Centroids and centers of gravity2D
Straight and curved wire centroid
Calculate signed-area, polygon, density-weighted, and line centroids with explicit invalid-geometry checks.
Open the complete lessonAdvanced engineering statics simulation
Centroids and Centers of Gravity Suite
Validated signed area, density weighting, polygon geometry, and length-weighted wire centroids.
Use length-weighted centroids for vertical, horizontal, and semicircular wire elements.
valid geometry
Total length
342.83
mm
x centroid
66.660 mm
y centroid
23.335 mm
| Component | measure | xi | yi | measure·xi | measure·yi |
|---|---|---|---|---|---|
| Vertical segment | 120.00 | 0.00 | 60.00 | 0.00 | 7200.00 |
| Horizontal segment | 160.00 | 80.00 | 0.00 | 12800.00 | 0.00 |
| Upper semicircular arc | 62.83 | 160.00 | 12.73 | 10053.10 | 800.00 |
For uniform areas use mᵢ=Aᵢ; use negative area for a fully contained hole, density-weighted area for nonuniform materials, and length for wires.
Model scope and verification
Scope: Educational rigid-body statics model using the selected geometry, stated idealizations, and displayed SI units.
Acceptance check: Check the governing equilibrium, compatibility, geometry, or limiting-condition statement before accepting the numerical result.