Why the average end areas can misstate a tapered box volume.
Do length and width both change along the height?
Use the matching calculator
Use this decision sequence
- Confirm rectangular cross-sections stay aligned and change linearly in both dimensions.
- Calculate the bottom and top areas separately.
- Calculate middle area from the average dimensions, not the average end areas.
- Use the bottom, middle and top areas in the stated prismoidal expression.
Keep the quantities distinct
| Quantity or assumption | How to use it |
|---|---|
| Average dimensions | Give the actual midpoint cross-section under linear change. |
| Average end areas | Do not capture the quadratic area change. |
| Measured stations | Are needed for a different or irregular profile. |
Worked comparison
An illustrative 3 m-high container changes from 2×1 m at the bottom to 4×3 m at the top. Midpoint dimensions are 3×2 m, giving area 6 m². Exact volume for linear dimension changes is 3×(2+4×6+12)/6 = 19 m³. Using the simple average end area gives 21 m³ instead.
Check before using the estimate
The stated cross-section model must match the container; height and two end areas alone do not establish it.
All dimensions, product properties, prices and specifications in this example are illustrative arithmetic inputs. Use the values from your measured plan, selected product data sheet and supplier quote. This guide does not choose construction specifications or certify safety.
Calculation and scope checked 2026-10-04. Methods and scope.
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