Calqor Engineering Methodology v1.0.0 • Standard Pallet Physics

Engineering Methodology & Mathematical Standards

Calqor provides mathematically rigorous, deterministic calculation models for supply chain, warehousing, and freight operations. This documentation details our formulas, dimensional constants, and modular computational architecture.

Methodology Modules:

1. Core Architecture 2. Pallet Standards Pallet Stacking (FBA) Container Loading (CBM) Dimensional Weight

01 Core Engineering Principles & Zero-Runtime Philosophy

Standard web-based logistics calculators often depend on heavy server round-trips, store confidential shipment data, or rely on linear approximations that produce dangerous rounding errors in real-world loading.

Calqor is engineered on three immutable tenets:

Zero Server Latency

All spatial packing, integer cuts, and unit transforms execute instantly inside the user's browser at 60 FPS.
Zero Data Storage

Commercial quantities, carton sizes, and proprietary SKU layouts are never transmitted, logged, or stored remotely.
Exact Integer Math

Geometric layouts are computed with exact boundary flooring to prevent fictitious fractional carton packing.

02 Physical Pallet Standards & Deck Constants

Our packing engines benchmark layouts against standardized international freight specifications:

US GMA Standard 48×40 ISO 6780

DECK LENGTH 48.0" (121.92 cm)

DECK WIDTH 40.0" (101.60 cm)

BASE HEIGHT 6.0" (15.24 cm)

TARE WEIGHT 45.0 lbs (20.41 kg)

Standard 4-way entry wooden pallet mandated across North American 3PLs and Amazon US fulfillment centers.

European Euro Pallet (EPAL 1) UIC 435-2

DECK LENGTH 47.24" (120.0 cm)

DECK WIDTH 31.50" (80.0 cm)

BASE HEIGHT 5.70" (14.48 cm)

TARE WEIGHT 40.0 lbs (18.14 kg)

Standard European block pallet required for cross-docking, EU distribution hubs, and Amazon UK/EU centers.

03 Pallet Optimization & Ti-Hi Stacking Methodology

Open Pallet Optimizer →

The FBA Pallet Optimizer calculates cartons per tier (Ti), vertical tiers (Hi), bounding weights, and deck coverage using clear, closed-form formulas:

Cartons Per Horizontal Tier (Ti)

Planar Geometry

To determine the maximum number of master cartons that can fit on a single pallet layer without overhang, the algorithm evaluates three distinct packing orientations:

Orientation A: Lengthwise

Columns = floor(Pallet_Length / Box_Length)
Rows = floor(Pallet_Width / Box_Width)
Ti_A = Columns × Rows

Aligns carton length along pallet length.

Orientation B: Widthwise

Columns = floor(Pallet_Length / Box_Width)
Rows = floor(Pallet_Width / Box_Length)
Ti_B = Columns × Rows

Rotates cartons 90° across the deck.

Orientation C: Pinwheel Interlock

Block 1 = Primary column fill
Block 2 = Remaining space rotation
Ti_C = Block 1 + Block 2

Interlocks cartons to eliminate dead space.

Optimal Tier Count (Ti): Optimal Ti = Maximum( Ti_A, Ti_B, Ti_C )

Vertical Layers (Hi) & Total Height

Vertical Clearance

Amazon fulfillment centers enforce a strict 72.0-inch (182.88 cm) total stack height limit (inclusive of the wooden pallet base):

USABLE CARGO HEIGHT 72.0" − Pallet Base Height GMA: 72.0 − 6.0 = 66.0 inches

TIERS HIGH (Hi) floor( Usable Height / Box Height ) Rounded down to whole layer

TOTAL ASSEMBLED HEIGHT (Hi × Box Height) + Base Height Must strictly remain ≤ 72.0"

Dual-Constraint Pallet Capacity

Weight vs Volume Bounding

A pallet's allowable load is governed by whichever ceiling is encountered first: volumetric space or gross carrier weight (1,500.0 lbs / 680.39 kg):

1. Volumetric Capacity:

Volume Capacity = Ti × Hi

Physical carton capacity based on dimensional fit.

2. Weight Capacity (1,500 lb Limit):

Weight Capacity = floor((1500.0 − Pallet Tare Weight) / Carton Weight)

Prevents exceeding gross weight safety thresholds.

Safe Cartons Allowed Per Pallet: Cartons Per Pallet = Minimum( Volume Capacity, Weight Capacity )

Derived Logistics Manifest Formulas

Dock & Carrier Deliverables

TOTAL PALLETS REQUIRED ceil( Total Order Boxes / Safe Pallet Count )

GROSS PALLET WEIGHT (Pallet Cartons × Carton Wt) + Pallet Tare Wt

DECK AREA UTILIZATION [ (Ti × Box Area) / Pallet Area ] × 100%

04 Ocean Freight Container Packing Methodology (CBM Stuffer)

For multi-SKU ocean freight loading (20GP, 40GP, 40HQ), the methodology incorporates:

3D Guillotine Cutting Algorithms: Solving 3D bin-packing optimization with container internal clearances (door header and corner cast deductions).
Axle Weight Distribution Models: Preventing trailer front-to-rear center of gravity (CoG) imbalances to comply with highway bridge weight formulas.

05 Air & Ground Dimensional (DIM) Weight Methodology

For express parcel and air freight billing verification, the methodology evaluates carrier divisor differentials:

DIM Weight = (Length × Width × Height) / Divisor Ratio
Standard Divisors: IATA Air Cargo (5000 / 6000), FedEx/UPS Domestic (139 / 166).