Recipe yields round up, so a crafting cost is never just multiplication
Paper makes 3 per craft. Needing 4 costs you 6 sugar cane and leaves 2 paper spare. Every level of a recipe tree does that, and the waste compounds downward.
Working out what something costs in raw materials looks like a multiplication problem. It is not, because a recipe produces a fixed batch and you cannot craft a fraction of one.
The rule
craftsNeeded = ceil(needed / makes)
produced = craftsNeeded × makes
leftover = produced − neededmakes is the recipe's yield. Paper is makes: 3 from 3 sugar cane. So:
| paper needed | crafts | sugar cane | leftover paper |
|---|---|---|---|
| 1 | 1 | 3 | 2 |
| 3 | 1 | 3 | 0 |
| 4 | 2 | 6 | 2 |
| 6 | 2 | 6 | 0 |
Needing one paper costs the same as needing three. Needing four costs the same as needing six. The cost function is a staircase, not a line, and every step you land just past doubles back on you.
It compounds down the tree
The ceiling is applied at every level, not once at the end. A book is 3 paper and 1 leather; paper is 3-per-craft from sugar cane. One book therefore needs one paper craft exactly — 3 sugar cane, no waste.
Two books need 6 paper, which is 2 crafts, still clean. But nudge any quantity in the tree off a batch boundary and the rounding at that level propagates as a larger requirement to everything below it, which then rounds up in turn. Deep trees accumulate this, and the total can exceed a naive quantity × unit cost by a wide margin while every individual step looks correct.
This is the single reason a cost calculator is worth having rather than doing the sums yourself: the arithmetic is easy and the bookkeeping is not.
Alternate recipes change the tree, not just the price
Some items have more than one way to make them, and the calculator lets you switch:
- Iron ingot — smelting in a furnace, or blasting in a blast furnace. Both consume 1 Raw Iron
and make 1, so the choice is speed and fuel, not materials.
- Gold ingot — the same pair, with the same equivalence.
- Stick — two genuinely different recipes, which is why it is the one the tool uses to
demonstrate switching.
The iron and gold cases are worth noticing precisely because they are not a cost decision. A tree that offers a choice does not always offer a cheaper branch, and swapping furnace for blast furnace changes nothing at all in the shopping list.
Where the tree stops
Fifteen items are treated as raw leaves — the expansion stops there rather than going further:
oak log · cobblestone · raw iron · raw gold · diamond · redstone dust · sand · nether star · obsidian · netherite scrap · sugar cane · leather · bamboo · wool · string
Two of those deserve a note. Netherite scrap is really Ancient Debris smelted, and is treated as raw for simplicity — so a netherite cost will under-report by one smelting step per scrap. And oak log stands in for "any log", so the tree does not fork into six wood types that all behave identically.
Knowing where a tree bottoms out matters as much as the tree itself: a cost in "raw materials" is only meaningful once you know which materials the calculation calls raw.