# How to calculate the middle point between two points on the Earth in matlab?

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Ray Lee on 9 Jul 2015
Commented: Ted Shultz on 20 Aug 2019
Given the latitudes and longitudes of two points, how to get the middle point efficiently?
My trouble is there are millions of point pairs to calculate....
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James Tursa on 9 Jul 2015
Middle point on a great circle arc assuming a sphere? Or something else?

Mohammad Abouali on 10 Jul 2015
Edited: Mohammad Abouali on 10 Jul 2015
Go to this page you will find bunch of useful formula. The one that you are looking for is called "midpoint" on that page. You have the JavaScript code, but implementation is rather easy
% lat1,lat2,lon1,lon2 should be in radian
Bx = cos(lat2) * cos(lon2-lon1);
By = cos(lat2) * sin(lon2-lon1);
latMid = atan2(sin(lat1) + sin(lat2), ...
sqrt( (cos(lat1)+Bx)*(cos(lat1)+Bx) + By*By ) );
lonMid = lon1 + atan2(By, cos(lat1) + Bx);
Ted Shultz on 20 Aug 2019
Here is the matlab code of the formula provided by Mohammad, but all in degrees. Often lat/lon are in degrees, so this nearly identical code my be easier to use.
function [latMid, lonMid] = midpointLatLon(lat1, lon1, lat2, lon2)
% midpoint of two lat long cord on a sphere, all units are deg
Bx = cosd(lat2) * cosd(lon2-lon1);
By = cosd(lat2) * sind(lon2-lon1);
latMid = atan2d(sind(lat1) + sind(lat2), ...
sqrt( (cosd(lat1)+Bx)*(cosd(lat1)+Bx) + By*By ) );
lonMid = lon1 + atan2d(By, cosd(lat1) + Bx);

Ted Shultz on 20 Aug 2019
There is a built in function in the matlab mapping toolbox that does what I think you are looking for: meanm
Mean location of geographic coordinates
Syntax
[latmean,lonmean] = meanm(lat,lon)
[latmean,lonmean] = meanm(lat,lon,units)
[latmean,lonmean] = meanm(lat,lon,ellipsoid)