How do I calculate distance between two latitude longitude points?

Question

Here's an easy one for you:

How do I calculate the distance between two points points specified by latitude and longitude?

EDIT: For clarification, I'd like the distance in kilometres, the points use the WGS84 system and I'd like to understand the relative accuracies of the approaches available.

Answer 1

This link might be helpful to you.

Excerpt:

This script calculates great-circle distances between the two points – that is, the shortest distance over the earth’s surface – using the ‘Haversine’ formula.

Javascript:

var R = 6371; // Radius of the earth in km
var dLat = (lat2-lat1).toRad();  // Javascript functions in radians
var dLon = (lon2-lon1).toRad(); 
var a = Math.sin(dLat/2) * Math.sin(dLat/2) +
        Math.cos(lat1.toRad()) * Math.cos(lat2.toRad()) * 
        Math.sin(dLon/2) * Math.sin(dLon/2); 
var c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1-a)); 
var d = R * c; // Distance in km

Answer 2

Thanks to the spherical nature of the earth the standard distance formula cannot be used. However, spherical geometry works well for this. The following article has a write up of exactly how to perform this operation. http://www.meridianworlddata.com/Distance-Calculation.asp

Answer 3

First hit on google with your header as search string: Calculate distance, bearing and more between two Latitude/Longitude points.

Answer 4

It rather depends how accurate you want to be and what datum the lat and long are defined on. Very, very approximately you do a little spherical trig, but correcting for the fact that the earth is not a sphere makes the formulae more complicated.

Answer 5

On an ellipsoidal model of the earth, you want Vincenty's formulae. A Google search will return a lot of hits. One of them is at Geoscience Australia.

Answer 6

I think we've had this one already:

http://stackoverflow.com/questions/23569/calculating-distance-between-2-cities

Answer 7

Here's an online calculator to do what you want. The code is client-side JavaScript, so you can view the source.

Here's an explanation of the math if you want to do it yourself.

Answer 8

To calculate the distance between two points on a sphere you need to do the Great Circle calculation.

There are a number of C/C++ libraries to help with map projection at MapTools if you need to reproject your distances to a flat surface. To do this you will need the projection string of the various coordinate systems.

You may also find MapWindow a useful tool to visualise the points. Also as its open source its a useful guide to how to use the proj.dll library, which appears to be the core open source projection library.

Answer 9

Here is a C# Implementation:

class DistanceAlgorithm
{
    const double PIx = 3.141592653589793;
    const double RADIO = 6378.16;

    /// <summary>
    /// This class cannot be instantiated.
    /// </summary>
    private DistanceAlgorithm() { }

    /// <summary>
    /// Convert degrees to Radians
    /// </summary>
    /// <param name="x">Degrees</param>
    /// <returns>The equivalent in radians</returns>
    public static double Radians(double x)
    {
        return x * PIx / 180;
    }

    /// <summary>
    /// Calculate the distance between two places.
    /// </summary>
    /// <param name="lon1"></param>
    /// <param name="lat1"></param>
    /// <param name="lon2"></param>
    /// <param name="lat2"></param>
    /// <returns></returns>
    public static double DistanceBetweenPlaces(
        double lon1,
        double lat1,
        double lon2,
        double lat2)
    {
        double dlon = lon2 - lon1;
        double dlat = lat2 - lat1;

        double a = (Math.Sin(dlat / 2) * Math.Sin(dlat / 2)) + Math.Cos(lat1) * Math.Cos(lat2) * (Math.Sin(dlon / 2) * Math.Sin(dlon / 2));
        double angle = 2 * Math.Atan2(Math.Sqrt(a), Math.Sqrt(1 - a));
        return angle * RADIO;
    }

Answer 10

LatLongLib is a library that provide the basic operations to deal with Latitude longitude points this post might help you

Answer 11

Hi! I've used the above Haversine formula to implement a ruler for Google Maps v3. Here it is: http://www.barattalo.it/2009/12/19/ruler-for-google-maps-v3-to-measure-distance-on-map/ Thank you!