How do you calculate distance between two hex tiles in cube coordinates?

The distance between hex A and hex B is `Max(|A.x - B.x|, |A.y - B.y|, |A.z - B.z|)` or equivalently `(|dx| + |dy| + |dz|) / 2`.

Updated: August 2026 • Verified v1.2

Hexagonal Grid Coordinate Converter (Axial to Cube)

Creative & DesignDesign

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x = q, z = r, y = -x - z; Distance = Max(|dx|, |dy|, |dz|)

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Understanding Your Results

Converts Axial $(q, r)$ to 3D Cube $(x, y, z)$ verifying the $x + y + z = 0$ mathematical invariant, calculates step distance to a target tile, generates all 6 adjacent neighbor coordinates, and provides copy-ready TypeScript functions.

Practical Guidance & Next Steps

Cube coordinates simplify hexagonal geometry by turning 6-directional hexagonal movements into 3-axis integer additions, making distance and line-drawing trivial.

What is this?

A game development geometry utility that translates hexagonal tile coordinates between 2D Axial and 3D Cube representations.

How does it work?

1. Enter current hex origin (q, r). 2. Enter destination target hex (q, r) to measure grid step distance. 3. View equivalent 3D Cube vector, adjacent neighbor ring, and copy TypeScript helper functions.

Why use it?

Simplifies pathfinding, line-of-sight, and neighbor queries in hexagonal game engines.

Technical Scope & Calculation Limitations

Calculates standard regular hexagonal planar geometry.

Frequently Asked Questions

In hexagonal cube coordinates, the three axes must always satisfy the invariant `x + y + z = 0`. This reflects the fact that a hexagonal grid is a 2D plane embedded within 3D space.

Windows Desktop & Widget Options