← Daily Dose Fourteen Greenlands — Daily Dose No. 037
Daily Dose  /  Aug 21, 2026  /  Map Projections

Fourteen
Greenlands

Almost every map you have ever seen was built for sailors in 1569. It keeps compass bearings honest by stretching the world sideways and lengthwise as you move away from the equator — and the further north or south a place sits, the bigger the map draws it. The distortion is not a bug. It is the entire mechanism. Here is exactly how much it costs.

14×
Africa's true area divided by Greenland's: 30,370,000 km² against 2,166,086 km². On a Mercator map they look like near-equals.
CIA World Factbook · UN Statistics Division
01 — The map itself

One projection, two very different worlds

Below is a schematic Mercator world, shaded by how much the projection inflates each landmass. The dashed teal outline is Greenland moved to the equator at its true size — the same island, drawn at the scale Mercator uses for Africa.

ANTARCTICA — 14.2M km2, cannot be drawn: Mercator sends the poles to infinity75°60°45°30°-30°GREENLAND~10x too bigTRUE SIZEGreenland, at the equatorAFRICA14x Greenland · 30.37M km2
1× — drawn true ~4× ~10× — Greenland true size at the equator

Hand-simplified schematic, not survey-accurate. Shading uses sec² of each landmass's approximate centre latitudeillustrative

02 — The mechanism

The map lies by sec² of your latitude

Mercator's rule is simple and exact: to keep angles true, it must stretch north–south by the same factor it stretches east–west. That factor is sec(latitude), so area grows by its square. At 60° you are drawn four times too large. At 80°, thirty-three times.

Area inflation vs latitude · sec² of latitude
1x10x20x30x20°40°60°80°0° · 1.0x80° · 33.2x60° · 4.0x
Five circles of identical true area, as Mercator draws them
30°45°60°75°

Each disc covers the same number of square kilometres on the globe. The 75° disc is drawn 14.9× the area of the one on the equator.

03 — The spectrum

How much bigger the map makes you

Read it as a tax on distance from the equator. Nairobi pays nothing. Stockholm pays four times. Northern Greenland pays more than ten. The web's own maps stop at 85.05° — not out of restraint, but because the arithmetic runs away.

1.00x1.07x15°1.33x30°2.00x45°4.00x60°14.9x75°134x85°

Web Mercator (EPSG:3857) is clipped at ±85.0511287798° = arctan(sinh π), the latitude that makes the world a perfect square for tiling. Beyond it the projection has no finite value: the poles are infinitely far away, which is why Antarctica — 14.2 million km² — simply cannot be drawn.

04 — The mismatch

What your eye gets wrong

Ranked by true area. The bar shading is the Mercator inflation each landmass receives — so the darkest bars are the ones your mental map has most badly oversized.

Africa30.37M1.0xRussia17.10M4.5xCanada9.98M4.0xUnited States9.83M1.7xChina9.60M1.5xBrazil8.52M1.0xAustralia7.69M1.2xIndia3.29M1.2xDR Congo2.34M1.0xGreenland2.17M10.5xMexico1.96M1.2xAlaska1.72M5.2xtrue area, million km2Mercator inflation
Four comparisons almost nobody guesses right
Greenland2.17M km2
<
DR Congo2.34M km2
Congo is 8% larger
Alaska1.72M km2
<
Mexico1.96M km2
Mexico is 14% larger
Norway+Sweden+Finland1.17M km2
<
India3.29M km2
India is 2.8x larger
Russia17.10M km2
<
Africa30.37M km2
Africa is 1.8x larger

Kai Krause's 2010 diagram made the point another way: the United States, China, India, Japan and the whole of Europe fit inside Africa's outline with room to spare.

05 — The alternative

Equal Earth, published 2018

Gauss proved in 1827 that no flat map can keep both shape and area. So the question is never “which map is correct” but “which error can you afford.” Equal Earth gives up a little shape to make every square centimetre worth the same number of square kilometres.

EQUAL EARTH (2018) — every square centimetre is the same number of square kilometres

Bojan Šavrič, Tom Patterson & Bernhard Jenny, IJGIS, August 2018. Schematic rendering of the projection's true equal-area geometry. Shipped in PROJ, QGIS and ArcGIS as +proj=eqearth.

06 — The turn

456 years, and the argument is live again

The complaint is old. What changed in 2025 is who is making it — and that the default map now lives on two billion phones rather than a classroom wall.

