How many total hexes are in a spiral of radius R?

The total number of hexes in a spiral of radius R is 3 * R * (R + 1) + 1 (e.g., radius 1 = 7, radius 2 = 19, radius 3 = 37).

Updated: August 2026 • Verified v1.2

Hexagonal Grid Spiral & Ring Traversal Algorithm Simulator

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Ring(R): Start = Center + Direction[4]*R; Next = Neighbor(Current, (dir_idx) % 6)

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Understanding Your Results

Animates step-by-step ring and spiral generation, displays sequential visitation numbers, and provides ready-to-use TypeScript algorithm implementations.

Practical Guidance & Next Steps

To generate a ring of radius R, scale direction vector 4 by R to find the starting hex, then step R times in each of the 6 cube directions.

What is this?

An interactive algorithm simulator for generating hexagonal grid concentric rings and outward spiral expansion paths.

How does it work?

1. Select algorithm mode (Outward Spiral vs Single Ring). 2. Set target radius and scrub through the step progression slider. 3. View sequential traversal ordering and copy the TypeScript implementation.