What Is a Cartogram? Definition, Types, Examples, and How to Make One

A cartogram is the map that looks wrong on purpose. Countries bulge, shrink, and slump into unfamiliar shapes, and that distortion is the data. If you have seen a world map where India and China swell to fill half the image, or an election map where a single dense city outweighs an entire rural state, you have read a cartogram.

This guide covers what a cartogram is, the four types you will actually meet, how they compare to choropleth maps, and how to build one from boundary data.

What a cartogram is

A cartogram is a thematic map in which the area of each region is proportional to a data value instead of its physical size.

Everything else about the map stays familiar. Regions keep their neighbours, their rough position, and often their colour scheme. Only the area carries the number. A population cartogram of Europe makes the Netherlands larger than Finland, because the variable is people rather than square kilometres.

Value-by-area maps go back to the 1870s, when French statisticians drew regions as squares scaled to population. Computers made the contiguous version practical: the diffusion algorithm published by Michael Gastner and Mark Newman in 2004 is still the method behind most world cartograms you see today.

Why cartograms exist: area bias

Open any choropleth map of a national election. The map is mostly the colour of whichever party wins in rural districts, because rural districts are enormous and cities are small. The colour is right in every district and the overall impression is wrong.

That failure has a name: area bias. A choropleth map encodes value in colour, but the eye reads area first. Big regions get more visual weight than their numbers deserve.

A cartogram fixes the mismatch by moving the variable into the channel the eye already prioritises. Scale each district by votes cast and the picture matches the result.

The same trap shows up far outside elections:

• Population maps where Siberia, the Sahara, and the Australian outback dominate
• Sales by territory, where a rep covering three provinces looks ten times more important than one covering a capital city
• Disease burden, where sparse regions with few cases fill most of the frame
• Internet users by country, where land area and connectivity have almost no relationship

Types of cartogram

Four families, in rough order of how often you will meet them.

Contiguous cartograms keep every region attached to its neighbours and stretch the shapes until the areas match the data. These are the warped world maps from Worldmapper. They preserve topology, which helps readers find their bearings, but shapes distort heavily and small regions can become slivers.

Non-contiguous cartograms shrink each region around its own centre, keeping the original shape and letting gaps open between neighbours. Judy Olson introduced the method in 1976. Shapes stay recognisable and the arithmetic is simple. The cost is the empty space, which some readers misread as missing data.

Dorling cartograms replace each region with a circle sized by the value, then nudge the circles apart until they no longer overlap. Named after Danny Dorling, who popularised them in the 1990s. Shape is gone entirely, so the map reads as a diagram, and it handles extreme ratios gracefully. Use it when your values span several orders of magnitude.

Grid and mosaic cartograms give each region a tile, or a block of tiles, on a regular grid. US news desks lean on these for election night, where every state gets one hexagon or a hexagon per electoral vote. They are the easiest to read at a glance and the least faithful to geography, and because the layout is hand-built they only exist for well-known region sets.

Demers cartograms are the square cousin of Dorling circles, useful when you want a tighter packing and less wasted space.

A worked example: enforcement cameras in Europe

Here is the same technique on data we collect ourselves. The MapAtlas Camera Index is a crowd-sourced record of speed, red light, average speed, and variable limit cameras, published under CC BY 4.0 from a 2024-05-21 snapshot. The figure below plots the 40 European countries in the index twice: once with circles sized by land area, once with circles sized by cameras recorded.

Same countries, same positions, same circle technique, one variable swapped. The left panel is a map of Europe as geography draws it, where Ukraine, France, Spain, and Sweden dominate. The right panel reorders the continent entirely.

Italy holds 10,707 cameras on 302,073 km². Ukraine, the largest country in the frame at 603,550 km², holds 348. On a choropleth those two would be shaded by rate and Ukraine would still take up eight times more of the image. On the cartogram Italy is the largest circle on the map, which matches the number.

Belgium is the case that makes the format worth the trouble. At 30,528 km² it is a speck in the left panel and the fifth largest circle in the right one, at 884.8 cameras per 10,000 km², the densest enforcement in the index.

The method matters as much as the picture. These 40 countries hold 42,762 of the 106,646 cameras in the index, which covers 106 regions worldwide. The index is built from driver reports, so a country with few cameras in it may be lightly enforced or lightly reported, and the two are not separable from this data alone. Read the right panel as reported enforcement density, and treat the thin countries as a question rather than an answer. Where the index can be checked against OpenStreetMap, four of ten European countries agree within 10 percent, which is covered in the enforcement camera article.

Cartogram vs choropleth map

The two are often presented as rivals. They encode the same data in different channels.

A choropleth map keeps true geography and puts the value in colour. It is accurate for navigation, familiar to every reader, and vulnerable to area bias. It handles rates well: cases per 100,000 people, percentage of households on fibre, average price per square metre.

A cartogram distorts geography and puts the value in area. It shows totals honestly, it is harder to read cold, and it needs a caption explaining what the sizes mean. It handles counts well: number of people, total revenue, seats won.

