How do you calculate distance between two hexagons?

Convert axial coordinates $(q, r)$ to cube coordinates $(q, r, s)$ where $s = -q - r$. The distance between hex A and hex B is $\max(|A.q - B.q|, |A.r - B.r|, |A.s - B.s|)$.

Updated: August 2026 • Verified v1.2

Hexagonal Tile Grid Dimensions & Coordinates Calculator

Creative & DesignDesign

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Pointy: w = sqrt(3)*r, h = 2r, dx = w, dy = 1.5*r; Distance: Max(|dq|, |dr|, |-dq-dr|)

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Understanding Your Results

Calculates single hex dimensions, horizontal/vertical center step offsets, total canvas bounding box, inradius, and generates ready-to-use JavaScript functions for coordinate projection (`axialToPixel`) and cube distance (`hexDistance`).

Practical Guidance & Next Steps

Pointy-topped hexagons use $w = \sqrt{3}r$ and $h = 2r$ with vertical step $(3/4)h$. Flat-topped hexagons swap the width and height relationships.

What is this?

A game design geometry utility that calculates dimensions and coordinate projection algorithms for hexagonal tile grids.

How does it work?

1. Select Pointy-Topped or Flat-Topped orientation. 2. Enter hex radius (r) and grid dimensions (columns and rows). 3. View tile bounding box, step offsets, and copy axial-to-pixel projection code.

Why use it?

Eliminates trial-and-error math when building hex grid tilemaps in Godot, Unity, or Canvas.

Technical Scope & Calculation Limitations

Calculates regular regular hexagon planar geometry.

Frequently Asked Questions

Pointy-topped hexagons have a vertex facing straight up and down, which is standard in turn-based strategy video games (e.g. Civilization). Flat-topped hexagons have a horizontal edge facing straight up and down, popular in tabletop wargames and Settlers of Catan.

Windows Desktop & Widget Options