Formula for the distance between 2 longitude lines on a globe at different latititudes

Posted on 2006-03-23
Last Modified: 2012-08-14
My goal: the distance between two lines of longitude on a globe at different latitudes.

Would this be accurate?

 cosine(latitude) * pi * radius^2  = latitudinal circumference?
 then, that circumference / # of longitude lines  = space between 2 of them at this latitude?

Anything simpler or more efficient in mind?


Working on a globe program

Question by:oxygen_728
    LVL 18

    Expert Comment

    LVL 53

    Accepted Solution

    >> cosine(latitude) * pi * radius^2  = latitudinal circumference?
    That whould be :

    2 * cosine(latitude) * pi * radius = latitudinal circumference

    when radius is the radius of the Earth and the Earth is seen as a perfect sphere.

    >> then, that circumference / # of longitude lines  = space between 2 of them at this latitude

    You might want to consult the link JR2003 posted though, because it explains how to calculate the distance between two points on the globe (not necessarily on the same latitude).

    I suggest the haversine formula :

    It's easy to calculate, and has a nice precision.

    Note that the Earth is NOT a perfect sphere, so a good choice of the used radius is important (average radius should be OK for most applications).
    LVL 22

    Assisted Solution

    If you want to add just that little bit extra of geodetic geekiness, you could make sure that your globe model conforms to the WGS84 ellipsoid.  See

    You'd probably be most interested in the ECEF <-> WGS84 lat lon height conversions in the "Datum Conversions" section.  They have the actual formulas there.

    Author Comment

    I should have some time tonight to review the comments, thanks for your input

    LVL 84

    Assisted Solution

    When you say "the distance between two lines of longitude on a globe at different latitudes"
    it sounds like you might not be wanting the great circle distance between two points.
    If you are wanting the lenght of the path between two lines of longitude while traveling at a constant latitude, then you could use
     cosine(latitude) * pi * radius*2  = latitudinal circumference
    assuming the globe in question is a sphere.
    Although I'm not sure of the purpose of your goal, since traveling at a constant latitude can be almost pi/2 times longer than a great circle path,
    e.g. from 90° East to 90° West when traveling along 89°59' North latitude instead of a direct path from 90° East 89°59' North to  90° West 89°59' North
    But then, if you aren't restricted to a particular latitide, then the distance between any two lines of longitude is 0, since they all meet at the poles.  

    Featured Post

    What Is Threat Intelligence?

    Threat intelligence is often discussed, but rarely understood. Starting with a precise definition, along with clear business goals, is essential.

    Join & Write a Comment

    Suggested Solutions

    Title # Comments Views Activity
    springs 17 41
    Octane 98 vs 95 petrol / gasoline : mileage,  pros & cons 10 65
    Probability Calculation 2 33
    Math homework question 5 44
    Foreword (May 2015) This web page has appeared at Google.  It's definitely worth considering! How to Know You are Making a Difference at EE In August, 2013, one …
    Have you ever thought of installing a power system that generates solar electricity to power your house? Some may say yes, while others may tell me no. But have you noticed that people around you are now considering installing such systems in their …
    Migrating to Microsoft Office 365 is becoming increasingly popular for organizations both large and small. If you have made the leap to Microsoft’s cloud platform, you know that you will need to create a corporate email signature for your Office 365…
    Excel styles will make formatting consistent and let you apply and change formatting faster. In this tutorial, you'll learn how to use Excel's built-in styles, how to modify styles, and how to create your own. You'll also learn how to use your custo…

    745 members asked questions and received personalized solutions in the past 7 days.

    Join the community of 500,000 technology professionals and ask your questions.

    Join & Ask a Question

    Need Help in Real-Time?

    Connect with top rated Experts

    16 Experts available now in Live!

    Get 1:1 Help Now