Section Properties Calculator

1 · Section Definition — Node Coordinates

Instructions:

Define the cross-section boundary as an ordered list of (X, Y) coordinates in mm.
The polygon must be closed: the last point must equal the first point.
Coordinate origin is arbitrary — centroid location adjusts automatically.
Points may be defined clockwise or counter-clockwise. Maximum 40 points.

Node	X_o (mm)	Y_o (mm)	Note

2 · Section Diagram

Figure 1 — Cross-section outline with centroid (interactive, not to scale)

Figure 2 — Centroidal & principal axes

3 · Section Properties

Cross-Sectional Area

— mm²

Centroid X_c

—

Centroid Y_c

—

Centroidal Axes (x–y)

I_x = — mm⁴

I_y = — mm⁴

I_xy = — mm⁴

r_x = — mm

r_y = — mm

Principal Axes (x'–y')

I_x' = — mm⁴

I_y' = — mm⁴

I_xy' = 0 mm⁴ (always 0)

r_x' = — mm

r_y' = — mm

θ = — ° (angle of principal axes)

Elastic Section Moduli (distance to extreme fibre)

About x-axis

y_top = — mm

y_bot = — mm

W_x,top = — mm³

W_x,bot = — mm³

About y-axis

x_left = — mm

x_right = — mm

W_y,left = — mm³

W_y,right = — mm³

Method: Green's Theorem (Shoelace Formula) for arbitrary polygonal cross-sections. Refs: Boresi & Schmidt, "Advanced Mechanics of Materials", 6th ed. · Pilkey, "Analysis and Design of Elastic Beams", Wiley 2002.