Azimuthal Projections Info

Example azimuthal map
Azimuthal projection from ARRL headquarters

This all started when I was interested in calculating the distance and bearing between amateur radio stations. I found this reference on calculating the great circle distance and bearing. Ultimately, this interest led to a web form for producing azimuthal maps.

For those who never heard of an azimuthal map, it is a special kind of map that prioritizes correctly showing the great circle distance and bearing from the center reference point. Azimuthal maps are particularly useful for ham radio operators with a directional antenna. For example, if you’re in Connecticut and you want to talk with someone in Cameroon (Africa), the azimuthal map will tell you to point your antenna to a bearing of 90° on a compass (technically you also must adjust for the difference between magnetic north and true north).

It occurred to me that this the bearing and distance calculation was the fundamental tool for making an azimuthal projection. All I needed was a database of land and political boundaries expressed in latitude/longitude pairs.

The azimuthal project is always made from a particular reference point on the globe, and I can convert the points in the  land and political boundary database into bearing and distance using the great circle calculations. This gives me a collection of points in polar coordinates (r, Θ) which is what I need for the azimuthal projection.

For the land and political boundary information, I used the database from the CIA World Databank II; however, it required some massaging. First it was too detailed, and I had to filter the data to an appropriate resolution. Next, I wanted land masses and water bodies to be represented by closed paths. The CIA World Databank II is a collection of unconnected paths, so I had to write a program to patch them together and reorder the points to be clockwise. Having closed paths of points ordered in clockwise orders is necessary to have water and land colored differently. Lastly, I had to identify which closed paths represent land and which represent water. Unfortunately, this work is incomplete. You’ll notice some lakes that aren’t colored blue.

Initially, my Ruby program was generating raw PostScript. However, I recognized that it would be easier for people to use if it generated a PDF.  Rather than using a Postscript to PDF convertor, I changed to generating PDFs directly using the Ruby PDF::Writer. By using PostScript or PDF, I get vector graphic output that is scalable from small to very large sizes without having to make a huge raster graphic files.  There is a limit to the resolution of the continent & political outline data, so at very large sizes, the outlines may not appear smooth.

Ultimately, I used the great circle distance formula from Wikipedia. According the article, it’s accurate for both long and short distances.

The hardest part of the whole project was getting the water blue. There are still some maps where the program gets it wrong, and you’ll see weird coloring. Things tend to go wrong when the reference point is inside a particular small region of land or water. In these cases, the floating  point accuracy seems to cause the colors approach to fail.

My plans for future improvements include:

  • add small tables of bearing & distance for important world cities around the margins
  • add US and world cities to the map (particularly for area map)
  • adjusting political boundaries and labels to be more accurate
  • adding more views to allow people to report lakes that aren’t colored correctly

472 thoughts on “Azimuthal Projections Info”

  1. Hi, what you’ve provided is a wonderful and useful tool… Many thanks for that.
    Also, is it possible to import regular map data, say google maps, with roads and markings.

    Your response is appreciated… TIA

  2. Just got this error:
    “Internal Server Error

    The server encountered an internal error or misconfiguration and was unable to complete your request.

    Please contact the server administrator at webmaster@localhost to inform them of the time this error occurred, and the actions you performed just before this error.

    More information about this error may be available in the server error log.”

  3. Thank you. Your information is wonderfully concise among the unfocused internet.

    btw, I am newly FRN 0032053464 in training at the Anne Arundel Radio Club in Davidsonville, MD.

  4. Fabulous job. I wish I had this tool back in the 70’s when I was a teenager into CB & DXing across the world with my homemade 5 element Yagi.
    Back then I managed to get a GC map centred on Sydney, which is 1000km from my location of Melbourne, but it was close enough to get my antenna bearings close enough.

  5. Hi there,
    love the azimuthal chart creator. Just one question..

    Would it be possible to include an option where users can input lat and long co-ordinates that create little coloured map pins (of locations of interest) within the azimuthal chart?

    That would be great to print out as a PDF…

    And worthy of my donation to your good work 😉

    Warm Regards,

    Bobby G.

    1. Thanks for the recommendation. If you would like to do the programming to add this feature, I would be happy to work with you.

