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Centroids and centers of gravity2D

Parameter-edited polygon 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.

Move the two upper vertices through dimensional controls and apply the shoelace centroid equations.

Primary width
160 mm
mm
60–300

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

Primary height
120 mm
mm
40–260

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

Upper-left vertex x
40 mm
mm
0–180

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

Upper-right inset
25 mm
mm
0–180

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

valid geometry
Signed area
16650.00
mm²
x centroid
81.396 mm
y centroid
59.760 mm
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

Composite-area centroid builderPlate with circular openingDensity-weighted center of gravityStraight and curved wire centroid