Composite Area and Centroid Calculator
Combine axis-aligned rectangles and circles, subtract holes, and calculate a centroid and centroidal second moments of area.
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Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Sum signed component areas, find the area-weighted centroid and apply the parallel-axis theorem to signed second moments.
A=ΣsAᵢ; x̄=ΣsAᵢxᵢ/A; Ix=Σs[Ixᵢ+Aᵢ(yᵢ−ȳ)²]
Worked example
A centered 4 by 2 rectangle with a centered circular hole of radius 0.5 has area 8−π/4, centroid (0,0), and Ix=16/6−π/64 in the corresponding fourth-power units.
Assumptions and input details
1–30 axis-aligned components, with circles entered by radius. The last column is ignored for circles; enter 0. Overlapping material components are counted twice and hole containment is not checked: enter a valid non-overlapping material decomposition. This is additive planar geometry, not a material-strength, stress or structural-design check. Ix and Iy are area moments, not mass moments.
References: Purdue: centroids and parallel-axis theorem
Unit definitions
Unit selection is independent of language. Each selector contains only units for its physical quantity. Calculations use defined base units internally.
Choose from 23 length definitions, including explicitly labelled regional measures. Area conversions square the length factor; geometric volumes cube it.
Regional measures are not interchangeable merely because their names look similar. This is a documented selection, not a claim to include every historical unit.
NIST measurement tables · Japanese traditional units · Mainland China and Hong Kong unit distinctions
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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