The useful test is whether your number is a rate or a count. Rates belong on a choropleth. Counts, especially counts that vary by orders of magnitude, belong on a cartogram.

You do not have to choose. A common production pattern is a cartogram layout with a choropleth fill: area shows how many people, colour shows how they voted. Two variables, one map. That map needs a careful map legend, because the reader now has to decode two channels.

Cartogram examples

Recurring uses, each of which fails as a plain choropleth:

• World population by country. The classic. Nigeria, Bangladesh, and Indonesia swell; Canada, Russia, and Australia collapse.
• Election results by constituency. Area becomes votes or seats, so the map matches the parliament.
• GDP or trade flows. Financial centres dominate, which is the point.
• Carbon emissions per country, usually paired with a second cartogram of population to show the gap.
• Hospital capacity or case counts, where a per-capita choropleth hides how concentrated the load is.
• Retail footprint by region. Store count or revenue by area, useful for territory planning where a choropleth flatters empty regions.

Cartograms in AP Human Geography

Cartograms turn up in the AP Human Geography thematic map unit, next to choropleth, dot density, isoline, and proportional symbol maps. The definition the exam wants is short: a cartogram is a map whose region sizes are scaled to a statistic rather than to land area, most often population.

Two points earn most of the credit. First, area encodes the variable. Second, distortion is the feature, because it lets a reader compare a small dense country against a large empty one without the land area shouting over the number. If you need the wider family, the types of maps guide sets out where each thematic map fits.

How to make a cartogram

Three ingredients, the same three as any thematic map:

1. Boundary polygons for your regions, with a stable identifier on each: ISO 3166 for countries, NUTS for EU regions, national postal codes for local work.
2. One numeric value per region, keyed to those identifiers. It has to be a count for the area encoding to mean anything.
3. An algorithm that resizes the polygons, or replaces them with scaled shapes.

For contiguous cartograms, use an existing implementation rather than writing your own. The diffusion method is subtle and the fast flow-based variant published in 2018 is what most tools now ship:

• QGIS with the Cartogram3 plugin, for desktop work
• R with the cartogram package, which covers contiguous, non-contiguous, and Dorling in a few lines
• go-cart.io, a browser tool that takes a GeoJSON file and a value column
• cartogram-chart on npm, if the output has to live in a web app

Dorling cartograms are the one type worth building yourself, because the maths is a centroid and a square root. Radius scales with the square root of the value, so that circle area stays proportional:

import centroid from '@turf/centroid';

const MAX_RADIUS_PX = 48;
const maxValue = Math.max(...Object.values(valuesByRegion));

const circles = regions.features.map((feature) => {
  const value = valuesByRegion[feature.properties.id] ?? 0;
  return {
    type: 'Feature',
    geometry: centroid(feature).geometry,
    properties: {
      id: feature.properties.id,
      value,
      radius: MAX_RADIUS_PX * Math.sqrt(value / maxValue),
    },
  };
});

map.addSource('cartogram', { type: 'geojson', data: { type: 'FeatureCollection', features: circles } });

map.addLayer({
  id: 'cartogram-circles',
  type: 'circle',
  source: 'cartogram',
  paint: {
    'circle-radius': ['get', 'radius'],
    'circle-color': '#0958a8',
    'circle-stroke-color': '#ffffff',
    'circle-stroke-width': 1,
    'circle-opacity': 0.85,
  },
});

That renders overlapping circles. Turning it into a true Dorling cartogram means one more step: iterate over the circles and push any overlapping pair apart along the line between their centres until the gaps close. Twenty or thirty iterations is usually enough for a few hundred regions, and the result stays close to real positions.

Scaling by the square root matters. Scale the radius by the raw value and a region with ten times the population looks a hundred times bigger.

Pitfalls to watch

Unrecognisable shapes. Heavy distortion loses readers. Label generously, keep a familiar reference map next to it, or animate from true geography into the cartogram.

Rates on an area channel. A cartogram of unemployment rate is close to meaningless, because area then encodes a percentage. Put counts on area and rates on colour.

Zero and near-zero values. Regions with a value of zero vanish. Decide in advance whether they are dropped, drawn at a minimum size, or called out in a note.

No legend. Area is harder to judge than colour, so give the reader one calibration circle or square with a value on it. Without it the map is decorative.

Small multiples. Cartograms are poor candidates for a grid of small maps. Each one distorts differently, so the reader has to relearn the shape every time.

Where MapAtlas fits

Cartograms need clean boundary geometry with stable IDs, which is the slow part of the job. The Dynamic Maps API serves country, region, and postal code boundaries as vector tiles keyed to ISO 3166, NUTS, and national postal systems, so the join between your values and the geometry is a lookup rather than a data-cleaning project. The boundaries are EU-hosted and version-stamped, which matters when a map has to be reproducible months later.

For the values themselves, the GeoEnrich API returns per-region aggregates on the same identifiers, so a single dataset drives both the cartogram and the table beside it. If your data is a rate rather than a count, start with the choropleth map guide instead, and the thematic map guide covers how the whole family fits together.