{"id":39,"date":"2008-02-17T16:46:35","date_gmt":"2008-02-17T21:46:35","guid":{"rendered":"http:\/\/jaimerios.com\/?p=39"},"modified":"2025-12-02T23:51:08","modified_gmt":"2025-12-02T23:51:08","slug":"calculating-distance-between-2-points-on-earth-using-the-haversine-formula","status":"publish","type":"post","link":"https:\/\/jaimerios.com\/?p=39","title":{"rendered":"Calculating distance between 2 points on Earth using the Haversine formula"},"content":{"rendered":"\n

2016 Update<\/strong>
The code and the Xcode project for this article is now also available on GitHub<\/a>.<\/p>\n\n\n\n

A while ago, I worked on a project where I had to implement code in C\/C++ that could calculate the distance between 2 locations within the United States. It would be nice if the Earth was flat, since this would make my job a little easier, but the Earth is round and I needed to find a way that I could calculate distance. From the research that I have done, I found that plenty of people have worked on this problem before and one popular article is sited over and over again is this: R. W. Sinnott, “Virtues of the Haversine”, Sky and Telescope 68 (2), 159 (1984).<\/p>\n\n\n\n

The Math used in all of the articles I read refer to the Haversine formula. Every example I found of this formula were either written in plain Math or shown in JavaScript. Although it was nice finding examples of this in JavaScript, there were a couple of problems with this:<\/p>\n\n\n\n

    \n
  1. C datatypes aren\u2019t the same as JavaScript datatypes and<\/li>\n\n\n\n
  2. All examples used Latitude and Longitude, but I had to use Zip codes<\/li>\n<\/ol>\n\n\n\n

    So I had some more hurdles to overcome. They didn\u2019t seem like big ones, but ones that I had to overcome nonetheless.<\/p>\n\n\n\n

    Now the funny thing about this project was that this was one of those endeavors where a spec wasn\u2019t available before or during development. As a consequence, I would have designed the code differently than what I had have delivered. Not that there is anything wrong with what I ended up with, it\u2019s just that I like neat code and what I wrote for this article is what I would have done if I had known all of the variables.<\/p>\n\n\n\n

    Example Code<\/strong><\/p>\n\n\n\n

    What I am going to show you is how to calculate distance between two points within the United States, using the Haversine formula, implemented in C. The code will show you how to do that using Latitude and Longitude coordinates. The example application that is posted will show you how to use Zip codes in place of Latitude and Longitude.<\/p>\n\n\n\n

    The example code is demonstrated in an application written for Mac OS X. Win32 developers shouldn\u2019t have to worry, since the Math code is done in a separate C file. Objective-C is used only for the UI file so you won\u2019t have to read my Objective-C code to understand how to implement this formula in your own application. For the zip code implementation, I use the standard template library to contain the information I need in map so that I can extract the Latitude and Longitude for a particular postal code.<\/p>\n\n\n\n

    Creating the example code required these steps:<\/p>\n\n\n\n

      \n
    1. Creating a Cocoa Application<\/li>\n\n\n\n
    2. Creating the Haversine C code and<\/li>\n\n\n\n
    3. Creating code that can handle Zip codes and finally<\/li>\n\n\n\n
    4. Creating a routine to check the validity of the output<\/li>\n<\/ol>\n\n\n\n

      Creating a Cocoa Application<\/strong><\/p>\n\n\n\n

      This is pretty simple step that most Apple developers are familiar with. I\u2019m using Xcode 3.0, however, I set the project settings to be compatible with Xcode 2.4. Once the Cocoa application was created, I needed to create an interface that would take my Longitude and Latitude parameters and display the resulting output.<\/p>\n\n\n\n

      I also created a section that would take in Zip codes and get the result that way too! The logic is pretty simple and contained within the Objective-C code.<\/p>\n\n\n\n

      Creating the Haversine C code<\/strong><\/p>\n\n\n\n

      This part was a little tough to work with. Every example I saw on the web used JavaScript. Here is the Math and JavaScript code I found at http:\/\/www.movable-type.co.uk\/scripts\/latlong.html<\/a> :<\/p>\n\n\n\n

      Haversine Formula:<\/strong><\/p>\n\n\n\n

      \n
      \u03c6 is latitude<\/div>\n
      \u03bb is longitude<\/div>\n
      R is earth\u2019s radius (mean radius = 6,371km)<\/div>\n
      a = sin\u00b2(\u0394\u03c6\/2) + cos \u03c61 \u22c5 cos \u03c62 \u22c5 sin\u00b2(\u0394\u03bb\/2)<\/div>\n
      c = 2 \u22c5 atan2( \u221aa, \u221a(1\u2212a) )<\/div>\n
      d = R \u22c5 c<\/div>\n<\/div>\n\n\n\n

      (Note that angles need to be in radians to pass to trig functions).<\/p>\n\n\n\n

      JavaScript Implementation:<\/strong><\/p>\n\n\n\n

      JavaScript<\/span><\/span>