Convert Arcminutes to Gradians (′ to gon)
1 minute of arc (′) = 0.01851851852 gradians (gon). 1 gon = 54 ′. Example: 15 ′ = 15 × 0.01851851852 = 0.2777777778 gon.
Also searched as minutes of arc to gon, minutes of arc in gon, minutes of arc into gradians, ′ to gon, ′ in gradians, ′ into gradian, minute of arc to gradian, ′ to gradians converter and how many gradians in a minute of arc.
1 ′ = 0.01851851852 gon
Type in either box. Scientific notation works: 1.5e-3.
Converting a list? Use the bulk minute of arc to gradian converter to paste a column from Excel.
How to Convert Arcminute to Gradian
- 1 ′ = 0.01851851852 gon
- 1 gon = 54 ′
- Example: convert 15 ′ to gon: 15 ′ = 15 × 0.01851851852 gon = 0.2777777778 gon
Formula
gon = ′ × 0.01851851851852
or gon = ′ ÷ 54
Derivation from SI units:
- 1′ = (1/60)° = π/10 800 rad.
- 1 gon = π/200 rad; a right angle is 100 gon and a full turn 400 gon.
- 1 ′ = 0.0002908882086657 rad ÷ 0.01570796326795 rad per gon = 0.01851851851852 gon
Both units are defined exactly, so the factor is exact. Arcminute definition: minute of arc; Gradian definition: gradian.
Worked examples
- A reading of 15 ′ converts to 0.2777777778 gon.
15 ′ × 0.01851851852 = 0.2777777778 gon - A value of 45 ′ is 0.8333333333 gon.
45 ′ × 0.01851851852 = 0.8333333333 gon
Arcminute to Gradian conversion table
| Arcminutes (′) | Gradians (gon) |
|---|---|
| 1 ′ | 0.01851851852 gon |
| 5 ′ | 0.09259259259 gon |
| 10 ′ | 0.1851851852 gon |
| 15 ′ | 0.2777777778 gon |
| 20 ′ | 0.3703703704 gon |
| 30 ′ | 0.5555555556 gon |
| 45 ′ | 0.8333333333 gon |
| 60 ′ | 1.111111111 gon |
| 90 ′ | 1.666666667 gon |
| 120 ′ | 2.222222222 gon |
Where it's used
Arcminutes are used for latitude and longitude (degrees, minutes, seconds), while gradians appear in land surveying in Europe. Both measure plane angle, so the conversion is a fixed factor.
Arcminute to other angle units
| Conversion | 1 ′ equals |
|---|---|
| minute of arc to gradian | 0.01851851852 gon |
| minute of arc to radian | 0.0002908882087 rad |
| minute of arc to degree | 0.01666666667 ° |
| minute of arc to revolution | 0.0000462962963 rev |
| minute of arc to second of arc | 60 ″ |
Frequently asked questions
How many gradians are in 1 minute of arc?
1 ′ = 0.01851851852 gon.
How do I convert minutes of arc to gradians?
Multiply the value in ′ by 0.01851851852, or divide it by 54. For example, 15 ′ × 0.01851851852 = 0.2777777778 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 Arcminutes to Gradians (′ to gon). Retrieved October 25, 2026, from https://scientificconverters.com/angle/arcminutes-to-gradians/
IEEE
Scientific Converters, "Convert Arcminutes to Gradians (′ to gon)," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/angle/arcminutes-to-gradians/