Minecraft anvil mechanics explained

The full cost formula

total_xp_cost = sum_over_enchants(bookMultiplier * result_level)
              + prior_work_penalty(target)
              + prior_work_penalty(sacrifice)
              + repair_material_cost
prior_work_penalty(n) = 2^n - 1
      

Read carefully: the cost contribution per enchantment uses the result level on the merged item, not the sacrifice's level. Sharpness IV + Sharpness IV upgrades to Sharpness V (cost 5), not to a second Sharpness IV (cost 4).

Book vs item multipliers

Each enchantment has a book multiplier and (implicitly) an item multiplier at half (rounded up, minimum 1). The anvil uses the book multiplier when the sacrifice is a book and the item multiplier when the sacrifice is a sacrificed gear piece. This is why books are nearly always cheaper than item-on-item combines.

The prior-work penalty (2^n - 1)

Every anvil use increments the prior-work counter on the resulting item by 1. The penalty for the next anvil use scales exponentially:

Both inputs contribute their penalty to the cost - which is why combining two high-prior-work items is borderline impossible without triggering 'Too Expensive!'.

Conflicts and incompatibilities

Modern Minecraft (1.14+) refuses any combine where the sacrifice's enchantments include one that conflicts with the target's. The classic examples: Sharpness vs Smite vs Bane of Arthropods on swords; Silk Touch vs Fortune on tools; Infinity vs Mending on bows; Loyalty vs Riptide on tridents; Density vs Breach on the mace (1.21+).

1.20+ vs Legacy

The August 2023 update (1.20) tweaked the way the anvil charges multi-book chains. The cap stayed at 40 - what changed is which merge orders are cheap. Specifically, book-pair-first plans got relatively cheaper because the prior-work growth on book-pair-first plans stays lower for longer. The calculator toggle switches between the 1.20+ accounting and the pre-1.20 'Legacy' accounting.