1569Mercator publishes18 copper plates1855James Gallequal-area alternative1973Arno Petersrelaunched as justice2005Google MapsWeb Mercator ships2017Boston schools~600 maps, ~$12,0002018Equal EarthSavric / Patterson / Jenny2025African Union#CorrectTheMap, Aug 14456 years of the same argument
2B+
monthly Google Maps users, all served Web Mercator by default.
Google, 2024
200+
major world map projections exist. One of them is on nearly every screen.
The Conversation, 2025
Aug 14, 2025
the African Union endorses #CorrectTheMap — the largest body yet. The World Bank says it is phasing Mercator out.
Reuters / NPR, 2025
Why it matters

A map is an argument about what is worth seeing

Mercator was not propaganda; it was a navigation instrument, and for holding a compass bearing across an ocean it is still the right tool. The distortion only becomes a lie when the instrument is repurposed as a picture of the world — on a classroom wall, in a news graphic, behind a dataset. A continent of 1.5 billion people has spent four centuries being drawn small.

  • Never use Mercator for anything shaded by area — choropleths, population maps, land-use, emissions. Use an equal-area projection.
  • Ask for +proj=eqearth. Equal Earth is one line in QGIS, ArcGIS, PROJ, D3 and matplotlib.
  • Drag a country to the equator on thetruesize.com and watch it collapse. It is the fastest cure for the illusion.
  • Keep Mercator where it earns its keep: navigation, and any zoomed-in local map where the distortion is negligible.

Sources & notes

  1. Mercator's 1569 wall mapNova et Aucta Orbis Terrae Descriptio ad Usum Navigantium Emendate Accommodata — 18 engraved copper sheets, 131 × 208 cm, drawn so that a constant compass bearing (a rhumb line) appears as a straight line. Historical record of the 1569 map.
  2. Area figuresCIA World Factbook and UN Statistics Division. Africa 30,370,000 km²; Russia 17,098,246; Antarctica ~14,200,000; Canada 9,984,670; United States 9,833,517; China 9,596,960; Brazil 8,515,767; Australia 7,692,024; India 3,287,263; DR Congo 2,344,858; Greenland 2,166,086; Mexico 1,964,375; Alaska 1,723,337.
  3. The sec² ruleMercator's areal scale factor equals sec²(latitude) exactly — it follows from the projection's definition. See J. P. Snyder, Map Projections — A Working Manual, USGS Professional Paper 1395, 1987.
  4. Web Mercator (EPSG:3857)Defined only between ±85.0511287798°, which is arctan(sinh π) — the latitude that makes the world a perfect square for power-of-two tiling. EPSG Geodetic Parameter Dataset. Used by Google Maps, Apple Maps, Bing, Mapbox and OpenStreetMap.
  5. Google Maps scaleMore than 2 billion monthly users (Google, 2024).
  6. Equal Earth projectionB. Šavrič, T. Patterson & B. Jenny, “The Equal Earth map projection”, International Journal of Geographical Information Science, August 2018 — an equal-area pseudocylindrical projection built explicitly in response to the 2017 Boston decision.
  7. Boston Public SchoolsSwitched classroom maps to Gall–Peters in March 2017: about 600 laminated maps, roughly $12,000, for a 57,000-student district. WBUR and The Boston Globe, March 2017.
  8. #CorrectTheMapCampaign by Africa No Filter and Speak Up Africa; endorsed by the African Union on 14 August 2025 — the largest body to sign on. The World Bank told NPR it is phasing out Mercator in favour of Equal Earth. Reuters / NPR, August 2025.
  9. The True Size of AfricaKai Krause, 2010 — the diagram fitting the USA, China, India, Japan and all of Europe inside Africa's 30.37M km² outline.
  10. Context figuresMore than 200 major world map projections exist; the #CorrectTheMap petition has passed 4,500 signatures. The Conversation, August 2025.
  11. Why no map can winGauss's Theorema Egregium (1827): a sphere cannot be flattened without distortion. Every projection chooses what to sacrifice — Mercator sacrifices area.
  12. Illustrative, not measuredThe per-country inflation multipliers (×) are computed as sec² of each landmass's approximate centre latitude. They are illustrative of the scale of the effect, not integrated measurements of drawn area. The world map here is hand-simplified and schematic, not survey-accurate.
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