**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:

Table of contents |

2 The Formula 3 Practical Application 4 See Also |

## Definitions

## The Formula

## 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:

- 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: