Overlapping CAD Solids: When a Volume Total Is 20% Too High
Technical note prepared for CADProps with AI assistance. The example below uses synthetic geometry and checked arithmetic. It is not a report of a CAD software test or a customer project.
Two valid solids can produce a misleading material estimate even when their individual volumes are correct. If they overlap, adding their volumes counts the shared region twice. Whether that is an error depends on what you are trying to measure.
This example separates two questions: how much volume belongs to the listed bodies, and how much space their geometric union occupies.
A two-block example
Use millimetres and create two rectangular solids as separate bodies:
Body A: x = 0 to 40, y = 0 to 20, z = 0 to 10.
Body B: x = 30 to 50, y = 0 to 20, z = 0 to 10.
Both blocks have the same height and width. Their shared region is x = 30 to 40, so the overlap is 10 × 20 × 10 mm.
A volume = 40 × 20 × 10 = 8,000 mm³.
B volume = 20 × 20 × 10 = 4,000 mm³.
Sum of body volumes = 12,000 mm³.
Overlap volume = 10 × 20 × 10 = 2,000 mm³.
For two solids, the union volume is:
V(A union B) = V(A) + V(B) − V(A intersection B)
Here, that gives 10,000 mm³. A second check is available without any Boolean calculation: the union is a single 50 × 20 × 10 mm block, also 10,000 mm³.
If the intended product is one continuous, homogeneous solid occupying that union, using 12,000 mm³ overstates its material volume by (12,000 − 10,000) / 10,000 = 20%. Notice the denominator: the excess is 16.67% of the summed total, but 20% of the intended union volume.
What happens to estimated mass?
Choose an illustrative density of 2.70 g/cm³. This is an assumption, not a material certificate. Divide mm³ by 1,000 to obtain cm³.
Body-sum estimate: 12 cm³ × 2.70 = 32.4 g.
Union estimate: 10 cm³ × 2.70 = 27.0 g.
Difference: 5.4 g.
Changing the density cannot fix the double-counted geometry. First choose the correct geometric quantity, then apply a suitable density.
Reproduce the check in your CAD system
Work on a copy. Create the blocks as separate bodies and verify their dimensions and positions.
Record each body’s volume and the selected-body total. Record the units and exactly which bodies were included.
Use the system’s interference or Boolean-intersection tool to identify the shared region. The analytic target here is 2,000 mm³.
On another copy, join the two bodies. Measure only the resulting solid, excluding any retained input bodies. The target is 10,000 mm³.
Inspect the result and any geometry warnings. A failed Boolean operation is not evidence that the intersection volume is zero.
For terminology, Autodesk’s Fusion Combine documentation distinguishes Join, Cut and Intersect, and its Keep Tools option can retain input bodies. Inventor’s interference documentation describes reporting the volume of intersecting components. These references explain operations; they are not evidence that this example was run in either product.
Do not automatically fuse an assembly
A bill-of-materials estimate may legitimately sum the masses of separate manufactured parts. If those parts overlap in the assembly model, investigate placement, duplicate instances and design intent. An intentional press fit can also produce nominal interference. Replacing the assembly with a union would change the question and discard component boundaries.
Likewise, a repeated component is not automatically a duplicate mistake. Two correctly placed instances should both contribute to a parts total. For three or more intersecting bodies, subtracting every pairwise overlap without accounting for triple intersections is also unsafe. Use a validated union when occupied material volume is actually the target.
Label the number before using it
A useful report says “sum of these two body volumes” or “volume of their Boolean union,” rather than simply “total volume.” Include the model revision, configuration, selection, units, method and unresolved warnings.
The CADProps volume-tool documentation states that ordinary assembly properties sum instances and do not subtract overlapping material. That is the product’s documented behavior, not an independently tested result here. Regardless of the tool, establish whether its number answers your material, component or occupied-space question before using it for a quote.