# Real Country Sizes Shown on Mercator Projection (Updated)

Posted In: Maps

Hover or click on a country to see how much it shrinks from the Mercator projection size.

I remember as a child thinking that Alaska was as large as 1/2 of the continental US. Later, however, I learned that while it is the largest state, it is actually only about 1/5 the size of the lower 48 states. My son has also remarked that Greenland is very big. And while it is very big, it’s nowhere near the size of the continent of Africa.

The map above shows the distortion in sizes of countries due to the mercator projection. Pressing on the button animates the country ‘shrinking’ to its actual size or ‘growing’ to the size shown on the mercator projection. It was inspired by a similar animation that I saw on reddit and decided I wanted to try to build the same thing.

The mercator projection is a commonly used projection on computer maps because it has perpendicular latitude and longitude lines (forming rectangles). It is formed by projecting the globe onto a cylinder A variant of the was adopted by Google maps, which helped establish it as the informal standard for web-based maps (although Google maps now also uses a globe view, instead of a map projection when zooming out to a very wide view).

Areas far from the equator are distorted in terms of their distances and are shown much larger than they actually are. This is one of the major issues with a projection of a globe onto a cylinder area. This is why Greenland, Russia and Canada shrink so much in height and width in the animation, they are fairly high in latitude in the Northern Hemisphere. Also important is that the closer you are to the poles, the more the distortion when a country is shown on the Mercator projection. Since longitude lines converge at the poles, but are parallel on a Mercator, the closer a part of a country is to the poles, the more that part will get stretched wider relative to a part of a country that is not as close to the poles. As a clear example, see what happens to the southern part of Australia, relative to the northern end. Similarly, the latitude lines also get further apart on a Mercator projection, while on a globe they stay equidistant. This means that the parts of countries that are nearer the poles will get taller, i.e. stretched out from a north-south perspective relative to parts of countries that are further from the poles. You can see this clearly in the northern ends of Russsia and Greenland, where the tops get smushed down.

This next graph shows each country plotted with their actual land area and apparent land area as shown on a Mercator projection. The further the countries are from the 1:1 line the greater the overestimate of their size from the Mercator (also color coded to be red). It is a logarithmic plot showing many different orders of magnitude in country size. The table also shows the top 10 countries whose size is overestimated (and the difference in land area in square kilometers or as a percentage reduction from the size in the Mercator projection).

As it shows, Greenland is the country that has the largest percent difference between its apparent size in a Mercator projection and it’s real size (it’s only about 1/4 of the apparent size). And Russia is the country with the largest absolute difference between these two sizes.

This is the original graph that keeps the shape of the countries exactly the same and just scales the size. This is incorrect because as you move towards the poles the distances between longitude lines decreases. As a result the tops (northern ends) of countries will shrink more than the bottoms (southern ends) of countries in the Northern Hemisphere and vice versa in the Southern Hemisphere.

#### Old map that changes sizes but incorrectly preserves the Mercator shape

Calculations:

I calculated the area in two ways, one assuming latitude and longitude are rectangular coordinates (i.e. Mercator projection) and the other was the actual area.

The new coordinates needed to draw the “real size” of the countries are derived by calculating the distance between the center of the country and each of the coordinates in the country’s shapefile. As you move towards the poles on a globe, the distance between longitude lines decreases as a function (cosine) of latitude. In a mercator projection, the longitude lines are shown as equi-distant regardless of latitude. In this calculation, we create a new set of coordinates by calculating the distance between the center of the polygon and each set of coordinates and change the coordinates to reflect the shrinking of distance between longitude lines as you head towards the poles.

In the previous version of this animation, I calculated the latitude and longitude coordinates for the outline of the “real” size by modifying the original latitude and longitude by the ratio of these two areas to draw the new smaller, “real” country size.

Data and tools: This visualization was made using the Leafletjs javascript mapping library and country shapefiles (converted to geojson).

### 14 Responses to Real Country Sizes Shown on Mercator Projection (Updated)

Absence of the location of the equator makes things confusing.

2. Dory says:

I was wondering where you were able to find coordinate points as used in the Mercator map projection to make those calculations. Are there set points for each location like in traditional latitude and longitude or do they change?

• chris says:

The ‘outlines’ of all the countries is a series of points, which are specified as latitude and longitude coordinates. You can find them in geojson format by googling “geojson countries”. These geojson polygons are plotted here using the Mercator projection using the leaflet javascript library. I recalculated the latitude and longitude coordinates so that the mercator projection would show the correct sizes.

3. Simon says:

I’m wondering how this is scaled between Mercator and Real. I’m assuming it’s accurate based purely on area (sqkm) based around a centroid; however, when I visually compare the northern border of the US with the southern border of Canada in the “real” view, it’s clear they don’t fit together. Is it fair to call it “real”?

• Julie says:

Canada and the USA segments fit together for me.
For those who wonder why the northern hemisphere shrinks so much, the equator runs through Borneo, which is low down on the map; at the top of the bottom third of the map. Most maps are very distorted to the Northern Hemisphere.

4. Mike Soulsby says:

Actually Mercator was a navigator and his map works for navigation, other projections don’t do that

• Ian says:

This makes sense. Thanks

• Peter G. says:

Of course Mercator doesn’t “work for navigation” in the general sense. Only a globe “works.” A heading selected on a Mercator projection will be wrong unless it’s due east, west, north, or south. The further you go away from the equator, the worse the error. If you’re starting out from 51º N—the latitude of Flanders, where Mercator was from—a Mercator-derived course from Bruges to Edinburgh could be so far off that you’d miss the UK entirely.

• Davef says:

All headings are correct on Mercator projection. If you followed a constant compass bearing from Bruges to Edinburgh it would be a straight line on a Mercator map and if you could keep to that exact bearing it would get you exactly there. It would not be the shortest route – for that you would follow a great circle but that does involve adjusting your compass bearing as you progress so you need to know where you are. Following a fixed compass bearing is only the shortest route if heading due north,south, east or west.

5. David, that is because when two thirds of the map is allocated to the northern hemisphere (see where the equator is, two thirds of the way down) and only one third to the southern hemisphere, then northern hemisphere countries are over-sized (hugely towards the top of the map) – hence this accurate representation of “shrinkage” when you represent them accurate to surface area. See the Peters Projection Map or the Hobo-Dyer, with the equator in the MIDDLE of the map in order to give an accurate representation.

6. David Wallance says:

Don’t understand why nearly all of the shrinkage is north of the equator. Shouldn’t it be distributed equally north and south?

• chris says:

The shrinkage is a function of latitude and the confusion stems from the fact that the equator isn’t shown on the map. Most countries lie north of the equator (which is south of the wide part of Africa and south of India).

• Paul Birks says:

David, If you look at the Map, Germany is dead centre, (map created by a German Cartographer, so the equator is in the bottom third of the map.

• george costanza says:

the northern hemisphere was in the pool!