Second to Grad (Gon)

One arcsecond of latitude corresponds to roughly 31 meters (about 101 feet) on the ground. This is why high-precision GPS coordinates are quoted to fractions of arcseconds — a shift of just 0.01″ means about 30 cm. Longitude arcseconds cover less ground as you move toward the poles because the meridians converge; at 45° latitude, one arcsecond of longitude spans about 22 meters.

Stellar parallax is the tiny apparent shift of a nearby star against distant background stars as Earth orbits the Sun. Even the closest star, Proxima Centauri, shifts by only 0.768 arcseconds over six months — far too small for the naked eye. The parsec (parallax-arcsecond) is defined as the distance at which a star would show exactly 1″ of parallax. No star is close enough to reach that threshold, which gives you a sense of how mind-bogglingly far away even our nearest neighbors are.

Hubble resolves details down to about 0.05 arcseconds — roughly the angular size of a coin seen from 80 km away. At that resolution it can distinguish individual stars in nearby galaxies, spot the discs of Pluto and large asteroids, and detect gravitational lensing arcs. Ground-based telescopes are blurred to about 0.5–1″ by atmospheric turbulence unless they use adaptive optics, which is why space telescopes remain essential for sharp imaging.

Arcseconds per pixel is the standard metric for imaging sensors in astronomy because it directly links detector geometry to sky coverage. A telescope with 0.3″/pixel resolution can separate objects that close together on the sky. Photographers encounter this too — the resolving power of any long telephoto lens is ultimately limited by atmospheric seeing (typically 1–2″), which is why even a perfect 600 mm lens produces soft images of distant objects on a hazy day.

The average human eye resolves about 60 arcseconds (1 arcminute) under good conditions, though some people with exceptional vision reach 30″. This is why the standard eye test chart (Snellen chart) defines 20/20 vision as the ability to resolve details that subtend 1 arcminute. For comparison, Jupiter at its brightest subtends about 50″, just below that threshold — which is why it looks like a bright dot to the naked eye, not a disc.

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.