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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 lesson

Advanced 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.

Horizontal segment length
160 mm
mm
60300

Drag for exploration or enter an exact value. Press Enter to apply and Escape to restore.

Vertical segment length
120 mm
mm
40260

Drag for exploration or enter an exact value. Press Enter to apply and Escape to restore.

Semicircular arc diameter
40 mm
mm
10180

Drag for exploration or enter an exact value. Press Enter to apply and Escape to restore.

valid geometry
Total length
342.83
mm
x centroid
66.660 mm
y centroid
23.335 mm
Componentmeasurexiyimeasure·ximeasure·yi
Vertical segment120.000.0060.000.007200.00
Horizontal segment160.0080.000.0012800.000.00
Upper semicircular arc62.83160.0012.7310053.10800.00
xˉ=miximi,yˉ=miyimi\bar{x}=\frac{\sum m_i x_i}{\sum m_i},\qquad \bar{y}=\frac{\sum m_i y_i}{\sum m_i}

For uniform areas use mᵢ=Aᵢ; use negative area for a fully contained hole, density-weighted area for nonuniform materials, and length for wires.

Concept question: Predict the x-coordinate of the centroid.

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.