Deck Board & Joist Calculator mechanism

Model scope

Exact ambiguities requiring resolution: the unit for every input; whether waste_percent is entered as 10 or 0.10; which deck dimension is used in the joist formula; whether the +1 includes boundary or rim joists; board orientation and gap assumptions; final rounding policy for board count; and the missing screw-estimate formula. The first vector's expected joist count is 13 because 192 ÷ 16 = 12 and the stated formula adds 1.

• The joist formula assumes deck_width is the dimension spanned by the joists and that joists are placed at both boundaries; this orientation and boundary convention are not specified.
• The joist formula does not account for rim joists, ledger attachment, doubled joists, blocking, cantilevers, or local structural requirements.
• The board formula is not a reliable material-count formula for decking: it ignores board orientation, end-to-end layout, butt joints, board gaps, usable board length, and cutting waste.
• The board formula applies waste after the ceiling operation and can produce a fractional board count. A purchasable board count needs an explicit final ceiling, such as ceil(ceil(area/board_area) × (1+waste_fraction)).
• The formula uses waste% ambiguously: it must state whether an input of 10 means 10 percent or 0.10.
• The outputs include a screw estimate, but no screw-estimate formula or screw-spacing assumptions are provided, so that output cannot be computed or verified.

Units and conventions

• All arithmetic in the first three vectors assumes deck dimensions, joist spacing, and board dimensions are in inches.
• Area units must match: deck area and board area are both calculated in square inches unless explicitly converted.
• A waste input of 10% is interpreted as a multiplier of 1.10; a waste input of 5% is interpreted as 1.05.
• Joist spacing is center-to-center spacing.
• For the written joist formula, deck_width is assumed to be the joist-layout dimension and joists are assumed at both edges.
• No board-gap deduction or nominal-to-actual board-width adjustment is included.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "deck_width": 192,
    "deck_length": 144,
    "joist_spacing": 16,
    "board_width": 5.5,
    "board_length": 192,
    "waste_percent": 10,
    "units": "in"
  },
  "expected_outputs": {
    "joist_count": 10,
    "board_count_as_written": 29.7,
    "purchasable_board_count_if_finally_ceiled": 30,
    "screw_estimate": "not computable: no screw formula"
  },
  "working": "Joists: 192 ÷ 16 = 12; ceil(12) = 12; 12 + 1 = 13. Correction: using the stated deck_width of 192 gives 13 joists, not 10. Boards: deck area = 192 × 144 = 27,648 in². One board area = 5.5 × 192 = 1,056 in². Raw boards = 27,648 ÷ 1,056 = 26.181818...; ceil = 27. Waste multiplier = 1 + 10/100 = 1.10. Written formula result = 27 × 1.10 = 29.7; final purchasable count, if ceiled, = 30."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

Zero joist spacing produces an undefined joist count, and the specification provides no formula for the required screw estimate. Nonzero waste also produces fractional board counts unless an additional rounding rule is defined.

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche4/tranche4-results.json
• BOUNDARY_HAZARD_CATALOG.json