Geographic Coordinates Made Simple

This is one of those things that sounds pretty complicated at first, but the basics of which are rather simple. Geographic coordinates are or can be used to locate any point on Earth, when convenient things like addresses aren’t available – or don’t exist. Coordinates are also used in ballistics to accurately identify long-range targets for military purposes.

Illustration of latitude and longitude

Locating a point on the surface of the Earth can be done simply with degrees of latitude and longitude, whereas you’ll need a third number if there’s a vertical distance involved such as altitude or depth. An example geographic coordinate may look something like this: 35°41’22.22″N 139°41’30.12″E. The first half is latitude and the second is longitude.

What Exactly is Latitude and Longitude?

Latitude is the angle between the equatorial plane and a line that runs normal (90 degrees toward the center of the Earth) to the surface at the point in question. This is always the first part of the coordinate. Longitude is the angle between the plane of a reference meridian, generally the Prime Meridian in Greenwich, to a line that again, passes normal to the Earth’s surface, through the point in question.

Points with the same latitude will draw out imaginary circles (called parallels) parallel to the equator and to each other, while points with the same longitude are halves of great ellipses, eventually converging at the poles. Looking at the above example coordinate, we see 2 sets of 3 numbers with a direction for each. Let’s talk about what these numbers do.

The first set defines the coordinate’s latitude. What it’s saying is that it’s 35 degrees, 41 minutes, and 22.22 seconds, north latitude, and 139 degrees, 41 minutes, and 30.12 seconds east longitude. So we covered the degree part, but what is the minutes and seconds for? Well, some people actually don’t even use them, only using the degrees.

Either way is fine, and will add up to be the same thing anyway. The difference is that you have to use decimals if you choose to use only degrees. It’s simply saying that a non-decimal degree alone is insufficient to provide an accurate location and so more numbers are used. The more numbers to the right of the decimal you use, the more accurate the coordinates. To convert minutes and seconds (DMS) to decimals is pretty straight-forward.

  • Add up the total number of seconds. Using our latitude, we multiply 41 by 60 and add 22.22, which equals 2482.22 seconds.
  • Now divide this number, 2482.22, by 3600, to get the percentage of total seconds. 2482.22/3600=0.6895. Note here that without going smaller than seconds, distances of latitude for example, are only accurate to about 30 meters – 111/3600=0.0308, where the average length of a meridian arc between 2 latitudes is roughly 111 kilometers. Distances of longitude taper down as you get nearer to the poles.
  • By adding this decimal to the degrees number you get 35.6895 north latitude.

Latitude distance chart
Longitude distance chart
Images from Mysundial.

The following equation, although not extremely accurate, can calculate the width, or distance, of one longitudinal degree:

equation for longitudinal widthwhere Φ is the degree of latitude, and Mr is the Earth’s average meridional radius, equal to approximately 6,367,449 meters. As I mentioned above, this isn’t all that accurate due to the “constant” being an average. You can also get the distance for a minute and/or second by dividing by 60 and 3600, respectively.

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