Methodology & editorial policy

The exact maths and game mechanics behind every CraftCalc tool, written so you can verify any number we show.

Last updated: 08 Oct 2026

Core formulas & mechanics

  • Circle outline: midpoint circle algorithm (Bresenham, 1965) plotted on the block grid, with four-fold symmetry preserved.
  • Ovals: parametric ellipse sampling, rounded to block cells.
  • Spheres: stacked circles; layer radius = floor(√(r² − y²)) for each height y from −r to +r.
  • Nether coordinates: overworld ÷ 8 to enter the Nether; nether × 8 to return (overworld-to-nether ratio is 8:1, per Minecraft's documented dimension scaling).
  • Beacon range: pyramid levels 1-4 give effect radii of 20, 30, 40 and 50 blocks respectively; full pyramid costs are 9, 34, 83 and 164 mineral blocks (81, 306, 747, 1476 ingots).
  • Enchanting: each bookshelf row contributes 2 to the table's max enchant level, to a cap of 30 (15 bookshelves).
  • XP: the standard level-cost formulas (2L+7 for L≤15, 5L−38 for 16≤L≤30, 9L−158 for L≥31).

Sources & conventions

  • Game mechanics (coordinate scaling, beacon ranges, enchanting): the Minecraft Wiki's documented mechanics, which track the official game behaviour.
  • Circle/ellipse/sphere maths: standard rasterization and solid geometry; the code is short and auditable in your browser's dev tools.
  • Version note: mechanics on this page reflect the Java Edition current release at the time of writing; Bedrock differences are called out where they matter.

Known limits

  • Small circles: at radius 1-3, no grid pattern looks perfectly round; we show the closest rasterized form.
  • Non-Euclidean builds: the circle generator works in block (Chebyshev grid) space, which is what placing blocks actually is.
  • Beacon pyramids: block costs assume full solid pyramid levels as the game requires.

Testing & QA

  1. Every formula has a hand-calculation test case that must pass before deploy.
  2. Grid rendering is verified against known patterns (e.g., radius-10 outline symmetry).
  3. Mechanics change only with a changelog entry and a source link.

AI use disclosure

Pages are drafted with tooling assistance and reviewed before publishing; every formula and claim is verified against the sources above. No invented statistics appear on this site.

Corrections policy

Found an error or a mechanic that changed in a recent patch? Report it with a source. Confirmed corrections ship within a week and are listed in the changelog.