/// Reproduce the quantity math

Calculation validation

Use seven published reference cases with exact inputs, formulas, intermediate values, rounding rules, and product-scoped assumptions.

First-party evidence boundary

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.

/// Start from the review question

Choose a reproducible case

User task to validation case and calculator
Review taskPublished caseCalculator
Does a 10 ft × 10 ft × 4 in slab with 10% waste produce 1.3580 yd³ and 62 bags?Concrete slab volume and 80 lb bag countOpen calculator
Does an 8 ft × 5 ft × 3 ft box contain 120 ft³ and about 4.4444 yd³?Rectangular cubic feet and equivalent unitsOpen calculator
Does one 20 ft × 1.5 ft × 0.75 ft footing produce 0.8333 yd³ net and 42 bags after 10% waste at 0.60 ft³ per bag?Concrete footing volume and entered bag yieldOpen calculator
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?Deck board rows and whole stock boardsOpen calculator
Does a 30 ft × 20 ft footprint at 6:12 pitch and 10% waste produce about 738 ft², 7.38 squares, and 23 bundles?Simple sloped roof area, squares, and bundlesOpen calculator
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?Tile pieces and full boxesOpen calculator
Does a 20 ft × 10 ft bed at 3 in deep contain about 1.8519 yd³ before waste and 2.0370 yd³ with 10%?Mulch bed volume before and after allowanceOpen calculator

/// Case 01

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?

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Concrete slab volume and 80 lb bag count exact inputs
CheckpointPublished value
Slab10 ft × 10 ft × 4 in
Waste allowance10%
Selected package80 lb QUIKRETE Concrete Mix No. 1101
Published package yieldApproximately 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.

Concrete slab volume and 80 lb bag count intermediate values
CheckpointPublished value
Base volume33.3333 ft³ = 1.2346 yd³
Adjusted volume36.6667 ft³ = 1.3580 yd³
Unrounded packages61.1111 bags

Rounding and expected result

Display volume to four decimals and round the final package quantity up to the next whole bag.

Concrete slab volume and 80 lb bag count expected results
CheckpointPublished value
Base volume1.2346 yd³
Volume with 10% waste1.3580 yd³
80 lb bags62 bags
Scope boundary

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

Rectangular cubic feet and equivalent units

Question: Does an 8 ft × 5 ft × 3 ft box contain 120 ft³ and about 4.4444 yd³?

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Rectangular cubic feet and equivalent units exact inputs
CheckpointPublished value
ShapeRectangular box
Dimensions8 ft × 5 ft × 3 ft
Quantity1

Formula

Multiply length × width × height for cubic feet, then divide by exactly 27 for cubic yards and use the exact international-foot relationship for metric equivalents.

Rectangular cubic feet and equivalent units intermediate values
CheckpointPublished value
Cubic feet8 × 5 × 3 = 120 ft³
Cubic-yard divisor27 ft³ per yd³

Rounding and expected result

Keep the engine value at full precision and display the cubic-yard equivalent to four decimals.

Rectangular cubic feet and equivalent units expected results
CheckpointPublished value
Volume120 ft³
Cubic yards4.4444 yd³
Scope boundary

This is geometric volume only. It does not add material density, compaction, waste, package coverage, shipping capacity, or price.

Related sources: nist-sp811-foot-metre

/// Case 03

Concrete footing volume and entered bag yield

Question: Does one 20 ft × 1.5 ft × 0.75 ft footing produce 0.8333 yd³ net and 42 bags after 10% waste at 0.60 ft³ per bag?

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Concrete footing volume and entered bag yield exact inputs
CheckpointPublished value
Footing1 × 20 ft × 1.5 ft × 0.75 ft
Waste allowance10%
Entered bag yield0.60 ft³ per bag

Formula

Multiply footing quantity × length × width × depth; divide ft³ by 27 for yd³; multiply by 1.10; divide adjusted ft³ by the entered 0.60 ft³ yield and round up.

Concrete footing volume and entered bag yield intermediate values
CheckpointPublished value
Net volume22.5 ft³ = 0.8333 yd³
Volume with waste24.75 ft³ = 0.9167 yd³
Unrounded packages41.25 bags

Rounding and expected result

Display volume to four decimals and round the final package quantity up to the next whole bag.

Concrete footing volume and entered bag yield expected results
CheckpointPublished value
Net volume0.8333 yd³
Volume with waste0.9167 yd³
Bags42 bags
Scope boundary

The 0.60 ft³ bag yield is an entered example and must be replaced with the selected product's label or current technical data. The calculator does not size or approve a footing.

Related sources: nist-sp811-foot-metre

/// Case 04

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?

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Deck board rows and whole stock boards exact inputs
CheckpointPublished value
Deck12 ft long × 10 ft wide
Board face and gap5.5 in + 0.125 in
Stock length12 ft
Cutting allowance10%

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).

Deck board rows and whole stock boards intermediate values
CheckpointPublished value
Board rows22 rows
Board length before allowance264 linear ft
Board length with allowance290.4 linear ft

Rounding and expected result

Round the row count up first, retain length precision, then round the final stock-board count up.

Deck board rows and whole stock boards expected results
CheckpointPublished value
Stock boards25 boards
Scope boundary

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 05

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?

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Simple sloped roof area, squares, and bundles exact inputs
CheckpointPublished value
Horizontal footprint30 ft × 20 ft
Pitch6 in rise per 12 in run
Waste allowance10%
Product coverage3 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).

Simple sloped roof area, squares, and bundles intermediate values
CheckpointPublished value
Horizontal footprint600 ft²
Slope factor1.118034
Base sloped roof area670.82 ft²
Adjusted roof area737.90 ft²
Bundle quotient before rounding22.137 bundles

Rounding and expected result

Retain area and square precision for display, then round only the final bundle order up to a whole bundle.

Simple sloped roof area, squares, and bundles expected results
CheckpointPublished value
Roof area with wasteAbout 738 ft²
Roofing area7.38 squares
Bundles23 bundles
Scope boundary

The footprint model covers one simple pitch and one product coverage set. Mixed pitches or products, starters, caps, valleys, flashing, manufacturer coverage, access, and safety require separate takeoffs and review.

Related sources: arma-residential-manual-roofing-square

/// Case 06

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?

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Tile pieces and full boxes exact inputs
CheckpointPublished value
Surface12 ft × 10 ft
Tile face12 in × 12 in
Cutting allowance10%
Package count10 tiles per box

Formula

Adjusted area = length × width × 1.10; individual tiles = ceil(adjusted area ÷ tile face area); boxes = ceil(individual tiles ÷ 10).

Tile pieces and full boxes intermediate values
CheckpointPublished value
Base surface120 ft²
Area with allowance132 ft²
Tile face area1 ft²

Rounding and expected result

Round individual pieces up before dividing by package count, then round the package result up again.

Tile pieces and full boxes expected results
CheckpointPublished value
Individual tiles132 tiles
Full boxes14 boxes
Scope boundary

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 07

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%?

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Mulch bed volume before and after allowance exact inputs
CheckpointPublished value
Bed20 ft × 10 ft
Placed depth3 in
Allowance10%

Formula

Convert 3 in to 0.25 ft; multiply length × width × depth; divide cubic feet by 27; multiply the base volume by 1.10.

Mulch bed volume before and after allowance intermediate values
CheckpointPublished value
Placed volume50 ft³
Cubic-yard divisor27 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.

Mulch bed volume before and after allowance expected results
CheckpointPublished value
Base volume1.8519 yd³
Volume with allowance2.0370 yd³
Scope boundary

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