Map tile for a point (XYZ, TMS, quadkey)

Model: Spherical Web Mercator (EPSG:3857) tile grid

Show your work

1. Tiles across the map

   $$n=2^{\mathrm{zoom}}$$

   2^12 = 4,096

2. Column

   $$x=\lfloor (\mathrm{lon}+180)/360\times n\rfloor$$

   ⌊(-79.982222 + 180) / 360 × 4,096⌋ = 1,137

3. Row

   $$y=\lfloor (1-\ln (\tan \phi +\sec \phi )/\pi )/2\times n\rfloor$$

   from latitude 40.446111° at zoom 12 = 1,544

4. Tile

   tile = zoom/x/y

   12/1137/1544 = 12/1137/1544

The same steps an agent gets from the MCP server with explain: true.

Accuracy: Exact tile; resolution on the Web Mercator sphere

When to use this: Use this to find which web map tile a point falls in at a zoom level, in XYZ, TMS, and quadkey form, with the ground resolution at that point. It is how a coordinate is turned into a tile request, a cache key, or a pyramid lookup. It is also how a point is matched to the imagery or terrain tile that covers it, which is the first step in reading a value out of a tiled raster.

Limitations: Web Mercator distorts with latitude, so a tile covers far less ground near the poles than at the equator, and the projection stops short of the poles themselves. The tile is an area containing the point, and the y convention matters: XYZ and TMS number rows in opposite directions. At high zooms the tile numbers grow large, and a coordinate outside Web Mercator's latitude limits has no tile at all rather than one at the edge.

Worked example: Pittsburgh at zoom 12. Source: add-spatial-indexing-and-raster scenario: 12/1137/1544, TMS y 2551, quadkey 032001112001, about 29.08 m/px. It is golden test vector v001, and every build checks the tool still gives its answer within its tolerance.

Review: Not yet independently reviewed by a GIS professional.

Last verified: 2026-09-18, when a maintainer last confirmed this tool's sources at the issuer. See the sources ledger.

Status: version 1.0.1, core 0.1.0. See this tool in the verification report.

Changes

• 2026-09-23, fixed: Tile from point (version 1.0.1) rejected a tile size given as the number 512 ("Tile size must be a string"). Every tool now accepts a numeric option such as 512 as a number or as text. Changelog
• 2026-09-19, result change: The geohash encoder, map tile for a point, tile bounds, H3 grid disk, and haversine distance are now stable, so their results no longer carry the EXPERIMENTAL_TOOL warning; the Web Mercator clamp and pentagon warnings moved to the first position. Each matches published worked examples (Wikipedia, the mercantile README, the Bing Maps Tile System, H3 C, and Rosetta Code) and agrees with a separately written library on 250 to 1,000 cases. No numbers changed. Changelog

Checked against: 25 golden test vectors (download the test vectors, each with its source and tolerance). See how results are checked and every source.

Sources

• Slippy map tilenames, OpenStreetMap Wiki, Current wiki page. Lon./lat. to tile numbers, tile numbers to lon./lat., resolution and scale.
• Bing Maps Tile System, Microsoft, Online documentation. Tile coordinates and quadkeys; ground resolution = cos(lat) × 2π × 6,378,137 / (256 × 2^level).

Terms

TMS: Tile Map Service

A web map tile numbering like XYZ, but with rows counted from the south edge. Source: Slippy map tilenames

XYZ: XYZ web map tiles

The common web map tile numbering, zoom/x/y, with rows counted from the north edge. Source: Slippy map tilenames