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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:

### Solve

Coming soon.  