Werner cordiform world map: how country sizes change

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Werner cordiform projection: key facts and what it does to country sizes

Distortion class
Equal-area
Graticule type
Pseudoconic
Creator
Johannes Werner (based on Johannes Stabius' design)
Year
1514
Area
Preserved (equal-area projection)
Shape
Distorted: only the central meridian is free of distortion, and deformation grows with distance from it (strongest at the edges of the heart)
Distances
Partially preserved: true along every parallel and the central meridian, and from the North Pole to every point
Angles and directions
Distorted, especially near the outer margins

The Werner projection preserves area but treats shapes very unevenly. The entire central meridian is free of distortion, and every parallel keeps its true length, running as an arc of a circle around the North Pole. Angles suffer only through shearing: the farther from the prime meridian and the farther south, the more the grid slants. The North Pole is the notch at the top of the heart, and the South Pole its bottom tip. The area-distortion heatmap shows no differences at all here, because area is preserved at every point, so only the shapes of the ellipses and the angular isocoles tell you how good this map is.

The Tissot indicatrices show this very clearly. At 60°N they are almost circles across the whole row, and even at 150° longitude angles change there by only 13°. On the equator the ellipse at 30° longitude changes angles by 19°, the one at 90° by 53°, and the one at 150° by 80°. At 60°S and 150° longitude the change reaches 108°, and the long axis of the ellipse is nearly ten times its short axis. Every one of these ellipses still has the same area as its circle on the globe.

As a result, Greenland, far north and close to the central meridian, has an almost true shape here, and Poland's angles change by only about 3°. Few world maps show both of them this well. Drag Poland to Australia's position: it keeps its area but leans so far that its angles change by about 90°, much like Australia's own. New Zealand, at the edge of the heart, is distorted even more.

Werner cordiform map: frequently asked questions

Why does Greenland look almost right on the Werner map?

The whole central meridian is free of distortion, and Greenland lies far north, close to it. It keeps its area and almost its true shape, and Poland changes angles by only about 3°. On very few world maps do both look this good.

Where does the Werner cordiform map distort most?

In the south and far from the prime meridian. On the equator the ellipse at 30° longitude changes angles by 19°, at 90° by 53° and at 150° by 80°. At 60°S and 150° longitude the change reaches 108°, and the long axis is nearly ten times the short one.

Does the Werner map preserve area?

Yes, at every point, so the area distortion layer shows no differences at all. Only the shapes of the Tissot ellipses and the angular isocoles tell how good the map is. The North Pole is the notch at the top of the heart and the South Pole its lower tip.

What happens to Poland dragged to Australia's place?

It keeps its area but skews so much that its angles change by about 90°, like those of Australia itself. New Zealand, near the edge of the heart, is distorted even more.