S2 cells covering a region

The cells that cover a latitude and longitude rectangle, or a circle around a point, within a level range and a cell budget.

Computing your own values needs JavaScript and WebAssembly. The worked example below was computed when this page was built, and the documentation under "How we got this" applies.

That region takes 6 S2 cells, from level 10 to 11.

Covering
Cell	Level	Latitude	Longitude
8834f14	11	40.4229554 deg	-79.9864071 deg
8834f1c	11	40.4190459 deg	-79.9416549 deg
8834f24	11	40.4593947 deg	-79.9416549 deg
8834f3c	11	40.4633051 deg	-79.9864071 deg
8834f5	10	40.4892989 deg	-80.0534923 deg
8834f7	10	40.4085968 deg	-80.0534923 deg

Covered area
Finest level
Coarsest level

Provenance

Computed by: indexing.s2.covering 1.0.0, core 0.1.0
Model: Refinement from the six faces: the coarsest candidate that meets the region is split into its four children, keeping any cell the region contains whole, until the budget is reached; a cell that only partly overlaps is kept, so the covering contains the region
Accuracy: The covering always contains the region. It is not the smallest such set: S2's own coverer uses a priority order that can find a tighter cover for the same budget, so treat the cells as a superset rather than a canonical answer.
Notes: None
Cites: Google, S2 Geometry

Something look off?

Your values

Showing an example. Change anything.

Paste a coordinateany notation

South edgeoptional Of the rectangle, like 40.4 deg · plain numbers mean degrees North edgeoptional Of the rectangle, like 40.5 deg · plain numbers mean degrees West edgeoptional Of the rectangle, like -80.1 deg · plain numbers mean degrees East edgeoptional Of the rectangle, like -79.9 deg · plain numbers mean degrees Center latitudeoptional For a circle, like 40.44 deg · plain numbers mean degrees Center longitudeoptional For a circle, like -79.99 deg · plain numbers mean degrees

More options 4

Radiusoptional For a circle instead of a rectangle, like 5 km · plain numbers mean km Lowest leveloptional Coarsest cell allowed, 0 to 30; default 0 Highest leveloptional Finest cell allowed, 0 to 30; default 16 Cell budgetoptional How many cells at most, like 8

Run many at once from a CSV

Loading…

How we got thisFormula, worked example, sources, and proof

Model: Refinement from the six faces: the coarsest candidate that meets the region is split into its four children, keeping any cell the region contains whole, until the budget is reached; a cell that only partly overlaps is kept, so the covering contains the region

Accuracy: The covering always contains the region. It is not the smallest such set: S2's own coverer uses a priority order that can find a tighter cover for the same budget, so treat the cells as a superset rather than a canonical answer.

When to use this: Use this to turn an area into index keys: the cells of a covering are what you query a cell-indexed store with, then filter the results by the true geometry. The budget and the level range are the two knobs — more cells or finer levels mean a tighter cover and a larger key set.

Limitations: A covering is a superset: every cell overlaps the region but the cells together cover more ground than it, which is why a covering query still needs a second filter. This covers a rectangle or a circle; polygons are not covered yet. The cells are a valid covering rather than S2's own choice, so a set from another library may differ while covering the same ground. The cell budget is not a hard cap: the lowest level wins over it, so a region that needs more cells than the budget just to reach that level gets them, with a warning saying so -- a smaller set would leave part of the region out. Past four times the budget the request is refused instead.

Worked example: A small box near Pittsburgh in at most 8 cells. Source: add-spatial-indexing-and-raster hierarchical-cells scenario: at most 8 cells, all between levels 10 and 16, together covering the region. It is golden test vector v001, and every build checks the tool still gives its answer within its tolerance.

You enter

East edge: -79.96 deg
Cell budget: 8
Highest level: 16
Lowest level: 10
North edge: 40.46 deg
South edge: 40.43 deg
West edge: -80.01 deg

You get

Cells: 6
Covered area: 203.756 km²
Finest level: 11
Coarsest level: 10

Review: Not yet independently reviewed by a GIS professional.

Last verified: 2026-09-22, 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: 22 golden test vectors (download the test vectors, each with its source and tolerance). See how results are checked and every source.

Sources

S2 Geometry, Google, S2 Geometry library. Cell ids, the quadratic projection, the Hilbert curve, tokens, and cell hierarchy.

Terms

S2: S2 Geometry: A way of indexing the sphere: the Earth is projected onto a cube, each face is traced by a Hilbert curve, and a cell is a position along that curve at a level from 0 to 30. Source: S2 Geometry

S2 — S2 Geometry

A way of indexing the sphere: the Earth is projected onto a cube, each face is traced by a Hilbert curve, and a cell is a position along that curve at a level from 0 to 30.

Source: S2 Geometry

Your values

You enter

You get

Sources

Terms

Related tools