what your map says vs what the planet says, for the worst offenders. ratio = visible area ÷ real area.
same dataset, same math, one run. africa is drawn — times its true size; greenland is drawn — times its true size — so on this map greenland and africa appear nearly similar, while in reality africa is about — times larger. the textbooks say 14[1]; the geometry says —.
Each country polygon from Natural Earth 110m[3] was measured twice:
true area — spherical polygon area on a sphere of radius 6371008.8 m (Chamberlain–Duquette formula: sum over edges of Δλ·(2+sin φ₁+sin φ₂)·R²/2, absolute value, holes subtracted).
visible area — the same polygon projected to Web Mercator (x=λ, y=ln tan(π/4+φ/2), latitude clamped to ±85.051129° — the Web Mercator square cut[2]), then measured by the shoelace formula in the projected plane. the ratio of the two is the inflation.
consequences fall straight out of the projection: mercator area scale is sec²φ,[1] so a country at 60° north is drawn about ×4 bigger than its true area, and everything near the equator is drawn at roughly true size. the lie is geometric, not editorial — but it is the lie every web map tells you by default.
● every source fetched, read, and quoted verbatim 2026-08-27; the numbers on this page were computed from [3] by the formulas described above — the ledger and build scripts are in the build log.
[1] Mercator projection — Wikipedia — “the Mercator projection inflates the size of lands the farther they are from the equator”; “Greenland appears the same size as Africa, when in reality Africa's area is 14 times as large”
[2] Web Mercator projection — Wikipedia — “Services such as Google Maps cut off coverage at 85.051129° north and south”
[3] Natural Earth — About — “versions of Natural Earth raster + vector map data found on this website are in the public domain”