Use this reference to check three common calculations by hand and understand what their results mean. It covers simplified box strength, rectangular pallet counts and geometric tipping. It is a selected methods note, not a complete specification of every PackCalc calculator or a certificate of compliance.
1. Simplified McKee box strength
The Box Compression Strength Calculator uses this simplified relation when estimating BCT from board properties:
BCT = 5.87 × ECT × sqrt(caliper × perimeter)
perimeter = 2 × (length + width)For this form, enter ECT in lb/in, caliper and perimeter in inches, and read BCT in pounds-force (lbf). The constant belongs to this unit convention; substituting millimetres directly changes the answer incorrectly. Convert all inputs first. For example, 0.14 in is exactly 3.556 mm.
Worked example: a 16 × 12 in footprint, 44 lb/in ECT and 0.14 in caliper give:
- Perimeter:
2 × (16 + 12) = 56 in. - Square-root term:
sqrt(0.14 × 56) = 2.8 in. - Raw BCT estimate:
5.87 × 44 × 2.8 = 723.184 lbf, about 723 lbf.
This is a short-duration strength estimate before environmental, storage, support and design-margin adjustments. A box-height input is not a substitute for board caliper. Measured BCT from the specified converted box provides a separate evidence basis.
The simplified equation uses perimeter, so it cannot distinguish every footprint shape or construction. PackCalc marks a length-to-width ratio above 3:1 as outside its McKee footprint range. Low-height and other applicability warnings also matter. Urbanik describes limits including length no greater than three times width and perimeter no greater than seven times box depth. Urbanik (1996), geometry and buckling review An entered case-proportion adjustment is a user-supported assumption, not a factor that PackCalc independently validates. Research comparing box-compression models documents differences between McKee estimates and measured datasets. Urbanik and Frank, Box compression analysis of world-wide data spanning 46 years (2006)
See the BCT guide for the distinction between the estimate, allowable loading and laboratory evidence.
2. Pallet layer counts and total height
For a simple upright rectangular grid with no overhang, divide each pallet dimension by the corresponding outside case dimension and round each count down. Try the rotated footprint as well.
Worked example: 400 × 300 × 250 mm cases on a 1200 × 800 mm pallet:
- First orientation:
floor(1200/400) × floor(800/300) = 3 × 2 = 6cases per layer. - Rotated footprint:
floor(1200/300) × floor(800/400) = 4 × 2 = 8cases per layer. - With a 1500 mm total-height limit and a 150 mm pallet, the case stack has
1500 - 150 = 1350 mmavailable. - Full layers:
floor(1350/250) = 5. - This grid gives
8 × 5 = 40cases at a total loaded height of150 + 5 × 250 = 1400 mm.
These are geometric counts. Check payload and pallet limits separately, including tare where the limit is gross weight. Compression or stability can reduce the permitted layers. Other arrangements can outperform a simple grid, and changing which case axis is vertical changes both layer geometry and stack height.
The Pallet Calculator compares supported arrangements. The hand calculation above is a useful check of one feasible arrangement, not proof of the global maximum. Read the boxes-per-pallet guide for more examples.
3. Geometric tipping and its limits
For a centered, rigid unit with a support width b and combined center-of-gravity height h above the supporting plane:
critical angle = arctan((b / 2) / h)
static acceleration equivalent, a/g = (b / 2) / hKeep b and h in the same length unit. For a 1000 mm support width and 1200 mm CG height, the ratio is 500/1200 = 0.4167 and the angle is about 22.6°. This falls below a 0.5g geometric screening target.
PackCalc’s palletized-unit model includes pallet height and, when supplied, pallet tare in the combined CG. It assumes the load is secured to the pallet and uses the pallet footprint as support. An off-center load must use the distance to the relevant tipping edge, not automatically half the width.
A geometric screen does not model sliding, wrap relaxation, case deformation or the acceleration pulse of a road event. EUMOS 40509 evaluates load-unit rigidity dynamically; a calculated angle cannot establish compliance with that test. EUMOS standards overview
Use the Pallet Load Stability Calculator to inspect the modeled directions and assumptions, then choose physical verification appropriate to the shipment. The stability guide explains the distinction in more detail.
4. What to record with a result
Keep the engineering basis with the number: input dimensions and whether they are inside or outside, units, gross weights, board properties, selected arrangement, conditions, assumptions and the calculation date. Treat rounded displays as presentation. Re-entering them as if they were the original dimensions can change a tight fit or limit check.
When comparing a saved calculation with new work, check that the geometry, material and shipment assumptions still describe the same design. A saved estimate records a planning decision; it does not replace a laboratory report, carrier classification or a current customer specification.
For environmental calculations, continue with absolute humidity and conditioning and the Accelerated Aging Calculator, including its temperature-based Q10 assumptions.
Sources
- US Forest Service: Urbanik and Frank (2006), box-compression model analysis.
- EUMOS: standards and scope of the load-unit rigidity test.
- The worked numbers on this page are PackCalc examples, with their units and assumptions stated above.