Calculation Methodology & Standards
We believe calculation tools should be completely transparent about how results are derived. This document details the mathematical formulas, physical standards, assumptions, limitations, and primary data sources behind Calqor.
01 Pallet Optimization & Ti-Hi Stacking Math
Open Tool →The FBA Pallet Optimizer determines how many cartons fit onto a standard pallet deck by evaluating three common planar orientations and bounding the load by height and weight limits:
rows = floor(Pallet_W / Box_W)
Ti_A = cols × rows
Carton length aligns with pallet length.
rows = floor(Pallet_W / Box_L)
Ti_B = cols × rows
Cartons rotated 90° across pallet deck.
block2 = rotated residual fill
Ti_C = block1 + block2
Combines perpendicular blocks to fill remaining deck space.
Usable_Height = Max_Stack_Height (72.0") − Pallet_Base_Height (6.0")
Hi = floor( Usable_Height / Carton_Height )
Volumetric_Capacity = Optimal_Ti × Hi
Weight_Capacity = floor( (Max_Pallet_Weight − Tare_Weight) / Carton_Weight )
Allowed Cartons = min( Volumetric_Capacity, Weight_Capacity )
02 Container Packing & CBM Stuffer Math
Open Tool →The CBM Container Stuffer evaluates floor and volumetric capacity for 20ft GP, 40ft GP, and 40ft High Cube containers based on ISO 668 internal dimensions:
| Container Type | Internal Dims (L × W × H) | Nominal CBM | Usable CBM (85–90%) | Payload (Road / Structural CSC) |
|---|---|---|---|---|
| 20ft General Purpose (20GP) | 5.90 × 2.35 × 2.39 m | 33.2 CBM | ~28.0 CBM | ~21,800 kg road / 28,180 kg CSC |
| 40ft General Purpose (40GP) | 12.03 × 2.35 × 2.39 m | 67.7 CBM | ~58.0 CBM | ~21,500 kg road / 26,730 kg CSC |
| 40ft High Cube (40HC) | 12.03 × 2.35 × 2.69 m | 76.3 CBM | ~68.0 CBM | ~21,500 kg road / 26,580 kg CSC |
*Note: Exact payload ratings are stamped on each individual container's CSC safety approval plate and vary slightly by container manufacturer and shipping line. Road hauling limits often dictate a lower cargo weight threshold than the container's structural payload rating.
03 Dimensional Weight & Carrier Surcharges Math
Open Tool →Carriers bill whichever is higher: the actual scale weight or the volumetric (dimensional) weight:
Common Divisors: 139 (FedEx / UPS Daily Rates), 166 (USPS / Retail)
Common Divisors: 5,000 (Commercial Express / DHL), 6,000 (IATA Air Cargo standard)
Total Size = Length + (2 × Width) + (2 × Height)
Packages exceeding 105 or 130 inches total size trigger Additional Handling or Oversize surcharges under major parcel carriers. Packages over 165 inches combined length + girth are typically non-conveyable or refused.
04 LCL vs. FCL Break-Even Math
Open Tool →Less-than-Container-Load (LCL) freight is quoted per revenue ton (CBM or 1,000 kg), while Full-Container-Load (FCL) is quoted as a flat lump-sum per container.
Typically, when cargo volume exceeds 13–16 CBM, booking a full 20ft container (even if partially empty) becomes more cost-effective and significantly faster than paying LCL consolidation, de-consolidation, and warehouse storage fees.
05 Assumptions & Limitations
To use these tools effectively, shippers should understand what the models assume and where real-world variations occur:
- Single-SKU Uniformity: The FBA Pallet Optimizer and CBM Container Stuffer model shipments of identical carton sizes. They do not simulate heterogeneous 3D bin-packing of varying box sizes in a single run.
- Corrugate Deflection & Bulge: Calculations assume rigid, rectangular cartons. In practice, cartons packed with soft goods or heavy items can bulge outwards by 0.25 to 0.5 inches (6 to 12 mm). If your cartons bulge, effective dimensions increase, which may reduce your layer count or create pallet overhang.
- Structural Compression & ECT: The tools do not model vertical crush strength or humidity-induced box degradation. Always verify your box Edge Crush Test (ECT) rating when stacking heavy cargo 5–7 layers high.
- Highway Weight Limits: The CBM Stuffer checks container maximum payload ratings (e.g., ~21,800 kg for 20ft). However, over-the-road trucking regulations often cap gross vehicle weight lower (e.g., US federal limit of 80,000 lbs gross vehicle weight, typically restricting container cargo to ~40,000–44,000 lbs unless tri-axle chassis permits are arranged).
06 Verified Primary Data Sources
| Rule / Standard | Standard Specifications | Source Document | Last Verified |
|---|---|---|---|
| Amazon FBA Pallet Requirements | 48×40 GMA Wood, 72" Max Height, 1,500 lb Max Weight | Amazon Seller Central LTL/FTL Guidelines | September 2026 |
| ISO Shipping Containers | ISO 668 Series 1 Container dimensions (20GP, 40GP, 40HC) | ISO 668:2020 Standard | September 2026 |
| European Euro Pallet | 1200×800 mm (EPAL 1), 4-way block specification | EPAL Technical Regulations | September 2026 |
| UPS Parcel Dimensional Weight | Divisor 139 (Daily Rates), AHS triggers (>48" longest side or >50 lb) | UPS Rate & Service Guide | September 2026 |
| FedEx Parcel Dimensional Weight | Divisor 139, AHS and Oversize (>130" Length + Girth) thresholds | FedEx Service Guide | September 2026 |
| Air Freight DIM Factors | Divisor 6,000 cm³/kg (IATA Resolution 606); commercial 5,000 cm³/kg | IATA Cargo Guidelines | September 2026 |
07 Worked Test Cases
You can verify our math against these sample benchmark cases:
Inputs: Carton 16.0" L × 12.0" W × 10.0" H, weight 20.0 lbs. Standard GMA 48×40 pallet.
• Ti (Orientation B) = floor(48/12) × floor(40/16) = 4 × 2 = 8 cartons
• Ti (Orientation C Pinwheel) = 10 cartons (3 length + 1 rotated block)
• Optimal Ti = 10 cartons/tier
• Hi = floor((72.0 - 6.0) / 10.0) = 6 tiers high
• Volumetric capacity = 10 × 6 = 60 cartons
• Weight capacity = floor((1500 - 45) / 20) = 72 cartons
• Output: 60 cartons per pallet, gross weight 1,245.0 lbs (Height-limited at 66.0" cargo + 6.0" base = 72.0" total).
Inputs: Carton 20" L × 16" W × 14" H, actual weight 15.0 lbs. Shipped via domestic commercial carrier.
• Divisor 139: ceil(4480 / 139) = 33.0 lbs billable weight
• Billable Weight Penalty = 33.0 − 15.0 = +18.0 lbs over scale weight (120% increase)
• Length + Girth = 20 + 2(16 + 14) = 80 inches (No oversize surcharge triggered).
08 Corrections Policy & Version Log
We are committed to maintaining accurate, up-to-date calculation logic. When carriers revise volumetric divisors or Amazon updates receiving thresholds, we review and patch our algorithms promptly.
Discovered a discrepancy or have an updated carrier rate guide? Please submit details through our Contact page or email [email protected].