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I snipped Germany and Afghanistan from the same Google Maps view:

Germnany_and_Afganistan

They look like they are about the same size. Here is the full screenshot:

Google_Maps_screenshot

The problem: Afghanistan has an area of Afghanistan_Area while Germany has an area of Germany_Area (according to Wikipedia).

Now, I know that Germany appears larger because higher latitudes are stretched more when drawn on 2D. But I calculated the difference between the perimeter on latitude 34° (Afghanistan) and latitude 50° (Germany).

Given that the Earth's radius at the equator is 1, the relationship between latitude and the radius on that latitude should follow the circle function

  • formula_1
  • formula_2 gives us y = 0.926
  • formula_3 gives us y = 0.831

So the radius is 0.926 in Afghanistan and 0.831 in Germany.

This is only a difference of 11% caused by the higher latitude. According to Wikipedia, however, Afghanistan is 83% larger than Germany.

So where does the rest of Germany's scaling on Google Maps come from?

Please excuse my incorrect naming of geographic terms, I have absolutely no experience in geography.

  • 8
    You need to research projections, more specifically, the areal distortion of the Web Mercator projection. – Vince Oct 1 '17 at 22:39
  • 3
    also areas go as the square of the error not linearly – Ian Turton Oct 2 '17 at 7:50
  • 1
    xkcd.com/2082 – pLumo Dec 13 '18 at 15:13
1

Before August 2018

Germany looks equally as large as Afghanistan on Google Maps because of the Web Mercator projection that was applied.

Web Mercator is a slight variant of the Mercator projection, one used primarily in Web-based mapping programs.

Wikipedia says about the Mercator projection that

The Mercator projection is a cylindrical map projection. It became the standard map projection for nautical navigation because of its ability to represent lines of constant course, known as rhumb lines or loxodromes, as straight segments that conserve the angles with the meridians. Although the linear scale is equal in all directions around any point, thus preserving the angles and the shapes of small objects (making it a conformal map projection), the Mercator projection distorts the size of objects as the latitude increases from the Equator to the poles, where the scale becomes infinite.

The Mercator projection exaggerates areas far from the equator.

If we consider the geo-centroid coordinates (data were taken from Country centroids) for both countries

Country         Latitude         Longitude
Germany         51.1069818075    10.385780508
Afganistan      33.8352307278    66.0047336558

it is easy to see that the Latitude value of Germany is greater than Afganistan which means that Germany located closer to the North pole where the distortion is bigger.


After August 2018

I think with a new edition of Google Maps, the issue about area distortion is not a big concern anymore.

Wikipedia says that

Google Maps used a variant of the Mercator projection (Web Mercator projection), and therefore cannot accurately show areas around the poles. However, in August 2018, the desktop version of Google Maps was updated to show a 3D globe.

Have a look at the "nearly" the same view of Google Maps.

Google_Maps_view

I suppose it quite obvious now that there is an areal difference between Germany and Afganistan.

References:

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