A newsroom is building an interactive world map of population, and the design lead wants it in Web Mercator because that is what the tile provider serves. The data editor objects that Mercator makes the tropics — where most people live — look small. The editor in chief wants the disagreement settled with figures, not adjectives: how much bigger does Greenland appear than DR Congo on that map, and how much bigger is it really?
Measure four things from the countries layer and report them:
greenland_true_km2 — Greenland's area on the ellipsoid (geodesic, or an equal-area projection), km², whole numberdrc_true_km2 — the Democratic Republic of the Congo's true area, the same waygreenland_mercator_inflation — Greenland's planar area in EPSG:3857 divided by its true area, 2 decimalsapparent_ratio_greenland_drc — Greenland's planar EPSG:3857 area divided by DR Congo's planar EPSG:3857 area, 2 decimals — how many times bigger Greenland looks on the newsroom's mapWeb Mercator area is what you get by projecting the polygon to EPSG:3857 and taking the ordinary planar area of the result. That is not a trick: it is literally the number of map pixels each country gets.
These are where the teaching is. Read them twice.
Every world choropleth on a web map inherits this distortion, and being able to state it as a number is what lets a cartographer argue for a different projection.
Work the problem in whatever tool you like, then enter the answers here.
greenland_true_km2drc_true_km2greenland_mercator_inflationapparent_ratio_greenland_drc4 scored, 0 informational
Greenland's true area
20%DR Congo's true area
20%How many times Mercator inflates Greenland
30%How many times bigger Greenland looks than DR Congo
30%