Formula Reference

Complete documentation of all pricing, coating, and weight formulas used in the Invicta Foam material calculator.

1. Global Settings (Input Variables)

These values are configured in the Settings panel and stored in the database.

Variable	Default	Description
foamCost	$350	Cost per foam block
foamH × foamW × foamD	47 × 52 × 96 in	Foam block dimensions
meshCost	$30.64	Cost per mesh roll
meshW × meshL	38 in × 150 in	Mesh roll dimensions
glueCost	$106.25	Cost per glue unit
glueCoverage	475 sq ft	Coverage per glue unit
cementCost	$12	Cost per 50lb bag of base coat cement
cementCoverage	30 sq ft	Coverage per bag
laborHourly	$20	Hourly labor rate
laborTax	1.15	Labor tax/burden multiplier
meshPerHour	30	Pieces meshed per hour

Manual Coating Settings

Variable	Default	Description
manualCrew	1	Number of workers for hand coating
manualAnchor1Sqft	2.04	Surface area of small reference piece (sq ft)
manualAnchor1Min	20	Time to coat anchor 1 (minutes)
manualAnchor2Sqft	29.19	Surface area of large reference piece (sq ft)
manualAnchor2Min	60	Time to coat anchor 2 (minutes)

Anchor 1 = PCI-108 A=10" post cap (small). Anchor 2 = PCI-108 A=38" post cap (large).

2. Per-Product Variables

Each product in the catalog has these attributes:

H, W, L — Height, Width, Length (inches)

aSize — "A" dimension (nominal size)

pieces — Pieces cut from one foam block

corners — Number of mesh corners

wasteMultiplier — Waste factor (e.g. 1.05 = 5%)

laborCoatingMult — Machine coating length multiplier

coatingMode — "machine" or "manual"

coatingOverride — Override coating length (inches)

pyramidHeight — Post cap pyramid height

baseProfilePerim — Post cap base profile perimeter

3. Derived Constants

Formula	Expression	Typical Value
costPerCuIn	foamCost / (foamH × foamW × foamD)	$0.00149/cu in
meshCoverage	meshW × (meshL / 12)	475 sq ft
glueCostPerSqFt	glueCost / glueCoverage	$0.2237/sq ft
cementCostPerSqFt	cementCost / cementCoverage	$0.40/sq ft
laborPerMin	laborHourly / 60	$0.333/min
cuttingPerIn	laborPerMin / 30	$0.0111/in
meshingPerCorner	(laborHourly / meshPerHour) / 4	$0.1667/corner
coatingPerSqFt	(laborHourly × 2.5) / 250	$0.20/sq ft

coatingPerSqFt breakdown: 2.5 = crew size (2½ people operating the spray machine), 250 = machine coating rate (250 sq ft/hr). So: $20/hr × 2.5 people / 250 sqft/hr = $0.20/sq ft.

4. Geometry Calculations

Detailed guides: Corbel Calculation & Coating Guide

Standard Trim

perimeter = (H + W) × 2
coatingLength = perimeter - aSize (subtracts the back/hidden face)
lengthFactor = L / 12 (piece length in feet; 96"/12 = 8 for standard trim)

Post Caps

postCapPyrH = pyramidHeight > 0 ? pyramidHeight : H
postCapSlantH = √((aSize/2)² + postCapPyrH²)
postCapBaseArea = baseProfilePerim × 4 × aSize (sq in)
perimeter = 4 × aSize
coatingLength = 2 × postCapSlantH + 4 × baseProfilePerim
lengthFactor = aSize / 12 (converts to feet)

Post caps are modeled as a 4-sided pyramid top with a profiled base molding that wraps all 4 sides.

Round Columns

perimeter = π × W (circumference)
coatingLength = perimeter
lengthFactor = π × W / 12

Square Columns

perimeter = 4 × W
coatingLength = perimeter
lengthFactor = 4 × W / 12

5. Material Costs

Cost	Formula
foamCostCalc	((foamCalcH + 0.2) × (foamCalcW + 0.2) × L) × costPerCuIn / pieces
meshCostCalc	(meshCost / meshCoverage) × (meshLengthWithOverlap / 12) × lengthFactor
glueCostCalc	glueCostPerSqFt × (meshLengthWithOverlap / 12) × lengthFactor
baseCostCalc	cementCostPerSqFt × (coatingCalc / 12) × lengthFactor
materialTotal	foamCostCalc + meshCostCalc + glueCostCalc + baseCostCalc

meshLengthWithOverlap = coatingCalc + 4 (4 inches of overlap for mesh wrapping; respects coating override)

6. Labor Costs

Cost	Formula
laborCutting	perimeter × cuttingPerIn
laborMeshCut	laborHourly / 120
laborGlue	meshingPerCorner × corners
laborCoating	depends on coating mode — see below
laborTotal	(laborCutting + laborMeshCut + laborGlue + laborCoating) × laborTax

7. Coating Modes

Machine Coating (default for standard trim)

coatSurfArea = (coatingLength / 12) × lengthFactor (sq ft)
laborCoating = (coatingCalc / 12) × coatingPerSqFt × laborCoatingMult

The laborCoatingMult is the piece length factor (default 8 for an 8-foot piece). The formula computes: coating width in feet × cost per sq ft × piece length = total labor per piece.

Manual Coating (hand-applied: post caps, corbels, shutters, wall caps, columns)

coatSurfArea = (coatingLength / 12) × lengthFactor (sq ft)
manualP = ln(anchor2Min/60) - ln(anchor1Min/60)) / (ln(anchor2Sqft) - ln(anchor1Sqft))
manualK = (anchor1Min / 60) / anchor1Sqft^p
time (hours) = K × surfaceArea^p
laborCoating = time × laborHourly × manualCrew

Why a power law? Hand-coating time doesn't scale linearly with surface area. Larger pieces have more continuous surface and less fiddly detail work per square foot, so they're more efficient. A power law (exponent < 1) naturally captures this: doubling the surface area less than doubles the time.

Anchor points: The power law is defined by two real-world time estimates:

A small piece (default: PCI-108 A=10", 2.04 sq ft, 20 minutes)
A large piece (default: PCI-108 A=38", 29.19 sq ft, 60 minutes)

From these, the exponent p ≈ 0.413 and coefficient K ≈ 0.2483 are derived. To re-calibrate, simply update the anchor points in Settings.

Comparison at default settings

Piece	Surface (sq ft)	Machine Labor	Manual Labor	Manual Time
PCI-108 A=10"	2.04	$16.64	$6.67	20 min
PCI-108 A=20"	8.08	$19.12	$11.77	35 min
PCI-108 A=38"	29.18	$37.11	$20.00	60 min
PCI-108 A=52"	54.68	$54.73	$25.92	78 min

8. Final Price

total = materialTotal + laborTotal
totalWaste = total × wasteMultiplier
price = totalWaste × 3 (default 3x markup, or × setPrice if custom)

9. Weight Calculation

Auto-calculated from physical properties (overridden by setWeight if set).

Component	Formula
Foam volume	(H-0.125) × (W-0.25) × L (subtracts coating thickness)
Foam weight	volume × 0.0005787 × 16 (1 lb EPS density in oz/cu in)
Mesh weight	meshWidth × meshLength / 1296 × 4.5 (sq in to sq ft, 4.5 oz/sq ft)
Base coat weight	surfaceArea × 0.005275 × 16 (density × thickness in oz/sq in)
Total weight	foam + mesh + baseCoat (converted to lbs)

Last updated: March 2026. Formulas can be customized per-product via the Settings panel in the calculator.