      73 de Tom NS6T

  6. There is something really weird going on with Fiji.
    Centre the map near Korolevu e.g. -17.809870626695197, 177.90002248298418, and the island to the northeast has a bit sliced off by a straight edge northeast-southwest.
    Centre the map on the island, or in the water nearby, or off to the south, e.g. -16.703120358351537, 178.9190224210907; -16.502657779991786, 179.7862365944284; -17.67941619556715, -178.81925617462636; or in Tokyo or Pearl Harbor and weirdness happens.

  7. Sir:
    1st Thanks for creating such a truly cool and helpful mapping system.
    2nd I would like your permission to incorporate and suggest your pages/maps use in a Net procedure manual I am drafting. Your tool really makes the idea I am illustrating much more achievable for the regular ham.
    If you need additional information about my request, Please contact me at


      1. Among a group of local hams, there are 2 fellows that talk about DXing to distant lands.
        One comment from one was; Which way to Australia if we are in NY state ?
        Well after finding this fine site, the graphical answers is, not much different from NY or NC! Printed the map and observed, not much different from NC !
        But when I tried using the Request an Azimuthal Map and literally used; “35.89802,-78.56920”, it did not work, that perplexed me. It was entered as shown. Well, then tried with out the apostrophes (“), 35.89802,-78.56920 , it worked.
        You may want to consider adding, as shown 35.89802,-78.56920
        Thank you very much.

  8. Thank you for making this map maker. I had a problem where if I deviate from putting the north pole as the center, then I get distortions of continental size. For example, Australia spans 40 degrees on north pole central but spans 80 degrees with New York as the Center. Also, can you help me understand why Antarctica spans 360 degrees when the north pole is center (which matches the original Gleason map). Also, Antarctica looks bigger than South America when NY is center and smaller when the South Pole is center. Thank you.

    1. Sandy,

      Every two dimensional (i.e., flat) map of the earth has to distort something. This Wikiperdia article on map projections talks about some one the different tradeoffs that different types of maps make. The azimuthal map is basically trying to get two things right (distance and bearing from the center), and it’s willing to get everything else wrong. Hence the azimuthal map distorts land mass sizes and shapes to get distance and bearing correct.

      There are two locations on the globe where azimuthal maps basically break down: the north and south poles. If you’re exactly on the north pole, every direction you look has the same bearing (due south). A correct azimuthal map from the north pole should have everything on a single line headed to bearing 180 degrees. The south pole has an analogous situation; every direction is due north. In practice, it would be very difficult to get accurate bearing at the pole because magnetic north doesn’t equal true north.

      Any time the map center is on the opposite side of the earth from a land mass. That land mass is going to be all around the outside edge of the map. For ham radio uses of the azimuthal map, this basically means that when your trying to communicate with the opposite side of the earth all directions are essentially equivalent. The distance the signal needs to travel is identical regardless of what direction you point your antenna.

      I hope this helps.


  9. Hi! Thanks for the wonderful tool! Could you kindly add borders on the territory of former USSR (Russia, Ukraine, Kazakhstan, etc.) There are 17 different countries there, but it seems it’s still USSR on this map.

    Thank you!

    1. I apologize. The country outline data using for the website is very old, and it has several inaccuracies. I have a new program that uses a different database, but it isn’t set up to run as a web service.

  10. I am always amazed at how we perceive the angle in which to find other locations. One of these days I should go down to Staples and have a larger print done.

    As I was looking at this again today, I was thinking it would be interesting to see this map used in a “day and night world map”.


  11. I’d really appreciate an overlay that prints with the Call sign prefixes for each country on the map. This is a great tool!

  12. Would it be possible for your azimuth map to be printed larger? Maybe using a double page so it is larger for the wall, or a 4x A4 print for larger walls perhaps

    1. You can absolutely create maps for larger page sizes. If you select a paper size of A2, it will create a PDF that expects to be the size of four A4 pieces of paper. A1 is the size of eight A4 pieces of paper. This article on paper sizes is very helpful.

      If you take the PDF to a local print shop, I imagine they can print it as large as you’re willing to pay for.

      If you’re trying to print a poster sized PDF on your 8.5×11 (or A4) printer with multiple sheets, I believe the Adobe Acroread program can “tile” a large PDF onto the page size your printer supports.

