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Centroids and centers of gravity2D

Composite-area centroid builder

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.

Combine a flange and web without overlap and inspect their first-moment contributions.

Primary width
160 mm
mm
60–300

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

Web height
120 mm
mm
40–260

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

Flange thickness
40 mm
mm
10–100

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

valid geometry
Signed area
8800.00
mm²
x centroid
80.000 mm
y centroid
118.182 mm
Componentmeasurexiyimeasure·ximeasure·yi
Flange6400.0080.00140.00512000.00896000.00
Web2400.0080.0060.00192000.00144000.00
xˉ=∑mixi∑mi,yˉ=∑miyi∑mi\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.

Related simulations

Plate with circular openingParameter-edited polygon centroidDensity-weighted center of gravityStraight and curved wire centroid