How big is a square?

TLDR: they’re about a mile wide.

The squares (or tiles to use the usual term in mapping software) that are imported into VeloViewer are the “level 14” tiles from the OpenStreetMap  . To get to level 14, you start at level 0 which is one tile representing the whole world. You then zoom in to split that tile into 4 equal-sized tiles, each with a side half the length of the first tile. This gets you level 1. Then you zoom in again splitting those four tiles into four tiles each, making a total of 16 tiles covering the whole world at level 2, each with a length of a quarter of the length of the original. Do this splitting procedure 12 more times and you get 4 to the power 14 tiles (268,435,456 tiles) covering the world. The length of the tile is half each time.

This means, at the equator, the size of a tile S = (circumference of the earth)/2^14.

But I don’t ride at the equator, as we get further away from there, the tiles get smaller as they head towards the North Pole, where they vanish to nothing. In fact the formula for the width of the tile harks back to school and trigonometry:

Size = Circumference of Earth * cos(latitude) / 2^14
     = 40,075km * cos(51.5 degrees) / 16,384
     = 1.523km
     = 0.95 miles.

But it’s best just to say “about a mile”.

Edited to add: OpenStreetMap has a page all about zoom levels

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