i beam second moment of area calculator - Aaron Graves, PhDude Replica

Instant I-Beam Property Calculator

Use this tool to calculate the second moment of area (also called area moment of inertia) for a symmetric I-section. Enter all dimensions in the same unit.

Formulas used:

I_x = [b·h³ - (b - t_w)·(h - 2t_f)³] / 12

I_y = [h·b³ - (h - 2t_f)·(b - t_w)³] / 12

A = 2b·t_f + (h - 2t_f)·t_w

Overall height, h

Flange width, b

Flange thickness, t_f

Web thickness, t_w

Input unit

What is the second moment of area?

The second moment of area describes how strongly a cross-section resists bending around a given axis. For beams, this is one of the most important geometric properties because it directly affects deflection and bending stress.

For an I-beam, engineers usually care most about I_x (bending about the strong axis), while I_y is used for weak-axis behavior, lateral stability checks, and column buckling analysis.

How this I-beam calculator works

This page models a symmetric I section with:

Equal top and bottom flange width/thickness
A centered web
Sharp corners (no root radius)

The section properties are calculated by subtracting an inner rectangle from an outer rectangle. This method is fast and reliable for preliminary design, education, and quick checks.

Outputs included

Area, A
Strong-axis second moment, I_x
Weak-axis second moment, I_y
Elastic section moduli, S_x and S_y
Radii of gyration, r_x and r_y

Step-by-step usage

Enter height h and flange width b.
Enter flange thickness t_f and web thickness t_w.
Select your dimension unit (mm, cm, m, or in).
Click Calculate to get section properties instantly.

All input dimensions must use the same unit. The tool returns derived units automatically (for example, mm², mm⁴, and mm³).

Example

Suppose you input:

h = 300 mm
b = 150 mm
t_f = 12 mm
t_w = 8 mm

The strong-axis moment of inertia is much larger than weak-axis inertia, which is exactly why I-beams are efficient for vertical loading.

Common input mistakes to avoid

Using mixed units: e.g., h in mm and t_f in cm.
Impossible geometry: ensure h > 2t_f and b > t_w.
Assuming this is a code design check: this tool computes geometry only, not full code compliance.

Engineering note

This calculator is ideal for early-stage beam sizing, student assignments, and quick verification. For final structural design, include additional checks such as shear capacity, local buckling, lateral-torsional buckling, connection behavior, load combinations, and relevant code factors.

Why I-beams are so efficient

I sections place most material far from the neutral axis, which dramatically increases bending stiffness for a given amount of material. That is why steel and aluminum I-beams are common in buildings, bridges, machine frames, and supports.