Convert Arcseconds to Gradians (″ to gon)
1 second of arc (″) = 0.0003086419753 gradians (gon). 1 gon = 3240 ″. Example: 15 ″ = 15 × 0.0003086419753 = 0.00462962963 gon.
Also searched as seconds of arc to gon, seconds of arc in gon, seconds of arc into gradians, ″ to gon, ″ in gradians, ″ into gradian, second of arc to gradian, ″ to gradians converter and how many gradians in a second of arc.
1 ″ = 0.0003086419753 gon
Type in either box. Scientific notation works: 1.5e-3.
Converting a list? Use the bulk second of arc to gradian converter to paste a column from Excel.
How to Convert Arcsecond to Gradian
- 1 ″ = 0.0003086419753 gon
- 1 gon = 3240 ″
- Example: convert 15 ″ to gon: 15 ″ = 15 × 0.0003086419753 gon = 0.00462962963 gon
Formula
gon = ″ × 0.0003086419753086
or gon = ″ ÷ 3240
Derivation from SI units:
- 1″ = (1/3600)° = π/648 000 rad.
- 1 gon = π/200 rad; a right angle is 100 gon and a full turn 400 gon.
- 1 ″ = 0.000004848136811095 rad ÷ 0.01570796326795 rad per gon = 0.0003086419753086 gon
Both units are defined exactly, so the factor is exact. Arcsecond definition: second of arc; Gradian definition: gradian.
Worked examples
- A reading of 15 ″ converts to 0.00462962963 gon.
15 ″ × 0.0003086419753 = 0.00462962963 gon - A value of 60 ″ is 0.01851851852 gon.
60 ″ × 0.0003086419753 = 0.01851851852 gon
Arcsecond to Gradian conversion table
| Arcseconds (″) | Gradians (gon) |
|---|---|
| 1 ″ | 0.0003086419753 gon |
| 5 ″ | 0.001543209877 gon |
| 10 ″ | 0.003086419753 gon |
| 15 ″ | 0.00462962963 gon |
| 30 ″ | 0.009259259259 gon |
| 36 ″ | 0.01111111111 gon |
| 60 ″ | 0.01851851852 gon |
| 100 ″ | 0.03086419753 gon |
| 1000 ″ | 0.3086419753 gon |
| 3600 ″ | 1.111111111 gon |
Where it's used
Arcseconds are used for astronomy (parallax, star positions), while gradians appear in land surveying in Europe. Both measure plane angle, so the conversion is a fixed factor.
Arcsecond to other angle units
| Conversion | 1 ″ equals |
|---|---|
| second of arc to gradian | 0.0003086419753 gon |
| second of arc to radian | 0.000004848136811 rad |
| second of arc to degree | 0.0002777777778 ° |
| second of arc to revolution | 7.716049383 × 10⁻⁷ rev |
| second of arc to minute of arc | 0.01666666667 ′ |
Frequently asked questions
How many gradians are in 1 second of arc?
1 ″ = 0.0003086419753 gon.
How do I convert seconds of arc to gradians?
Multiply the value in ″ by 0.0003086419753, or divide it by 3240. For example, 15 ″ × 0.0003086419753 = 0.00462962963 gon.
Is the ″ to gon conversion exact?
Yes. Both units are defined exactly, so the ratio is exact; its decimal form does not terminate and is shown here to 10 significant figures (more with the precision selector).
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures , Table 4 (radian) and Table 8 (non-SI units accepted for use with the SI).
- Guide for the Use of the International System of Units (SI), NIST Special Publication 811, 2008 Edition, National Institute of Standards and Technology , Appendix B.8, "grad".
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). Convert Arcseconds to Gradians (″ to gon). Retrieved October 25, 2026, from https://scientificconverters.com/angle/arcseconds-to-gradians/
IEEE
Scientific Converters, "Convert Arcseconds to Gradians (″ to gon)," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/angle/arcseconds-to-gradians/