# Calculating Distance Between 2 Points on the Earth

Out of curiosity I had built myself a GPS Datalogger, I was able to get the raw NMEA data out of it but it only provided information regarding my position and time. I wanted to calculate the velocity of a vehicle at a given location and plot a graph of distance Vs velocity. I used the following calculations to calculate the distance between the two coordinates on the Earth’s surface. By dividing that distance with time I was able to calculate the velocity in KMPH at a given location.

To calculate the distance between two Latitude and Longitude coordinates, I am using the ‘Havesine’ formula. Haversine formaula calculates the great-circle distance between the two points i.e. the shortest distance given between the two points on the earth’s surface. It calculates the “as-the-crow-flies” distance between the points ignoring any terrain.

Here’s the formula (angles are assumed to be in Radians)

R = Earth’s radius = 6,371 Km

Dlat = latitude2 - latitude1

Dlong = longitude2 - longitude1

a = sin²(Dlat/2) + cos(latitude1)*cos(latitude2)*sin²(Dlong/2)
c = 2.atan2(√a, √(1−a))
d = R*c

### Haversine formula (Mathematical explanation)

haversin (d/R) = haversin(θ2 - θ1) + cos(θ1)cos(θ2)havesin(Δλ)

Where:

havesine(θ) = sin²(θ/2) = (1−cos(θ))/2

d is the distance between two points on a sphere

R is the radius of the sphere

θ1 is the latitude at point 1

θ2 is the latitude at point 2

Δλ is the longitude seperation

The arguments to the haversine function are assumed to be in Radians.

so, to calculate the distance we have

d = R haversine(inverse)(h) = 2Rarcsin(√h)

Where h = haversin (d/R) My implementation of the above formula is in Java, I be publishing the code as soon as I get some free time. I can email the code if anybody wants it urgently.