  13. Hello, and thank you for this wonderful map tool. I am wondering if there’s a way to show colorized countries, and maybe size adjustable. I want to have the circular part so I can cut it out and put it on the face of my rotator control dial.

  14. This is a truly excellent tool – many thanks for this outstanding work!
    There is one thing that I am missing: Maidenhead Locator fields. I regularly participate in VHF/UHF-contests with my portable station, and currently I calculate the best beam direction from my and the other station’s maidenhead locator. If I had an azimuthal map with radius 300 to 500km with a maidenhead grid in it, that would even be more convenient!

  15. When I tried to create a map I got this message:

    Internal Server Error

    The server encountered an internal error or misconfiguration and was unable to complete your request.

    Please contact the server administrator at webmaster@localhost to inform them of the time this error occurred, and the actions you performed just before this error.

    More information about this error may be available in the server error log.
    Apache/2.4.54 (Debian) Server at Port 443

  16. Thank you for this great tool! I came here to make improvement suggestion. Could you make grid letters filled with color? Gray maybe? Right now those are just outline shapes and visibility is very limited. And if I turn on this layer I’d like it to be there visible. Thanks again for your great work!

  17. Good day, firstly thank you for this tool, I have used it in the past. Today, however when I try create the map I get an internal server error and I am unable to create any maps.

    Could you please let me know when I may be able to try again.

    Thank you

  18. Hello Tom, first thank you for your Azimuth map generator!
    I am from Lyon (France), and looking to find the direction to Mecca (Saudi Arabia) with the Azimuth.
    – When I set the origin at Lyon (45.7485, 4.84671), I find the Azimuth Lyon->Mecca to be ~119°.
    – When I set the origin at Mecca (21.424946, 39.821995), I find the Azimuth Mecca-> Lyon to be ~319°.
    It disturbs me because I expected it to be (360°-119° = 241°). My intuition is that it has to be with the Nord or spherical coordinates (?), but I struggle to grasp & phrase it correctly. Could you help me phrase an explanation ofwhy the “reverse-azimuth” is not computed simply as “360°-azimuth”.
    I thank you in advance. Kind regards,

    1. I understand the issue. I found it unintuitive too. If you’re like me, you’ve probably spent much more time looking at two-dimensional maps than you’ve spent looking at an actual spherical globe. For me, looking at the 2-D maps distorts my view of the 3-D reality. The reality is that most straight lines on a 2-D maps are curved lines on a globe, and most straight lines on a globe are curved on a map. Experimenting with a site like can show this with the “Start a Course” button. You can get the same sense from a map of airline routes. On the 2-D map, the routes look curved, but in reality, they are usually as close to straight lines on the globe as they are able to do. There are various regulations and safety requirements that can change plane routes. I’ve also spent some time playing with a globe to reset my expectations.

      The site that I used as a reference also discusses this issue. If you were walking the route with a compass, you would have to gradually change your bearing as you journeyed.

      I hope this helps.

  19. IS there any way of reversing the North and South
    on your maps please.
    Since I live in the north, I have my antenna reversed.
    this make things a lot easier going SE to SW.
    I don not have to swing the antenna all the way around

    Steven VE3PTA

  20. Hi, Tom,

    Sincere kudos for creating, publishing, and most importantly supporting this valuable tool. I know – intimately – what it takes to do it. Your work is a credit to amateur radio.

    I have a question: you wrote “(technically you also must adjust for the difference between magnetic north and true north)”. I’m awfully literal-minded, so I want to know: does “you” refer to the programmer when creating the tool, or is “you” the user? That is, am I correct in assuming that the azimuthal projections your site generates are adjusted to reflect the declination at the specified center location, or must the user do so somehow?


    1. Yes, literal-mindedness is an occupational hazard for computer science types such as myself.

      The maps generated by my website are based on 0 degrees being true north (i.e., the direction of the northern axis of rotation for the planet). The 0 degrees bearing does not point to magnetic north (i.e., the direction a compass will show as north). Hence, it’s up to you as the map user to apply the correction for the difference between magnetic north and true north. For example, I imagine that most people when mounting a yagi antenna will figure out where true north is and have their antenna point to true north when the bearing is set to 0 degrees.

