A cartogram is a map where geographic areas are resized based on a variable like population, GDP, or disease rates instead of physical land area. The result looks like a familiar map that’s been stretched and squeezed: countries or regions with high values inflate while those with low values shrink. It’s one of the most effective ways to visualize data that would otherwise be hidden by the uneven relationship between a place’s size on a map and its actual importance to a dataset.
How Cartograms Work
On a standard map, Russia takes up about 11% of the world’s land area. But Russia is home to less than 2% of the global population. A population cartogram shrinks Russia down to roughly the size of Bangladesh, a country smaller than Florida that holds a comparable number of people. Canada, the second-largest country by land area with just 4 people per square kilometer, gets reduced to barely more than a thin line. Meanwhile, densely populated places like Bangladesh, Taiwan, and the Netherlands balloon in size to reflect how many people actually live there.
This reshaping forces viewers to see the world through the lens of the data rather than through geography. A standard map of global health outcomes, for example, gives enormous visual weight to sparsely populated regions like the Sahara or Siberia while cramming billions of people in South and East Asia into relatively small spaces. Cartograms correct that imbalance.
Types of Cartograms
There are three main styles, each with a different approach to distortion.
- Contiguous cartograms keep regions connected to their neighbors, preserving the overall shape of the map while warping boundaries. These are the most recognizable type. They look like the original map was made of rubber and pulled in different directions.
- Non-contiguous cartograms resize each region independently, which means gaps can appear between them. Individual shapes stay more recognizable, but the spatial relationships between places are harder to read.
- Dorling cartograms replace regions entirely with circles (or other geometric shapes) scaled to the data variable. They sacrifice geographic shape completely in exchange for clean, easy comparisons between values.
The Math Behind the Distortion
Early cartogram methods, pioneered by geographer Waldo Tobler in the 1960s, divided the map into small cells, then independently expanded or shrank each cell based on its data value. The problem: after resizing, the edges of neighboring cells no longer lined up. Tobler’s solution was to average the positions of mismatched corners, which produced a usable but imperfect result.
Later approaches abandoned the cell grid entirely. One method, developed by Gusein-Zade and Tikunov, treated high-population areas as sources of a repulsive force that pushes map points outward. This created a smooth, continuous displacement across the entire map surface rather than a patchwork of individually resized pieces.
The most widely used modern algorithm, published by Michael Gastner and Mark Newman in 2004, treats population density like heat. Imagine the data value in each region as a concentration of some substance. The algorithm lets that substance diffuse outward, the way heat spreads from a hot object into cooler surroundings, until the density is equal everywhere. As the “substance” flows, it carries the map boundaries with it, gradually inflating dense areas and deflating sparse ones. To keep the map from expanding infinitely, the area of interest floats in a surrounding “sea” set to the average density of the whole map. The process runs until the density has fully equalized, at which point each region’s area on the map is proportional to its data value.
This diffusion approach produces cartograms that look smooth and organic, with minimal topological errors like overlapping boundaries.
Origins of the Cartogram
Cartograms date to the second half of the 19th century. The French economist and geographer Pierre Émile Levasseur is credited as the first internationally recognized figure to use cartogram-like representations, publishing examples in his 1875 textbook on French geography. Around the same time, American school atlases included similar visualizations under names like “comparative chart” and “statistical diagram,” though they weren’t called cartograms yet.
The Hungarian-American cartographer Erwin Raisz, working in the early-to-mid 20th century, was the first to develop a scientifically grounded framework for cartogram design. The technique grew more popular from there but remained labor-intensive until computers made the underlying calculations practical.
Where Cartograms Are Used
Election maps are probably the most familiar application. A standard map of U.S. presidential results gives enormous visual weight to geographically large, low-population states in the West, making it difficult to gauge the actual vote totals each party received. A population cartogram resizes each state or county to reflect how many voters live there, giving a far more accurate picture of the electoral landscape.
In epidemiology, cartograms solve a persistent problem with disease mapping. Standard maps of disease rates exaggerate the visual prominence of low-density rural areas and compress potential disease clusters in dense urban areas. Researchers have used population cartograms as a base layer for epidemiological maps so that the visual size of a cluster on the map corresponds to the number of people at risk. This makes it possible to spot statistically significant clusters by looking at the rate, area, and shape of a region directly on the cartogram, rather than relying on separate statistical tables.
Economics and development organizations use cartograms to show global patterns in GDP, carbon emissions, internet access, and similar metrics. Our World in Data, for instance, publishes a global population cartogram specifically because standard world maps distort how people think about living conditions: improvements affecting billions of people in South Asia can look minor on a conventional map, while changes in sparsely populated regions look disproportionately large.
Strengths and Limitations
The biggest advantage of a cartogram is also its core purpose: it makes data visible that a standard map would hide. When you’re looking at a choropleth map (the kind where regions are shaded by color to represent values), your eye is naturally drawn to the largest areas, regardless of whether those areas matter most to the dataset. Cartograms fix this by making visual size proportional to the variable that actually matters.
The tradeoff is that cartograms distort geography, which can make it harder to identify specific places. Readers who aren’t familiar with the original map may struggle to recognize warped boundaries. Contiguous cartograms preserve topology (neighbors stay neighbors), but individual regions can become unrecognizable when their data values differ sharply from their geographic size. Dorling cartograms give up shape entirely, which makes comparison easy but geographic context almost nonexistent.
There’s also an inherent tension between mathematical precision and visual clarity. A perfectly area-accurate cartogram can produce shapes so distorted they confuse more than they inform. Most practical cartograms compromise slightly on accuracy to keep the map readable.
Tools for Creating Cartograms
If you want to make your own, several software options exist across skill levels. ArcGIS Pro, the professional GIS platform from Esri, includes a built-in “Generate Contiguous Cartogram” tool that accepts any polygon dataset and a numeric field, and can be scripted in Python for batch processing. QGIS, the free open-source alternative, offers cartogram plugins. For statistical programming, R has dedicated packages (notably “cartogram” and “Rcartogram”) that implement the Gastner-Newman diffusion algorithm. For quick, no-code results, web tools like the World Mapper project offer pre-built cartograms on dozens of global datasets.
The computational demands have dropped significantly since the early days. What once required mainframe processing time can now run on a laptop in seconds for most datasets, making cartograms accessible to journalists, students, and anyone working with geographic data.