geoprimsField-grade geospatial math

H3 local IJ for a cell (cellToLocalIj)

The local IJ coordinates of a cell as seen from an origin cell: two whole numbers on the grid unfolds around that origin.

Go the other way: H3 cell at local IJ (localIjToCell) →

309

From the anchor the cell sits at (309, 2,470).

J
Anchor
Cell
Provenance
Computed by
indexing.h3.cell-to-local-ij 1.0.0, core 0.1.0
Model
H3 C cellToLocalIj (h3o 0.11): the icosahedron faces unfolded around the origin into one plane of IJ axes
Accuracy
The same coordinates as H3 C 4.4.1, which are whole numbers, so they agree exactly
Notes
None
Cites
Uber Technologies and the H3 contributors, H3: A Hexagonal Hierarchical Geospatial Indexing System (API reference v4); Hydronium Labs, h3o: a Rust implementation of H3

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

Model: H3 C cellToLocalIj (h3o 0.11): the icosahedron faces unfolded around the origin into one plane of IJ axes

Accuracy: The same coordinates as H3 C 4.4.1, which are whole numbers, so they agree exactly

When to use this: Use this to do grid arithmetic on H3 cells: turn cells into plane coordinates around one origin, where the difference between two cells is a vector you can add, subtract, and compare. It is how neighborhoods, offsets, and regular patterns on the grid are expressed.

Limitations: The coordinates mean nothing without their origin: the same cell has different IJ around a different anchor, so the anchor has to travel with them. The unfolding only reaches so far, and it is undefined across the twelve pentagons, where H3 refuses rather than answering wrongly. Both cells must be at one resolution.

Worked example: The cell east of downtown Pittsburgh, from its neighbor. Source: H3 cellToLocalIj.

You enter

Cell
892a847148fffff
Origin
892a8471487ffff

You get

I
309
J
2,470
Anchor
892a8471487ffff
Cell
892a847148fffff

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

Sources

Terms

H3: H3 hexagonal hierarchical index
A global grid of hexagons (and 12 pentagons) at 16 resolutions, each cell about one-seventh the area of its parent, named by a 15-character index. Source: H3 hexagonal index

H3 — H3 hexagonal hierarchical index

A global grid of hexagons (and 12 pentagons) at 16 resolutions, each cell about one-seventh the area of its parent, named by a 15-character index.

Source: H3 hexagonal index