gradians. This figure is exact — it comes from the definition of the unit, not a measurement.
What is 1 arcsecond in gradians?
1 arcsecond is 0.000308641975 gradians. The working is 1 ÷ 3,240 = 0.000308641975.
How many degrees is one radian?
About 57.3°, or exactly 180/π. A radian is the angle you get when the arc along a circle is as long as its radius, which is why the number is awkward: it comes from the geometry rather than from someone choosing a round figure.
Why does maths use radians instead of degrees?
Because the calculus only comes out clean in radians. The derivative of sine is cosine only when the angle is in radians; in degrees a factor of π/180 turns up everywhere. Degrees are a human convention, radians are the circle's own unit.
Why 360 degrees in a circle?
Babylonian arithmetic, most likely, and it stuck because 360 divides so willingly — by 2, 3, 4, 5, 6, 8, 9, 10, 12 and more. Halves, thirds and quarters of a circle all land on whole numbers, which is more than can be said for 100.
What is a gradian for?
It is the metric attempt at angle: 100 gradians in a right angle, 400 in a full circle. It never displaced the degree in general use but survives in surveying in parts of Europe, and most scientific calculators still have a GRAD mode next to DEG and RAD.