# Distance Between Two Points on Earth Calculator

An online calculator to calculate the distance between two points on earth, given their latitudes and longitudes
, is presented. The distance in question is the shortest distance, arc of a circle, along the surface of the earth.

You may first need to know how to find the latitude and longitude of a position on earth using a laptop or desktop.

## Mathematical Formulas

Let \( \theta_1 \) and \( \phi_1 \) be the latitude and longitue of an initial point (origin) on earth and \( \theta_2 \) and \( \phi_2 \) be the latitude and longitue of an final point (destination) on earth.

Let \( \Delta \theta = \theta_2 - \theta_1 \) and \( \Delta \phi = \phi_2 - \phi_1 \)

In radians, the central angle \( c \) between the two points on the surface of the earth is given by

\[ c = 2 \arctan2 (\sqrt a , \sqrt {1-a} ) \]

where \( a = \sin^2(\Delta \theta/2) + \cos(\theta_1) \cos(\theta_2) \sin^2(\Delta \phi/2) \)

The distance \( D \) between the two points is given by Haversine formula

\[ D = R c \quad \] where \( R \) is the radius of the earth and is approximeted by \( R \approx 6378 \) km.

## Use of the Calculator

Enter the latitude and longitide in decimal format (with the plus or minus sign) as shown below and press calculate distance.

Note that if

1) the latitude is given (or known) as as North or South, the sign must be taken into account : example 23.7 North must be entered as 23.7. However for 23.7 South must entered as -23.7.

2) the longitude is given (or known) as East or West, the sign must be taken into account : example 56.7 East must be entered as 56.7. However for 56.7 West must entered as -56.7.

## More References and Links

Latitude and Longitude Coordinate System

https://en.wikipedia.org/wiki/Haversine_formula

https://www.movable-type.co.uk/scripts/latlong.html

Find the GPS Latitude and Longitude Using Google Map .