# Azimuth (bearing) changes depending on map/project projection

I'm trying to calculate the initial bearing that is needed for the great circle between 2 points. As an example, let's say from London to New York. There are multiple calculators online and they calculate this as 288.3658° (http://www.movable-type.co.uk/scripts/latlong.html?from=48.609890,-122.426991&to=48.592836,-122.421613).

However, when I try to get this figure I get different results depending on the map projection. For this I'm using the ne_10m_admin_0_countries, and the ne_10m_populated_places shapefiles. Along with a new layer (lets call it LDNNY) with a CRS of EPSG:4326. Finally, I've got 'on the fly' set to TRUE with a project CRS of EPSG:4326.

Step 1. Draw a straight line on LDNNY from London to New York. Using the CAD-tools's Azimuth tool I achieve an initial Azimuth of 261.7193°.

Step 2. Densify this line to achieve a great circle arc (I do this with the Shape Tools plugin). Now I measure the initial part of this line to get the initial bearing (if I measure from London to New York I wouldn't be getting the initial bearing). This time I get 281.5755°.

Step 3. Change the project CRS to EPSG:3857 and I get 288.2342°.
Change the project CRS to EPSG:54030 and I get 284.6549°.
Change the project CRS to EPSG:54002 and I get 292.4153°.

These are just some example - you can see that some are very close to the online calculator but...
Please could someone explain:

1. Why this is.
2. How would I know what is 'right'?

N.B. If needed I could add images to help explain better.

• Images are always a good addition. You mention that you've found things online that touch on the subject--are these the same as the calculators, or separate pages? If separate, could you link them? Commented Mar 20, 2018 at 23:31