Map Tile Maths

Metres per pixel, map scale (1:N) and tile width on the ground for a zoom level and latitude.

Convert latitude/longitude to Web Mercator EPSG:3857 metres, or metres back to degrees, with scale distortion.

Convert a tile x/y/z to a Bing Maps quadkey, or a quadkey back to x/y/z, with its parent and four children.

Latitude/longitude and EPSG:3857 metre bounds of a slippy-map tile x/y/z, with its centre and ground size.

Number of slippy-map tiles covering a lat/lon box for a zoom range, with a rough storage estimate at your average tile size.

Slippy-map tile x/y/z containing a latitude and longitude, plus the pixel position inside the 256 px tile.

Highest map zoom level at which a lat/lon bounding box fits a viewport of given pixel size, with centre and tile span.

Zoom-level ladder 0 to 24: tiles per side, metres per pixel, map scale and typical use, at a chosen latitude.