Map tile parent and children
The parent tile one zoom out and the four children one zoom in of a z/x/y tile or quadkey, in XYZ or TMS numbering.
The parent of this tile is 11/568/772.
| Tile | Quadkey |
|---|---|
| 13/2274/3088 | 0320011120010 |
| 13/2275/3088 | 0320011120011 |
| 13/2274/3089 | 0320011120012 |
| 13/2275/3089 | 0320011120013 |
- Parent quadkey
Provenance
- Computed by
- indexing.tile.family 1.0.0, core 0.1.0
- Model
- Parent = (z − 1, ⌊x/2⌋, ⌊y/2⌋); children = (z + 1, 2x + i, 2y + j). TMS y = 2^z − 1 − XYZ y
- Accuracy
- Exact
- Notes
- None
- Cites
- OpenStreetMap Wiki, Slippy map tilenames; Microsoft, Bing Maps Tile System
Something look off?
How we got thisFormula, worked example, sources, and proof
Model: Parent = (z − 1, ⌊x/2⌋, ⌊y/2⌋); children = (z + 1, 2x + i, 2y + j). TMS y = 2^z − 1 − XYZ y
Show your work
Children
(z + 1, 2x + i, 2y + j) for i, j in 0, 112/1137/1544= 4 tilesParent
(z − 1, ⌊x / 2⌋, ⌊y / 2⌋)12/1137/1544= 11/568/772
The same steps an agent gets from the MCP server with explain: true.
Accuracy: Exact
When to use this: Use this to walk a tile pyramid: the parent one zoom out, the four children one zoom in, with their quadkeys. It is the step you need when invalidating a cache upward, splitting a download, or reading a tile reference someone gave you in the other numbering.
Limitations: XYZ and TMS number the y axis from opposite ends, and the two agree only at zoom 0, where the grid is one tile tall -- which is exactly why an untested conversion looks right and is not. Say which convention you mean; the default is XYZ, what web maps use. A quadkey carries its own zoom in its length, so a six-character quadkey is a zoom-6 tile and cannot be a shorthand for a deeper one. Zoom 0 has no parent, and this says none rather than returning a tile that does not exist.
Worked example: Tile 12/1137/1544. Source: Slippy map tile arithmetic: parent 11/568/772. It is golden test vector v001, and every build checks the tool still gives its answer within its tolerance.
You enter
- Tile
- 12/1137/1544
You get
- Parent
- 11/568/772
- Parent quadkey
- 03200111200
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 1.0.0, core 0.1.0. See this tool in the verification report.
Checked against: 23 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).
Learn the concept: Map tiles, zoom levels, and quadkeys explained