Quick guide
How to use this calculator
- Choose the analysis mode that matches the physical model before entering values.
- Enter properties, geometry, loads, states and coefficients from one consistent unit and sign convention.
- Use the intermediate outputs to audit the relationship, then retain the stated idealization before applying it.
Calculation method
Transparent engineering model
A=ΣAᵢ; x̄=ΣAᵢxᵢ/A; centroidal moments use the parallel-axis theorem; principal moments follow the Ix–Iy–Ixy transformation.
The calculator evaluates only the declared relationship and preserves visitor-entered assumptions rather than selecting materials, factors, components or standards.
Worked example
Worked example
Two 100×20 rectangles centered at y=0 and y=80 have centroid y=40 and total area 4,000 square units.
A=ΣAᵢ; x̄=ΣAᵢxᵢ/A; centroidal moments use the parallel-axis theorem; principal moments follow the Ix–Iy–Ixy transformation.
Supported inputs
Precision and limits
Analysis, not approval
Rectangular ideal components only. Overlap must be avoided or modeled deliberately; thin-wall, plastic, torsional and local-buckling properties are excluded.
Standards and properties
Material properties, allowable values, load combinations, safety factors, correlations, manufacturer data, codes and jurisdictional requirements are not supplied automatically.
Units and precision
Use one consistent unit basis. Results retain working precision but cannot be more accurate than the entered measurements and properties.
Privacy
Entered engineering values and results stay in this browser and are not sent to analytics or third parties.