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How to Calculate Distance on the Earth's Surface

Any attempt to represent the surface of the Earth on a two-dimensional map is, at best, an approximation. Spatial information is distorted when one dimension of a multidimensional object is ignored, and compromises must be made in terms of accuracy. Similarly, the distance between two points on the Earth cannot be accurately measured on a map by using a ruler and the map's scale. The Great Circle formula must be used to accurately calculate distances.

Things You'll Need

  • Scientific calculator
  • Latitude and longitude of the two points
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Instructions

    • 1

      Determine the latitude and longitude of two points on the map as closely as possible. Set the measurements equal to the following variables:

      Latitude of first point = a1

      Longitude of first point = b1

      Latitude of second point = a2

      Longitude of second point = b2

    • 2

      Multiply the sine of a1 by the sine of a2 on a scientific calculator.

    • 3

      Subtract b2 from b1 and calculate the cosine of the result.

    • 4

      Multiply the cosine of a1 by the cosine of a2 and multiply the product by the result calculated in Step 3.

    • 5

      Add the result of Step 4 to the result of Step 2.

    • 6

      Calculate the arc-cosine of the result from Step 5.

    • 7

      Multiply your result from Step 6 by 6,371 to get the approximate Great Circle distance between the two points in kilometers.

K-12 Basics
K-12 Basics
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