GAME & ENTERTAINMENT – BOARD GAME & TABLETOP CALCULATOR
Hex Grid Distance
A precise tool.
What is the Hex Grid Distance & How does it work?
Hexagonal grids are a common choice for board games because they provide six directions of movement, which creates a more natural notion of distance than square grids.
One convenient way to address each hex is with cube coordinates (x, y, z) that satisfy x + y + z = 0. This redundancy makes arithmetic simple.
The shortest path between two hexes is given by the Manhattan distance in cube space, divided by two.
\frac{\lvert x_1 – x_2 \rvert + \lvert y_1 – y_2 \rvert + \lvert z_1 – z_2 \rvert}{2}
d = distance between the two hexes
Parameters
Result
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Frequently Asked Questions
What are cube coordinates in a hex grid?
Cube coordinates (x, y, z) represent each hex on a hexagonal grid where x + y + z = 0. This system simplifies movement and distance calculations.
How do I calculate the distance between two hexes using cube coordinates?
Calculate the Manhattan distance in cube space: |x1 – x2| + |y1 – y2| + |z1 – z2|. The actual hex grid distance is half of this value.
Why are hex grids used in board games?
Hex grids provide six directions of movement, creating a more natural and balanced playing experience compared to square grids.
Can cube coordinates be converted to other coordinate systems?
Yes, cube coordinates can be converted to axial or offset coordinates, which are also commonly used in hex grid calculations.
What is the advantage of using cube coordinates for hex grids?
Cube coordinates simplify arithmetic operations and make it easier to calculate distances and directions on a hexagonal grid.
Results are for informational purposes only and do not constitute professional advice.