These are first-party reproducible checks, not independent certification, structural design, or supplier quotes.
Validation checks the published quantity math. Verify measurements, selected-product specifications, supplier minimums, and local requirements before ordering.
/// Case 01 · Reviewed Jul 16, 2026
Concrete slab volume and 80 lb bag count
Question: Does a 10 ft × 10 ft × 4 in slab with 10% waste produce 1.3580 yd³ and 62 bags?
| Checkpoint | Published value |
|---|---|
| Slab | 10 ft × 10 ft × 4 in |
| Waste allowance | 10% |
| Selected package | 80 lb QUIKRETE Concrete Mix No. 1101 |
| Published package yield | Approximately 0.60 ft³ |
Formula
Convert depth to feet; multiply length × width × depth; divide ft³ by 27 for yd³; multiply by 1.10; divide adjusted ft³ by 0.60 ft³ per selected bag.
| Checkpoint | Published value |
|---|---|
| Base volume | 33.3333 ft³ = 1.2346 yd³ |
| Adjusted volume | 36.6667 ft³ = 1.3580 yd³ |
| Unrounded packages | 61.1111 bags |
Rounding and expected result
Display volume to four decimals and round the final package quantity up to the next whole bag.
| Checkpoint | Published value |
|---|---|
| Base volume | 1.2346 yd³ |
| Volume with 10% waste | 1.3580 yd³ |
| 80 lb bags | 62 bags |
The package result is scoped to the named QUIKRETE No. 1101 80 lb yield. Field conditions, delivery, placement, and other products require separate verification.
Related sources: nist-sp811-foot-metre · quikrete-1101-80-yield
/// Case 02 · Reviewed Jul 16, 2026
Deck board rows and whole stock boards
Question: Does a 12 ft × 10 ft deck using 5.5 in boards, 0.125 in gaps, and 12 ft stock plan 25 boards with 10% waste?
| Checkpoint | Published value |
|---|---|
| Deck | 12 ft long × 10 ft wide |
| Board face and gap | 5.5 in + 0.125 in |
| Stock length | 12 ft |
| Cutting allowance | 10% |
Formula
Rows = ceil((deck width in inches + one gap) ÷ (board face width + gap)); adjusted board length = rows × deck length × 1.10; stock boards = ceil(adjusted length ÷ stock length).
| Checkpoint | Published value |
|---|---|
| Board rows | 22 rows |
| Board length before allowance | 264 linear ft |
| Board length with allowance | 290.4 linear ft |
Rounding and expected result
Round the row count up first, retain length precision, then round the final stock-board count up.
| Checkpoint | Published value |
|---|---|
| Stock boards | 25 boards |
The case uses actual board face width and an entered gap. It excludes picture framing, breaker boards, stairs, fascia, diagonal layouts, and structural framing.
Related sources: nist-sp811-foot-metre
/// Case 03 · Reviewed Jul 16, 2026
Simple sloped roof area, squares, and bundles
Question: Does a 30 ft × 20 ft footprint at 6:12 pitch and 10% waste produce about 738 ft², 7.38 squares, and 23 bundles?
| Checkpoint | Published value |
|---|---|
| Horizontal footprint | 30 ft × 20 ft |
| Pitch | 6 in rise per 12 in run |
| Waste allowance | 10% |
| Product coverage | 3 bundles per square |
Formula
Slope factor = √(1 + (6 ÷ 12)²); adjusted roof area = footprint × slope factor × 1.10; squares = adjusted area ÷ 100 ft²; bundles = ceil(squares × 3).
| Checkpoint | Published value |
|---|---|
| Horizontal footprint | 600 ft² |
| Slope factor | 1.118034 |
| Adjusted roof area | 737.90 ft² |
Rounding and expected result
Retain area and square precision for display, then round only the final bundle order up to a whole bundle.
| Checkpoint | Published value |
|---|---|
| Roof area with waste | About 738 ft² |
| Roofing area | 7.38 squares |
| Bundles | 23 bundles |
The footprint model is for a simple roof. Complex planes, starters, caps, valleys, flashing, manufacturer coverage, access, and safety require separate takeoffs and review.
Related sources: arma-residential-manual-roofing-square
/// Case 04 · Reviewed Jul 16, 2026
Tile pieces and full boxes
Question: Does a 12 ft × 10 ft surface using 12 in square tile and 10 tiles per box require 132 tiles and 14 boxes with 10% waste?
| Checkpoint | Published value |
|---|---|
| Surface | 12 ft × 10 ft |
| Tile face | 12 in × 12 in |
| Cutting allowance | 10% |
| Package count | 10 tiles per box |
Formula
Adjusted area = length × width × 1.10; individual tiles = ceil(adjusted area ÷ tile face area); boxes = ceil(individual tiles ÷ 10).
| Checkpoint | Published value |
|---|---|
| Base surface | 120 ft² |
| Area with allowance | 132 ft² |
| Tile face area | 1 ft² |
Rounding and expected result
Round individual pieces up before dividing by package count, then round the package result up again.
| Checkpoint | Published value |
|---|---|
| Individual tiles | 132 tiles |
| Full boxes | 14 boxes |
The case is face-area based. Pattern matching, grout joints, borders, breakage, attic stock, trim, substrate, and the selected carton label remain separate checks.
Related sources: nist-sp811-foot-metre
/// Case 05 · Reviewed Jul 16, 2026
Mulch bed volume before and after allowance
Question: Does a 20 ft × 10 ft bed at 3 in deep contain about 1.8519 yd³ before waste and 2.0370 yd³ with 10%?
| Checkpoint | Published value |
|---|---|
| Bed | 20 ft × 10 ft |
| Placed depth | 3 in |
| Allowance | 10% |
Formula
Convert 3 in to 0.25 ft; multiply length × width × depth; divide cubic feet by 27; multiply the base volume by 1.10.
| Checkpoint | Published value |
|---|---|
| Placed volume | 50 ft³ |
| Cubic-yard divisor | 27 ft³ per yd³ |
Rounding and expected result
Retain engine precision and display cubic-yard quantities to four decimals; do not round to bags or loads.
| Checkpoint | Published value |
|---|---|
| Base volume | 1.8519 yd³ |
| Volume with allowance | 2.0370 yd³ |
The case estimates placed geometry only. Product type, settling, existing grade, density, bag coverage, supplier increments, delivery, and installation remain separate decisions.
Related sources: nist-sp811-foot-metre