Conversational Latitude and Longitude

How to read those gobbledygook numbers on a GPS

Val Noronha | The Geography 80-20 collection


GPS reports position in latitude and longitude. Around the turn of the 21st century, several researchers thought non-professionals would never be able to fathom lat-long, and they proposed some improbable alternatives. One scheme expressed coordinates as alphabets, describing a place as GH8JK QFGSD for example. Another expressed locations relative to city centers: LAX146275. These schemes flopped. Ordinary people do seem to embrace lat-long. But it remains a bit mysterious. Perfect candidate for 80-20 treatment.

Here's the fairly formal definition: The latitude (φ) of a point is the angle it makes at the center of the earth with the equatorial plane. In the figure, the point we're talking about is the gold dot on the earth. Drive a (long) knitting needle through it, to the center of the earth (the red line), and the angle it makes with the equatorial plane is the latitude. You'll see why the equator has a latitude of zero, and the north pole 90°N.

The longitude (λ) of a point is the angle between its meridional plane and the plane of the prime meridian. The meridional plane of the point is the vertical face running through it, with its edge marked “Meridian.” The other (reference) face runs through Greenwich (and Spain and western Africa). You can measure the angle at the equator or at the relevant latitude, it's the same.

Points with the same latitude form a parallel — think about spinning the earth around while that red knitting needle is held firmly in place at an angle of φ. Points with the same longitude form a meridian — that's what you get when you drop the knitting needle to the equator, down to the south pole and all the way around.

Latitude and longitude are not simply at right angles to each other, the way x and y are on a graph. Parallels are horizontal, of different sizes, getting smaller towards the poles, centered at intervals along the axis. The circles do not meet each other. Meridians, the north-to-south circles, are all the same size, centered at the center of the earth; they all converge at the north and south poles.

Nonetheless, for many purposes you could think of lat-long as regular coordinates on normal graph paper, just expressed in reverse order. Latitude is y, it measures north-south distance; longitude is x, it measures east-west distance. (Purists may protest, but the fact is that our world is full of maps built around this simplification.) Confounding matters a little, west longitude is treated as negative, as is south latitude. But it's just regular square graph paper.

+ =
Parallels
Meridians
On regular graph paper
Not bad, as long as we're aware of the limitations.

Conversational latitude

Now let's get a feel for the numbers.

Latitude is the number of hours it takes to drive to the equator at freeway speed. Panama, at 10°N, is a 10-hour drive to the equator. For Santa Claus at the North Pole (90°N), it would be a 90-hour drive, which is why he invented a flying sleigh.

Latitude is traditionally expressed in degrees, minutes and second (DMS), but we now tend to prefer decimal degrees (D.DD). 34.352° is easier to say, write and remember than 34° 21' 7.2", and you can run arithmetic on it, adding and subtracting, more easily. But both expressions can be friendly.

Decimal degrees

The fifth decimal place in latitude is about a meter (1.1 m actually). So 34.12345°N is one meter north of 34.12344°N, and 45 meters north of 34.12300°N. With this simple rule of thumb, you can translate latitude to distance on the ground. My dad's house is at 34.4°N, mine is at 34.1°N. That puts him 30,000 meters, or 30 km further north than I. That's not the entire distance between our houses, it's just the north-south component of it.

Degrees, minutes and seconds

DMS is readable too. It works like this:

Conversational longitude

Longitude does not translate to a fixed distance on the ground, because longitude is measured along parallels, which are of different sizes. To simplify this we can use reference points. Along the equator a longitude degree is the same as a latitude degree. At 30° (Baja California, Texas, Egypt, India, Australia), it's only 13% shorter, so for a casual application like getting around on a hike, we can equate the two without losing sleep. At 60° (northern Canada and Scandinavia), a degree of longitude drops to half a degree of latitude, so there the north-south and east-west interpretations of a degree are quite different.

It's not difficult to generalize these reference points to other latitudes. The 13% and 50% come from the cosine of the latitude. Cos 30°=0.866 (differs from 1.0 by 13%). Cos 60°=0.5 (differs by 50%).

That's almost all there is to lat-long. Now read your GPS with confidence.



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