Spurred by a mnemonic game while hiking in both fog and mountains, I am now trying to memorize GPS coordinates. But just how many of those little digits must I keep in my head? How big is a degree of longitude anyway?

Naively, we can divide the 40 megameter earth circumference by 360° and divide again by 60′ minutes and maybe 60″ again for seconds. And for latitude, that’s pretty damn close, about 15 cm short of a nautical mile. But like most spinning objects, the Earth is a little fat around the middle and not wrinkle-free, which throws a wrench in our trigonometry.

One latitudinal minute is 1842m on the equator, 1862 meters at the poles, with an average of 1852m defining a nautical mile, or roughly 111 km per degree. However, longitudinal lengths vary greatly as a trigonometric function of degrees from the equator, simplified as:

degree longitude = 111km * cos(latitude)

Using a bit more sophisticated equations, I’ve plotted a few longitudinal lengths (error < 1%):

So, in Nuuk (64° North), a degree latitude is more than twice the length of one degree longitude (about 1858m vs. 815m per minute) and almost ten to one at 86°.

Putting a box around Nuuk, the downtown southwest corner is N 64°09.7 W 51°45.2 and the northeast corner (north of the airport and west of Qinngorput 2010) is roughly N 64°12 W 51°40. One significant decimal seems appropriate downtown for an order of 100m precision, while 1km precision should be good enough for finding an airport – on foot at least. Three significant decimals is more precise than GPS provides as of 2010.