How big is it, really

One country's outline laid on another's at the same scale, each drawn true to its own area. Drag the smaller one to carry it about, pull either side of the frame to make the whole figure bigger, zoom in on it, or swap the two.

Two places, drawn to one scale. Countries, US states, and the first-order divisions of the eight other countries big enough for anybody to ask about: Russia's oblasts and krais, Australia's states, and the provinces of India, China, Brazil, Canada, Indonesia and South Africa. The number tells you it is two hundred and thirty-eight times, and the number is correct, and it is still hard to believe until you have seen the speck. Drag it about: that is the point of the picture. A shape sitting in the middle answers less than one you can carry to the corner you were wondering about.

Two more things you can do to it, and neither of them moves the ratio. Hover either side of the frame and pull, and the whole figure grows until it is as wide as your window. Zoom with the two buttons under it, with the wheel, with a pinch, or with plus and minus once the figure has the focus, and both shapes come closer together, never one of them without the other. The picture cannot be made to say a number the sentence above it did not say.

And it does not have to be two. The third box adds another shape to the same canvas, up to six of them together, each one laid out beside the others at the one scale. Their names are the row of buttons under the boxes, in the order they are drawn across, and pressing a name takes that shape off again. The count under the picture stays the ratio of the two you asked about, and says how many of the others are yours.

You get here from an answer. Ask the calculator how many times does Switzerland fit into the US and the same figure is drawn underneath it, set to the same two shapes, and the link out of it opens this page already there.

Why it is not the map you have seen

Every size comparison you have met is drawn on Mercator, and Mercator is the one projection that gets areas wrong. It has to: it keeps angles true, which is what it was for, and something has to give. On Mercator, Greenland reads about the size of Africa and is fourteen times smaller. Alaska reads about the size of Brazil and is five times smaller. The best-known page of this kind draws its overlay on Mercator and prints, under the picture, that Mercator "distorts the size of regions near the poles", which is an honest note attached to a picture that should have been drawn another way.

This one uses Lambert azimuthal equal-area, centred on each shape's own middle. Equal-area means what it says: a square kilometre is a square kilometre anywhere on the drawing, which is the one property a size comparison cannot do without. Every projection trades something, and this one trades shape, so centring it on the country being drawn puts the distortion out in the parts of the world that are not on the page. Switzerland drawn about Switzerland looks like Switzerland.

Then the part that matters more than the projection. The outlines carry shape and nothing else, and how big each thing actually is comes from the same table the calculator's answer came from. Each shape is scaled so the ground it covers on the page is the ground it covers on the earth. So the picture and the number cannot disagree: a map that contradicted the ratio above it would have to contradict itself first.

What that costs, said plainly: the two shapes are drawn in projections centred on two different places, so laying one inside the other is an illustration of a ratio and not a map of a nesting. Nobody is being told where in the United States the Switzerland goes. The areas are exact and the arrangement is not a claim.

What it will not draw

Only two areas, and only where both have an outline. Ask it by population and it draws nothing, because the two countries would be the same two shapes and the number underneath would be a different number, and a picture that disagrees with its own answer is worse than no picture. Golf balls, planets, lakes and rivers have no outline at all, and neither has Vatican City, which is too small to appear in any published set of them. Eleven countries are left out because their outline could not be made faithful at this size: an archipelago drawn without its islands is not that archipelago, and the Maldives came out at a ninth of its own area before it was dropped. Cities have no shape either, and the reason is measured rather than assumed: the published urban footprints merge into their neighbours, and the one for Beijing covers more ground than Ireland.

The other figures are the day ring, the compass and the clock board.