How to Calculate the Radius Between Two Cities Within a Radius

In this vast, wide world, our disparate geographies are linked by weather, time and even math. While the world seems flat, it is, of course, spread out across a great big blue sphere, and you can take advantage of its physical structure by calculating the distance between two cities based on radius. The mathematical formula involved in the calculation is rather complex, but with the correct information, you can compute it.

Instructions

    • 1

      Start with the earth's radius. The planet's mean radius is 3.9 miles.

    • 2

      Determine the difference in latitude and longitude of both cities, represented by the arithmetic formula "lat = lat2' lat1 and "long = long2' long1.

    • 3

      Compute the results according to the following formula: sin²("lat/2) + cos(lat1).cos(lat2).sin²("long/2). In other words, the sine squared times the difference of the latitude, times the cosine of the first latitude, multiplied by the cosine of the second latitude. Multiply that by the sine squared of the difference of the latitudes divided by 2. This will yield the value "a" for the purposes of the formula.

    • 4

      Compute the value "c" by multiplying 2 times the tangent of 2 times the square root of 1 minus a. In mathematical terms, it will be 2 x (a)tan2(√a, √(1'a)).

    • 5

      Calculate the radial distance between the two cities. The distance equals "radius times c," or 3.9 miles times what you found for "c" in Step 4.

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