Post Cap Pyramid Formula Reference

Geometry, cost, and weight formulas for PCI-101 through PCI-108 foam post caps

1. Pyramid Geometry

Post caps are square-base pyramids with no top face (open bottom). The coated surface is the 4 triangular slant faces only — the base sits on the column and is not coated.

H A (base side) slant h Apex (pyramid tip) Base corner
3D perspective view
H A A/2 slant h slant h = √( (A/2)² + H² )
Side cross-section (one triangular face)
Key Insight: Pythagorean Theorem The slant height of each triangular face runs from the apex down to the midpoint of a base edge. It forms a right triangle with the pyramid height (H) as one leg and half the base side (A/2) as the other.

Surface Area: 4 Triangular Faces (Unwrapped)

A slant h 1 A 2 A 3 A 4 = Each face: ½ × A × slant h × 4 faces = 2 × A × slant h
Total coated surface area (sq in) wSurfArea = 2 × A × √( (A/2)² + H² )

2. Post Cap Dimensions (PCI Models)

For post caps, the dimension mapping is different from standard trim profiles:

Dimension Mapping

VariablePost CapsStandard Trim
H (Height)"B" — pyramid height"A" dimension
W (Width)"A" — base side"B" dimension
A (aSize)"A" — base side (= W)"A" dimension (= H)
L (Length)= A (square base)Run length (96″ std)

Common Properties

PropertyValue
Corners4
Pieces1
Waste multiplier1.05 (5%)
Labor coating mult8.0
A range10″ – 52″
Note: H varies by model! Each PCI model (101–108) has a different pyramid height profile. Two caps with the same A (base) dimension will have different H values depending on which model they are. The H is stored per product entry in the catalog database — no lookup table is needed.

H Values by Model at A = 12″

ModelStyleH at A=12H/A RatioSlant HSurface Area
PCI-101Classic5.3750.4488.02″192.5 in²
PCI-102Raised5.6250.4698.19″196.6 in²
PCI-103Tapered5.6250.4698.19″196.6 in²
PCI-104Low Profile5.0000.4177.81″187.5 in²
PCI-105Mid Profile5.2500.4387.95″190.9 in²
PCI-106Flat5.1250.4277.88″189.2 in²
PCI-107Tall6.0000.5008.49″203.7 in²
PCI-108Standard5.3750.4488.02″192.5 in²
Slant H = √(6² + H²)  |  Surface Area = 2 × 12 × Slant H

3. Formula Definitions (Post Cap Path)

The calculator evaluates formulas sequentially. Each formula can reference all previously computed values. Below shows only the post cap code path for each branching formula.

Step 1: Derived Constants

postCapSlantH — Slant height of each triangular face √( (aSize / 2)² + H² )
H A/2 slantH

Step 2: Cutting Geometry

perimeter — Base perimeter for foam cutting 4 × aSize
A A A A Top-down view (base outline)
Cutting follows the base perimeter: 4 × A

Step 3: Coating & Mesh Dimensions

coatingLength — "Width" of unwrapped surface for area calc 2 × postCapSlantH
lengthFactor — "Length" of unwrapped surface (ft) for area calc aSize / 12
Why these values? Cost formulas compute area as (coatingLength / 12) × lengthFactor sq ft. For a pyramid:
(2 × slantH / 12) × (A / 12) = 2 × A × slantH / 144 sq ft — which equals the correct surface area in sq ft.
2 × slantH (coatingLength) A (lengthFactor × 12) → Equivalent rectangle 2×slantH A Area = 2 × A × slantH (same as 4 triangles)
4 triangular faces unwrap to a rectangle of (2 × slantH) × A

4. Cost Formula Flow

Material Costs

FormulaPost Cap ExpressionWhat It Computes
foamCostCalc ((H+0.2) × (W+0.2) × L) × costPerCuIn / pieces Foam block cost (rectangular billet before carving)
meshCostCalc (meshCost/meshCoverage) × (meshLen+4)/12 × aSize/12 Fiberglass mesh cost (area-based + 4″ overlap)
glueCostCalc glueCostPerSqFt × (meshLen+4)/12 × aSize/12 Adhesive cost (same area as mesh)
baseCostCalc cementCostPerSqFt × (2×slantH)/12 × aSize/12 Base coat cement (exact pyramid surface area)

Labor Costs

FormulaPost Cap ExpressionWhat It Computes
laborCutting 4 × aSize × cuttingPerIn Hot-wire cutting along base perimeter
laborMeshCut laborHourly / 120 Mesh cutting time (fixed)
laborGlue meshingPerCorner × 4 Gluing/meshing per corner (always 4 corners)
laborCoating (coatingCalc/12) × coatingPerSqFt × 8.0 Coating labor (8x multiplier for pyramid difficulty)
Final cost total = (foamCost + meshCost + glueCost + baseCost) + (cutting + meshCut + glue + coating) × laborTax
totalWaste = total × 1.05

5. Weight Formula Flow

Foam Volume (H-0.125) × (W-0.25)² (cube billet, not pyramid) × 0.0005787 × 16 = oz Mesh Weight width × length / 1296 × 4.5 (standard trim path, not pyramid-specific) Coated Surface 2 × A × slantH × 0.011574 × 16 = oz (base coat weight) + + Total Weight (oz) = foam + mesh + baseCoat wFoamOz wMeshOz wBaseCoatOz
FormulaPost Cap ExpressionNotes
wFoamVol (H-0.125) × (W-0.25) × (W-0.25) Cube billet volume (before carving)
wFoamOz wFoamVol × 0.0005787 × 16 EPS density: ~0.9 lb/ft³
wSurfArea 2 × aSize × postCapSlantH Pyramid surface area (4 slant faces)
wBaseCoatOz wSurfArea × 0.011574 × 16 Base coat coverage rate
wTotalOz wFoamOz + wMeshOz + wBaseCoatOz Shipping weight

6. Old vs New Formulas

FormulaOld (Incorrect)New (Correct)Impact
perimeter (H + aSize) × 2 4 × aSize Treated profile as rectangle; now uses actual base perimeter
coatingLength perimeter - aSize 2 × slantH Was a cross-section remnant; now represents unwrapped face height
lengthFactor aSize × 2 / 12 aSize / 12 Was double-counting; now correct base dimension in feet
wSurfArea coatingLen × aSize × 2 2 × aSize × slantH Core fix: uses Pythagorean slant height for true pyramid area

Numerical Example: PCI-101 at A = 12″

A = 12, H = 5.375

OldNewΔ
slantH — 8.02″ (new)
perimeter 34.75″ 48.00″ +38%
coatingLength 22.75″ 16.04″ -29%
lengthFactor 2.00 ft 1.00 ft -50%
wSurfArea 546.0 in² 192.5 in² -65%
cost area (sq ft) 3.79 1.34 -65%
The old formula was drastically over-estimating surface area — by ~2.8x for a typical post cap. This inflated mesh, glue, base coat costs, and shipping weight.

7. Interactive Calculator

Inputs

in
in
Slant Height--
Surface Area (4 faces)--
Surface Area (sq ft)--
Base Perimeter--
Coating Length--
Length Factor--
Area Check (coatLen/12 × lenFactor)--
Old Surface Area--
Difference--

Visual: Side Profile

Post Cap Formula Reference — Invicta Tools Calculator — Updated March 2026