Ebora Online Tutorial Services
Section Properties Solver — Ebora Online Tutorial Services

Cartesian Plane ⚠ Tap Set Origin (key O) to show the X & Y axes — needed for centroid distances

i Line: click on the canvas to set the starting point.
x: 0, y: 0
Solid (shaded) Hollow (a loop drawn inside another) Centroid (C) Origin (0,0) — hidden until Set Origin is used

Section Properties

🔓

Solve this section

Set the origin, then solve to reveal the area, centroid, the common-shapes (Varignon's theorem) breakdown, and every detailed value.

Common Shapes — finding x̄ & ȳ (Varignon's Theorem)

The section is split into simple shapes the way you would solve it by hand — rectangles, triangles, and circular parts (circle, semicircle, quarter-circle, or sector). Each colored piece matches its color on the drawing. x̄ᵢ, ȳᵢ are each piece's centroid measured from the origin axes; multiply by its area, sum, and divide by the total area to get the section centroid (Varignon's theorem).

⚠ This solver only handles straight edges and circular arcs (which break down into the shapes above). It does not support parabolas, ellipses, or other curves — don't use it for sections with those.

PartShapeArea Aᵢx̄ᵢȳᵢAᵢ·x̄ᵢAᵢ·ȳᵢ
🧩

Solve to see the common-shapes breakdown

Every common shape, its area, centroid, and the Varignon sums for x̄ and ȳ — shown once you solve.

Detailed Values

PropertySymbolValueUnit
🔓

Detailed section values

Every centroidal moment of inertia, principal axes, radii of gyration, and section moduli — shown once you solve.

© Ebora Online Tutorial Services
✂️ Crop — draw a box around just the cross-section
Drag to select. Resize using corner handles. Anything outside the box is ignored.
EboraBot
👋 Hi! I'm EboraBot — ask me a math problem!