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Great circle distance is the shortest distance between any two points on a sphere.

Because the Earth is approximately spherical, the great circle distance is commonly used to find the distance (e.g. in miles) between two coordinates (latitude/longitude pairs) on a map. First, some definitions:

Definitions

is the radius of the Earth ( meters)
is latitude
is longitude

Practical Application

Choose two points

In order to use this formula for anything practical you will need two sets of coordinates. For example, the latitude and longitude of two airports:

• Nashville International Airport (BNA) in Nashville, TN, USA: N 36°7.2', W 86°40.2
• Los Angeles International Airport (LAX) in Los Angeles, CA, USA: N 33°56.4', W 118°24.0'

Convert coordinates

You will have to convert these coordinates to a more mathematically friendly form using
a simple method before you can use them effectively in a formula. After conversion, the coordinates become:

• BNA:
• LAX:

You'll need to convert these coordinates to radians instead of degrees for them to be useful in the formula:

• BNA:
• LAX:

Substitute

The first step is simply to substitute numbers where appropriate. This is best done in small steps to keep each step manageable:

Coming soon.