Board Hex Cube Distance

Compute exact infinite-grid hex distance between validated cube coordinates; no obstacles, terrain or pathfinding.

Description

Compute exact infinite-grid hex distance between validated cube coordinates; no obstacles, terrain or pathfinding.

Cube coordinates represent a hex grid using three integers whose sum is zero. Their maximum coordinate difference gives unobstructed grid distance.

When to use this tool

Compute exact infinite-grid hex distance between validated cube coordinates; no obstacles, terrain or pathfinding.

Prepare the supplied from, to fields for this operation.
Compare the complete example with the representation used by your own input before carrying the result into another step.

How to use the tool and how it works

Enter from, to. Use the exact text syntax, units and index conventions explained below.
Run the tool. If input validation fails, correct the supplied fields before interpreting any result.
Read result.distance. Interpret false, null and empty lists using the distinctions below; they can be valid outputs.

Require two triples of integers within plus or minus one billion, each summing to zero. Return the largest absolute component difference.^[1]

Input field	Meaning and representation	Accepted input
from	from.	List of finite numbers; at most 128 entries
to	to.	List of finite numbers; at most 128 entries

Output field	Interpretation
result	Object containing the named outputs below.
result.distance	The distance value under the stated formula or text convention.

json

{
  "input": {
    "from": [
      0,
      0,
      0
    ],
    "to": [
      2,
      -1,
      -1
    ]
  },
  "output": {
    "result": {
      "distance": 2
    }
  }
}

Limitations and assumptions

This is hex-step distance without obstacles, terrain costs, wrapping or board bounds.
Every declared top-level field is required and unexpected fields are rejected. Numeric inputs must be finite; ordinary text fields are bounded to 8,192 UTF-16 code units, with tighter operation-specific limits where stated.
Lists are limited to 128 entries. JSON text must meet bounded size and depth checks, and numeric outputs beyond the safe finite magnitude are rejected. Exact large integers use decimal strings.
Indexes are zero-based and spans have an exclusive end unless explicitly stated otherwise. A valid false, null or empty-list result is distinct from malformed input.

Alternative or Complementary methods

Use a game-state-aware rules engine when occupancy, legal moves or scoring rules matter. These operations calculate coordinates, local geometry or supplied ledger totals without inferring a complete position.

References

Tool behavior and example: Board Hex Cube Distance — tool.io

Similar or alternative tools

Board Hex Axial Cube Converter
Convert integer axial hex coordinates q,r to cube x=q,z=r,y=-q-r, preserving the zero-sum invariant.
Board Hex Cube Axial Converter
Convert validated zero-sum integer hex cube coordinates to axial q=x,r=z; invalid cube coordinates are rejected.