Gradians to Arcminutes (grad to ′)
1 gradian equals 54 arcminutes exactly.
How to convert gradians to arcminutes
To convert gradians to arcminutes, multiply the number of gradians by 54. This factor is exact. To go the other way, multiply arcminutes by 0.01851851852 (rounded).
arcminutes = gradians × 54
Example: 10 gradians = 540 arcminutes.
About these units
Gradian (grad)
One 400th of a full turn, so a right angle is exactly 100 gradians. Used in surveying in parts of Europe, also called the gon.
The gradian came out of the French Revolution as part of the push to make measurement rational. It was first called the grade, and it divides the right angle into 100 parts, so a full turn is 400 grads and one grad is 0.9 degree. In northern Europe the word grad already meant an ordinary degree, which caused confusion, so the name gon was adopted, first regionally and later internationally. Gon is the symbol given in ISO 31-1, Annex B.
The link to the meter explains the appeal. The meter was originally set at one ten-millionth of a quarter of Earth's meridian, so one gon of arc along the surface spans about 100 kilometers and one centigon about 1 kilometer. Surveyors, mainly in Europe, still use it, along with some mining and geology work, and it is legally recognized in the European Union and Switzerland. It is not part of the SI, and the SI Brochure does not mention it. Many scientific calculators of the 1970s through the 1990s offered a gon mode, though some recent models have dropped it.
1 gradian = 0.0025 turns (exactly).
Sources: Wikipedia: Gradian; NIST Guide to the SI, Appendix B.8 (angle conversion factors); MDN Web Docs: CSS <angle>
Arcminute (′)
One sixtieth of a degree. Used in navigation, astronomy and rifle sighting (minute of angle).
An arcminute is a sixtieth of a degree, which makes it 1/21,600 of a turn or about 0.29 milliradian. The SI Brochure lists it among widely used non-SI units, equal to π/10,800 radian. The units come from Babylonian astronomy and its habit of splitting the degree into 60 parts.
It is a handy size for everyday precision. One arcminute of latitude is roughly one nautical mile, and navigation often writes positions in degrees and decimal minutes. Someone with 20/20 vision can just resolve details about an arcminute apart. The Sun and the Moon each measure around 30 to 32 arcminutes across. Property surveyors use degrees, minutes, and seconds in metes-and-bounds boundary descriptions. Shooters call the unit minute of angle, or MOA, where 1 MOA covers about 1.047 inches at 100 yards.
1 arcminute = 0.0000462962963 turns (approximately).
Sources: BIPM SI Brochure, 9th edition (2019); Wikipedia: Minute and second of arc; Wikipedia: Angular diameter
Related conversions
- Arcminutes to gradians (reverse)
- Gradians to degrees
- Gradians to radians
- Gradians to turns
- Gradians to arcseconds
- Degrees to arcminutes
- Radians to arcminutes
- Turns to arcminutes
- Arcseconds to arcminutes
See all angle units.