Thin-Wall CAD Mass: Why a Small Thickness Tolerance Matters
A nominal CAD mass is a result for one geometric model, not automatically a prediction of the full manufacturing variation. A hollow rectangular section makes that distinction easy to calculate.
Disclosure: Prepared on behalf of CADProps with AI assistance. This is an original synthetic example with checked arithmetic, not a customer experience, physical measurement, or benchmark of CADProps or another CAD application.
A square-cornered tube with fixed outer dimensions
Consider an open-ended rectangular tube, 100 mm long, with outer width 40 mm and outer height 30 mm. Model both outer and inner profiles as exact rectangles, with no fillets or chamfers. Let the wall parameter t reduce each inner dimension by 2t. This idealized profile is not a specification for a real extruded tube, whose corner radii and tolerances need separate treatment.
The material volume is:
V(t) = L[WH − (W − 2t)(H − 2t)]
V(t) = 100(140t − 4t²) mm³
At the nominal t = 2.0 mm, the inner opening is 36 × 26 mm, giving V = 26,400 mm³ = 26.4 cm³.
Change thickness, not the bounding box
Now vary only t, keeping the length and both outer dimensions fixed:
t = 1.8 mm: V = 23,904 mm³, 9.455% below nominal.
t = 2.0 mm: V = 26,400 mm³.
t = 2.2 mm: V = 28,864 mm³, 9.333% above nominal.
Every model still has a 40 × 30 × 100 mm outer envelope. A matching bounding box therefore says nothing about this particular source of material variation.
Using an illustrative constant density of 2.70 g/cm³ gives masses of 64.541 g, 71.280 g and 77.933 g, respectively. This density is an assumption for the calculation, not a material certificate. Convert mm³ to cm³ by dividing by 1,000 before multiplying by density in g/cm³.
A sensitivity check you can do by hand
The derivative is dV/dt = 100(140 − 8t). At t = 2 mm, it equals 12,400 mm². A small change of ±0.2 mm therefore predicts approximately ±2,480 mm³, or ±9.394% of nominal volume.
The exact changes are −2,496 and +2,464 mm³. Both differ from the linear prediction by −16 mm³ because the quadratic correction is −4L(Δt)². The unequal percentages are expected, not a rounding error.
Use the example as a CAD regression check
Create one outer rectangular prism and subtract a through-going inner prism. Keep the openings clear of end caps.
Make three independent configurations at 1.8, 2.0 and 2.2 mm. Confirm that only the inner dimensions change.
Record model units, body selection, volume and density. Compare volumes with the analytic values above before comparing mass.
If the numbers disagree, check for rounded corners, added caps, omitted bodies or a unit conversion problem. Do not tune density to conceal a geometric mismatch.
These are deterministic endpoint scenarios, not a statistical tolerance analysis. Real wall thickness may vary locally; outer dimensions, radii and density can also vary or be correlated. A drawing tolerance must define what is actually controlled before these endpoints can be treated as bounds.
For a file-based property-check workflow, CADProps is the associated product referenced by this note. The arithmetic here is tool-independent and does not claim that CADProps performs tolerance propagation. Check format and feature support before relying on any tool, and upload only geometry you are authorized to share.
Takeaway: report the nominal geometry and the assumptions behind it. Extra decimal places in a CAD mass cannot replace a thickness tolerance.