How can I figure out the geographical center of my country, state, province?

Centroid of the 50 United States (photo by Tim Pearce - CC-BY)

If you live in Wyoming or Colorado, the answer is quite simple, since these two states are virtually rectangular, but how does one find the geographical center of an irregularly shaped area?

In geometrical terms, that is the “centroid”. The centroid of a straight-edged polygon can be calculated by breaking it into smaller objects and using a weighted average by area. I think that I understand that much, but the mathematics that follow on websites about centriod calculation are beyond me.

Theoretically, even a very irregularly shaped area can be broken up into smaller objects to deal with the borders that follow rivers and coastlines and whatever else accounts for their windings. But that means dealing with many, many very small objects, grouping them into larger objects and finding their centriods, and so on.

Suchi Gopal of Boston University, together with grad students Hirshikesh Patel and Jared Newell, used the center of gravity method to find the centroid of New England:

“A mathematical calculation that uses a digital representation of the six New England states is the most accurate because it's based on a math algorithm that the computer uses to calculate the center based on the boundaries,” Gopal said. Her calculation, she added, also took into account the irregular coastline of Maine and the islands off the coast of Massachusetts.”

Congratulations! But the geographical centers of most political areas have been pinpointed by le

ss rigorous means. Pinpointed is both correct and incorrect. The method used a pinpoint, but the result was not pinpoint accurate. Wikipedia tells that the center of the contiguous United States was found this way:

“In 1918, the Coast and Geodetic Survey found this “center” by balancing on a point a cardboard cutout shaped like the U.S. Thus, measured in this manner, the actual “center” of the U.S. could be located twenty or more miles from this point, but still might not pinpoint the true “center” at all as an official measurement would have to be defined by an agreed upon standard which does not exist.”

That also does not take into account the fact that the piece of cardboard may not have been of uniform weight throughout. The plumb line method should give the same result. The cardboard map would be hung from a point near the edge, and a vertical (plumb) line drawn down. Then the map would be hung from another point, and another plumb line drawn. Where the two lines crossed would be the centroid of the USA, and where the map should balance on a pin.

All nice and simple, except that the edge of the cardboard map is inaccurate, obviously a simplification of the true borders and coastlines. And if the map were hung from a third point, it is unlikely that the plumb line would exactly cross the intersection of the other two lines. (It should be pointed out that mountains do not count, neither their weight nor the fact that that their steep surfaces create a greater land surface. Surveyors try to measure land area as though it were flat: much easier with aerial photos, and now even easier with GPS devices.)

That is not the sort of thing that bothers people who want to place a monument on the center of the area they are proud about. British Telecom put its 100,000st telephone booth very near the centriod of the island (including Scotland and Wales), near Dunsop Bridge in Lancashire. The centroid for the 48 contiguous United States is near Lebanon, Kansas.


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  • eiffel says:

    If you type “United States” into the Google Maps search box, then zoom in as far as you can go, you end up near Bolton, Kansas.

    But really, I wonder whether there’s any point knowing the centroid of a place, least of all visiting a monument that’s been plunked there.

  • larry says:

    No, but there are less centroids than there are Starbucks.

    One could also visit all the places that someone at sometime considered to be the center of Europe:

  • eiffel says:

    It has just occurred to me that there are “curved” countries whose centroid lies in another country. Somalia’s centroid may fall within Ethiopia, and that of Chile may fall within Argentina. Norway’s centroid is probably within Sweden. Vietnam’s centroid may fall within either Cambodia or Laos. It’s hard to tell, just by looking at a map.

    Then there are the countries whose centroid lies over water. Japan, Indonesia and the Philippines are candidates. Most of the pacific island groups would also have their centroid over water. Possibly also Panama.

  • larry says:

    True, and interesting. The one-piece countries’ centroids could be found by the plumb line method, which is easier to use than trying to balance a map in a pin point.
    Apparently Suchi Gopal’s method (see above) can deal with islands. I suppose it would be just a more tedious exercise to find the centroid of Japan or the Philippines.

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