SignificanceGeographic maps are a popular means to visualize spatial statistics. Conventionally, each map region is displayed with an area proportional to the actual land area. But equal-area maps can grossly misrepresent demographic data: Densely populated cities should be given more prominence than large, but sparsely populated territories. Cartograms solve this problem by rescaling map regions in proportion to, for example, population or gross domestic products. Until now, it has generally been cumbersome or slow to calculate map projections for contiguous cartograms. Here we describe and benchmark a fast flow-based algorithm that computes cartograms in a matter of seconds, yet maintains the strengths of previous methods—a development which may lead to a more widespread adoption of cartograms.