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How to Calculate Square Degree to Square Kilometer

A square degree is a value used in geometry, representing a portion of the surface of a sphere. The surface area corresponding to one square degree depends on the size of the sphere, so one square degree on the Earth is greater than one square degree on the Moon or on a tennis ball. The number of square degrees on a sphere is given by the equation (pi / 180i)^2, or 129,600 / pi, where pi is usually 3.1415.

Instructions

- 1
  Substitute pi into the equation for square degrees to calculate the number of square degrees on a sphere. The equation states that there are 129,600 / pi square degrees on the surface of a sphere, so divide 129,600 by 3.1415, the usual approximation for pi. The result, 41,253, indicates that there are approximately 41,253 square degrees on a sphere.
- 2
  Divide the surface area of the Earth by 41,253. The result is the earth surface area covered by one square degree. According to Dr. Hetherington of Oregon State University, the surface area of the Earth is approximately 5.101 x 10^8 km2, so the surface area of 1 square degree is approximately 12,365 km2 -- 5.101 x 10^8 / 41,253 = 12,365.1613.
- 3
  Find the surface area of multiple square degrees by multiplying the number of square degrees by the surface area corresponding to one square degree. For example, to calculate the area of 15 square degrees on the Earth's surface, multiply 12,365 km2 by 15. The result, 185,475, is the surface area of 15 square degrees.
- 4
  Reverse your calculations to check for errors. Divide the surface area of the Earth by your calculated value for the area of 1 square degree. Repeat your calculations if the result is not equivalent to the value you found for the number of square degrees covering a sphere. Dissimilar values indicate an error in the original calculations.

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