Almost every world map you have ever looked at, including the one in your phone, uses the Mercator projection. Gerardus Mercator drew it in 1569 for sailors. A straight line on his map is a line of constant compass bearing, which is exactly what a navigator wants. The price is that the map has to stretch the world more and more as it moves away from the equator. At 41 degrees south, roughly Wellington, everything is drawn 1.3 times too wide and 1.3 times too tall, which makes it 1.8 times too big by area. At 54 degrees north, the middle of Britain, the stretch is 1.7 in each direction and 2.9 by area. Greenland, up near 72 degrees, is drawn ten times too big.

So New Zealand is inflated on the map, but everything it gets compared with in the northern hemisphere is inflated more. Britain, Scandinavia, Germany, Canada, Russia and Japan all sit further from the equator than we do. That is why New Zealand looks like a small island off the bottom corner of the map, when in fact it is bigger than the United Kingdom, seven tenths the size of Japan, and almost exactly the size of Colorado.

The tool above corrects for this in the only honest way. When you drag the shape, the country is not stretched or scaled in pixels. It is rotated across the surface of the globe as a rigid body, the same way you would slide a cut-out across a beach ball, and then drawn through the same projection as the map underneath. Whatever distortion the map applies at that latitude applies equally to New Zealand and to the country beneath it, so the comparison is fair. Slide it north and it visibly grows, because the map is growing, not the country.

Over Europe, Cape Reinga sits in Denmark, Wellington and Christchurch are in Germany, Dunedin is up in the Italian Alps and Bluff is in France. Over the United Kingdom, New Zealand overhangs at both ends, with Cape Reinga out past Shetland in the North Sea and Bluff across the Channel in France. Over Japan, the two countries are close in length and shape, which is not a coincidence. Both are long, thin, mountainous island chains riding the edge of the Pacific plate. Over the United States, the country reaches from Minnesota to Texas, most of the height of the lower 48 states.

The population column in the table is the number that surprises visitors most. The United Kingdom fits inside New Zealand with room to spare and holds about 13 times as many people. Japan is 40 percent larger by area and has 23 times the population. Colorado, almost exactly our size, has about six million people.

The coastline is the New Zealand polygon from Natural Earth’s 1:10 million dataset, simplified to about 2,300 points, with the Chatham Islands, Kermadecs and subantarctic islands left off so the shape is the three main islands and their neighbours. Every point is converted to a position on a unit sphere. When you drag or rotate, the tool builds a single rotation matrix that carries the country’s centre to the new spot and applies it to every point, then hands the result to the map to draw. Because a rotation of the sphere preserves every distance and angle, the area is exactly what it was at home.

The place names under the anchor points come from Natural Earth’s 1:110 million country and state boundaries, so a point near a coast may report the sea when a finer map would say land. The basemap is Esri’s light grey canvas, which uses the same Web Mercator projection as Google Maps and OpenStreetMap.