Minute to Grad (Gon)

One arcminute of latitude was a convenient natural standard for sailors because it could be derived directly from celestial observations with a sextant. Measuring the Sun's altitude to the nearest arcminute and looking up the result in a table gave you your latitude to within one nautical mile — no sophisticated instruments needed. The modern nautical mile (1,852 m) is a standardized approximation of this relationship, and it still underpins all maritime and aviation distance calculations worldwide.

MOA stands for Minute of Angle. One MOA subtends about 29.1 mm (roughly 1.047 inches) at 100 meters, which conveniently rounds to "one inch at a hundred yards" for American shooters. Rifle scope turrets are typically calibrated in ¼ MOA clicks, so four clicks shift the point of impact about one inch at 100 yards. Competitive shooters obsess over MOA because a rifle that groups within 1 MOA is considered accurate enough for serious target work.

Divide arcminutes by 60 to get decimal degrees. So 30 arcminutes is 0.5°, and 7.5 arcminutes is 0.125°. Going the other way, multiply decimal degrees by 60. A GPS coordinate of 51.5074° means 51° plus 0.5074 × 60 = 30.444 arcminutes, or 51°30′26.6″. Most mapping software handles this conversion internally, but knowing it matters when reading older nautical charts or surveying records that use degrees-minutes-seconds notation.

The full Moon spans about 31 arcminutes (roughly half a degree). That means one arcminute on the lunar face corresponds to about 56 km of actual surface. The largest crater visible to the naked eye, Tycho, spans approximately 1.5 arcminutes. This is right at the edge of human visual resolution, which is why you can just barely make out the major dark maria (the "seas") but not individual craters without binoculars.

It really is a coincidence. The Sun is about 400 times the diameter of the Moon, but it also happens to be roughly 400 times farther away — so both subtend almost exactly 30 arcminutes (half a degree) as seen from Earth. This near-perfect match is what makes total solar eclipses possible, with the Moon barely covering the solar disc while leaving the spectacular corona visible. It won't last: the Moon recedes about 3.8 cm per year, so in roughly 600 million years total eclipses will no longer occur.

The revolutionaries wanted to decimalize everything — length (meter), mass (kilogram), time (decimal hours), and angle. The gradian divided a right angle into exactly 100 parts, making it compatible with the new metric system and decimal arithmetic. A slope of 1% grade corresponds neatly to gradian-based calculations. Decimal time flopped within a year, the Republican Calendar lasted 12 years, but the gradian quietly survived in surveying because it genuinely simplifies land measurement calculations.

They're all the same unit — 1/400 of a circle. "Gradian" is the international English term, "gon" is preferred in German-speaking countries and ISO standards, and "grade" is the original French name. The symbol varies too: grad, gon, or superscript g. This naming mess is partly why the unit never gained traction outside continental Europe — nobody could agree on what to call it.

Primarily in civil engineering and land surveying in France, Germany, Switzerland, and Scandinavia. Total stations (electronic surveying instruments) from Leica and other European manufacturers default to gon. Mining engineers in Germany use gon for underground surveys. French national mapping uses grades for geodetic calculations. If you buy a Leica total station in Europe, you may need to switch it from gon to degrees before using it elsewhere.

Calculator manufacturers include DEG, RAD, and GRAD modes because international standards (particularly IEC 60747) require it, and European civil engineering exams expect students to work in gradians. The mode exists for a real user base — it's just a user base concentrated in specific countries and professions. The most common calculator accident in the world is probably getting wrong trig answers because the calculator was accidentally left in GRAD mode after someone else used it.

Multiply gradians by 0.9 to get degrees, or multiply degrees by 10/9 to get gradians. A right angle is 100 grad = 90°. The conversion factor is 9/10 because 400/360 = 10/9. This means 50 grad = 45°, 200 grad = 180°, and 300 grad = 270°. The relationship is simple enough to do in your head, which is one of the few nice things about having two competing angular systems.