I-Beam Moment of Inertia Calculator

Calculator Inputs

Project name

Input unit

Total depth, H

Top flange width, Bt

Top flange thickness, Tt

Web thickness, Tw

Bottom flange width, Bb

Bottom flange thickness, Tb

Material density, kg/m³

Decimal places

Notes

Example Data Table

Example	H	Bt	Tt	Tw	Bb	Tb	Area	Ix	Iy
Equal flange beam	200 mm	100 mm	12 mm	8 mm	100 mm	12 mm	3,808.00 mm²	24,869,717.33 mm⁴	2,007,509.33 mm⁴
Deep light web beam	350 mm	160 mm	14 mm	8 mm	160 mm	14 mm	7,056.00 mm²	148,774,192.00 mm⁴	9,571,072.00 mm⁴
Unequal flange beam	300 mm	125 mm	12 mm	9 mm	175 mm	18 mm	7,080.00 mm²	101,726,611.02 mm⁴	10,008,590.00 mm⁴

Formula Used

The calculator splits the I-beam into three centered rectangles. These are the top flange, web, and bottom flange.

Web height: Hw = H − Tt − Tb

Area: A = BtTt + TwHw + BbTb

Neutral axis from bottom: ȳ = Σ(Ai yi) / ΣAi

Moment of inertia about the strong axis: Ix = Σ[(bi hi³ / 12) + Ai(yi − ȳ)²]

Moment of inertia about the weak axis: Iy = TtBt³ / 12 + HwTw³ / 12 + TbBb³ / 12

Section modulus: Sx top = Ix / (H − ȳ) and Sx bottom = Ix / ȳ

Radius of gyration: rx = √(Ix / A) and ry = √(Iy / A)

How to Use This Calculator

Select one unit system and keep every dimension in that unit.
Enter total depth from bottom flange face to top flange face.
Enter top flange width and thickness.
Enter web thickness. The tool calculates clear web height.
Enter bottom flange width and thickness.
Keep the default steel density, or enter another material density.
Choose decimal places, then press Calculate.
Use CSV or PDF buttons to save the same calculation.

What This I-Beam Tool Does

An I-beam carries load through a wide flange and a slender web. The shape is efficient because material sits far from the neutral axis. This calculator estimates geometric section properties from custom dimensions. It works for equal or unequal flanges. It also handles a centered web. You can model rolled shapes, built-up beams, or preliminary custom members.

Why Moment of Inertia Matters

The area moment of inertia shows how strongly a section resists bending. A larger value means less bending stress for the same moment. It also means lower deflection when material and span stay unchanged. Engineers often compare Ix for vertical bending. They compare Iy for side bending or weak-axis checks. The section modulus converts inertia into bending strength guidance.

Inputs Used by the Calculator

Enter the total beam depth, top flange width, top flange thickness, web thickness, bottom flange width, and bottom flange thickness. The web height is found by subtracting both flange thicknesses from the total depth. The tool then treats the section as three rectangles. Each rectangle has an area and a centroid. The combined centroid sets the neutral axis location.

Interpreting the Results

The output includes total area, neutral axis from the bottom, Ix, Iy, section modulus values, and radius of gyration. Sx top and Sx bottom may differ when flanges are unequal. Use the smaller section modulus for conservative bending checks. Radius of gyration helps with slenderness studies. Always keep units consistent. If dimensions are entered in inches, inertia is reported in inches to the fourth power.

Practical Design Notes

This calculator is best for layout, estimates, teaching, and quick comparison. It does not replace a full structural design check. Real beams may need checks for shear, buckling, lateral torsion, local flange slenderness, weld strength, bearing, vibration, and code rules. Manufacturing tolerances can change final values. Rounded corners in rolled sections can also add small differences. For final design, compare results with trusted steel manuals and local code requirements. Review loads carefully before selecting any beam.

For best accuracy, measure clear dimensions carefully. Do not mix metric and imperial inputs. Save a copy of the CSV file with project notes. Attach the PDF summary when sharing early sizing results.

FAQs

What is I-beam moment of inertia?

It is a geometric property that shows how the I-beam area is distributed around an axis. Higher values usually mean better bending stiffness for the same material and span.

Can this calculator handle unequal flanges?

Yes. Enter different top and bottom flange widths or thicknesses. The neutral axis and section modulus values will change automatically.

Which inertia value should I use for vertical bending?

Use Ix for common vertical bending about the beam strong axis. Use Iy when checking weak-axis bending or side bending.

Why are top and bottom section modulus values different?

They differ when the neutral axis is not centered through the depth. Unequal flanges move the centroid, so top and bottom fiber distances become different.

Does this replace a structural design report?

No. It gives section properties only. A complete design must check loads, stresses, deflection, buckling, connections, material grade, and local code rules.

What units should I enter?

Use one unit for all dimensions. If you choose millimeters, enter every length in millimeters. Results will use matching squared, cubed, and fourth-power units.

Why is density included?

Density lets the calculator estimate mass per meter and weight per meter. The default suits common steel, but you can enter another material value.

Does the formula include fillets or rounded corners?

No. It models the beam as three sharp-corner rectangles. Rolled beam fillets can cause small differences from handbook values.