      There are a few reasons why the maps are done based on true north:

      • The difference between magnetic north and true north varies with time, so true north is the only frame of reference that should remain constant.
      • The difference between magnetic north and true north varies as a complex function of location, and I am not aware of a convenient source for this function that’s easy to use in a program and covers the whole globe.
      • Most maps are made with north representing true north.
  21. I printed out the azimuthal Map with blue background, D&W distance : whole globe. I got oceans and seas nice blue. Whan I changed the distance to 3000 the oceans and seas were white and the landmass was blue, instead. What I did wrong ?

    1. It’s not something you did. It’s a bug in the program. The PDF rules for filling polygons with color are very detailed, and sometimes my program gets it wrong. It’s not a simple thing to fix. Although, I think I have a prototype of a newer system that does a better job. I usually just turn off the blue fill when it’s wrong.

      73 de Tom NS6T

  22. I am getting the following error message:
    The data in the form contained errors in the following fields:
    [“PAPER\nPaper argument is wrong ”\n”, “TITLE\nTitle has illegal characters.\n”]
    Please try again.

    I chose the ‘A4’ paper option.
    Title is ‘Azimuthal-map’

    Location is ‘QF46ms’

    Thank you for any suggestions,

    1. The I approach I used in the map generator to decide what was water and what was land isn’t always right. When it’s wrong, the water ends up white and the land ends up blue. When this happens, it’s usually best just to turn off the blue background.

  23. Not work

    The server encountered an internal error or misconfiguration and was unable to complete your request.
    Please contact the server administrator at webmaster@localhost to inform them of the time this error occurred, and the actions you performed just before this error.
    More information about this error may be available in the server error log.

  24. Hi,
    Can you add a feature to show CQ Zone directions in as many outer most bands as it takes, perhaps with facility to remove one’s own CQ zone and a set of user input zones – whereby one eliminate cq zone ranges I am not interested – typically my nearby cq zones, ?

    Thank you for the wonderful service you are providing.

    73 de Aravind vu2abs – nk03ca – chennai city, south india.

  25. Great tool, TNX
    Strangely, borders of countries from a former federation, don’t appear, while internal borders of a present federation. HI
    Guido (SWL)

  26. This is a great program! Is there a way to print a smaller scale map centered on my QTH but with an offset to blow up a different part of the globe? I’m in Northern California but would like to blow up the East Coast or Europe.

  27. Hi,
    I am trying to get one of you azimuthal maps. I am in Gallatin, TN. Every time I put in a location in I get a error message. I have tried city and state and lat longs. If I click on estimate my location it puts me in northern Washington state. Would you know what I am doing wrong?
    Thanks and I appreciate your service,
    Jim Hinds

  28. Hi,
    this is Cezary sp7ukl
    Your azimuthal map is not actualy.
    There is no coutries like:
    Ukraine, Belarus, Latvia, etc.
    Is there any chance to get it with all countries?

    1. I am working on a Javascript-based map generator that has a more recent database of country outlines. The current one is based on a very old database.

  29. Thank you for this! Is there a way to modify the lat/long lines that show (or chose to eliminate them)? I’m mostly looking for a blank polar AE map for my kids to color but the busyness of the automatic grid lines is distracting them.

  30. Thanks for producing the Great Circle Map generator.

    I am a new ham and this is a great thing to have access to.

    Before I head to staples to print out the map on big paper however, could you provide an option to use abbreviations such as NC, DE, NY instead of the full state names as this would result in a less cluttered view in my opinion.

    As a software developer for DX radio over many years – see – I know how helpful suggestions from users has been to the development of my own projects, so i hope you will be encouraged by my suggestion, and the strong vote of thanks I have to you for providing your excellent system.


    Martin Francis

  31. Thanks for giving us all a tool to get GC bearings from. It makes people recognize that a straight line from say Freemantle VK6 to Durban ZS is not the shortest route. I remember wandering up to the bridge as we progressed across the chart with its course alterations to obtain a GC routae. Cheers ZL1BBW

  32. Hi Tom,

    Thank you for such a terrific and helpful tool! I can only imagine the complexity and time required to make the program function properly!

    You must be a master and visionary to accomplish this task so well. You’ve likely helped a world a ham radio and SWLs tune in the stations they are seeking.

    Great job! It’s much appreciated!


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