How do I calculate the moment of inertia of an I-beam?

For a doubly symmetric I-shape it is the outer rectangle minus the two side voids: [bf d cubed minus (bf minus tw) h cubed] divided by 12, where h is the clear web depth. That is exact for square corners; a real rolled shape has fillets that add about 1 to 2%.

Does the IRC have a table for steel beams?

No. There is no prescriptive table for hot-rolled steel beams in dwellings anywhere in the IRC. Such a beam is an engineered member designed under AISC 360, and most jurisdictions will ask for that design at permit.

What does W8x18 mean?

W is wide flange, 8 is the nominal depth in inches, and 18 is the weight in pounds per linear foot. Only the weight is exact: a W8x18 is actually 8.14 in deep, and sections in the same nominal group can differ by inches.

How much does a steel beam weigh per foot?

Cross-sectional area in square inches times 12 times 0.2836, the density of steel in pounds per cubic inch. A 5.02 sq in section is about 17 lb per foot. The weight in the section name is that figure rounded.

What is section modulus used for?

Bending stress is moment divided by section modulus, so S is the property that governs bending. It is 2I/d for a symmetric section, and it is why depth is worth more than width: doubling depth roughly quadruples I and doubles S.

Is bending stress enough to check a beam?

No. Capacity also depends on the steel grade, the unbraced length of the compression flange, and local buckling of the flange and web. AISC 360 handles all of it. A bare stress figure is where the check starts.

Why do my numbers differ slightly from the AISC tables?

Fillets. A rolled shape has a curved transition between web and flange that adds a small amount of area and inertia. On a W8x18 the published inertia is 61.9 against 60.9 for square corners, about 1.6%. Use the AISC shapes database for real sections.

Home › Structural › Steel I-Beam Calculator

Steel I-Beam Calculator

Exact geometry for an I-shape. The IRC has no steel beam table at all

Two things are true about steel beams in houses. The geometry is exact and anyone can compute it: moment of inertia, section modulus and weight per foot follow from four dimensions. And the residential code contains no steel beam table whatsoever, so the sizing is engineered under AISC 360 and no calculator finishes it for you.

I-shape section properties

Depth d

Flange width bf

Flange thickness tf

Web thickness tw

Span (0 to skip)

Uniform load (0 to skip)

plf

Exact for a square-cornered I-shape. Real rolled shapes have fillets, so published AISC values are slightly higher.

Specification summary

Generated from on . Reopen that address to reproduce these figures exactly.

Entered

Result

The section you entered, drawn to its own proportions

Worked example

The real AISC dimensions of a W8x18: 8.14 in deep, 5.25 in flange, 0.330 in flange thickness, 0.230 in web, over a 16 ft span at 1,000 plf.

Inertia. The outer box minus the two side voids gives 60.9 in⁴. AISC publishes 61.9 for the real shape, the difference being the fillets.
Section modulus. 2I/d = 15.0 in³, against a published 15.2.
Weight. 5.19 sq in of steel at 0.2836 lb per cubic inch is 17.6 lb per foot, which is why it is called a W8x18.
Moment. 1,000 plf over 16 ft gives 32,000 ft-lb.
Stress. Moment over section modulus, which is a demand and not a verdict: whether it passes depends on grade, bracing and buckling.

The gap between 60.9 and the published 61.9 is the fillets, and it runs about 1.1 to 1.6% across the common shapes. It is small, consistent and always in your favour, which is why this page reports the square-cornered figure and tells you to use the AISC database for a real section.

The formula

An I-shape is a rectangle with two rectangles removed, so the inertia is exact:

I = [b_fd³ − (b_f − t_w)h⊂³] / 12 S = 2I/d A = 2b_ft_f + h t_w

d: overall depth, in
b_f: flange width, in
t_f, t_w: flange and web thickness, in
h: clear web depth, d − 2t_f
weight: A × 12 × 0.2836 lb per foot. Steel is 0.2836 lb per cubic inch

Section modulus is the number that matters for bending, because stress is moment over S. Doubling the depth of a beam roughly quadruples its inertia and doubles its section modulus, which is why depth buys far more than width does.

The code says nothing about steel in a house

The IRC has prescriptive tables for wood joists, wood rafters, wood girders, wood deck beams and cold-formed steel framing. It has nothing for a hot-rolled steel beam in a dwelling. If you are putting a W-shape across a basement to carry a floor, you have left the prescriptive path entirely.

That is not a warning about difficulty, it is a statement about what exists. There is no table to look it up in, so the member is designed under AISC 360 by someone who signs for it, and in most jurisdictions the permit will ask for that.

What is fully computable, and what this page does, is the geometry. Moment of inertia, section modulus, area and weight per foot follow exactly from four dimensions for a doubly symmetric I-shape. So do the moment and the bending stress under a uniform load.

The one caveat worth stating is fillets. A rolled W-shape has a curved transition between web and flange that adds a little area and a little inertia, so the published AISC value runs slightly above the square-cornered calculation. It is 60.9 against 61.9 on a W8x18, 116.5 against 118 on a W10x22 and 201.8 against 204 on a W12x26: consistently 1.1 to 1.6%, and always in your favour. For a real section use the AISC shapes database.

Why a W8x18 is called that

The W is the shape family, wide flange. The 8 is the nominal depth in inches. The 18 is the weight in pounds per linear foot, and it is the only part of the name that is exact.

Depth is nominal: a W8x18 is 8.14 in deep, a W8x10 is 7.89 in, and a W14x90 is 14.0 in while a W14x730 is 22.4 in. Members in the same nominal group share a rolling and the extra steel goes into thickness, which pushes the real depth around.

So you cannot order by depth and you cannot substitute by name. Two beams called W10 can differ by inches, and the weight is what identifies the section you are actually getting.

Section properties are not a capacity check

The bending stress this page reports is a demand: moment divided by section modulus. Whether the beam is adequate is a different question and it depends on several things the geometry does not tell you.

Grade. A992 is the usual modern W-shape steel at 50 ksi yield. Older buildings have A36 at 36 ksi. Same section, very different capacity.

Unbraced length. A beam's compression flange wants to buckle sideways. A beam with a floor deck fixed to it is fully braced; one carrying point loads with nothing attached between them is not, and its capacity can be a fraction of the fully braced value.

Local buckling of the flange and web, which is why AISC classifies sections as compact, noncompact or slender.

None of that is in four dimensions, which is why this page stops where it does.

What it lands on matters more than people expect

A steel beam concentrates load. The reaction figure above arrives at two points, and those points have to carry it down to a footing through a column and a pad sized for it.

Dropping a steel beam onto a masonry pocket, or onto a stack of wood that was sized for a distributed load, is a common way to move a problem rather than solve one. Bearing length and bearing stress at each end are part of the design, not an afterthought.

The same arithmetic as the load calculator applies below the beam: the reaction is the load on everything underneath it.

Frequently asked questions

How do I calculate the moment of inertia of an I-beam?: For a doubly symmetric I-shape it is the outer rectangle minus the two side voids: [bf d cubed minus (bf minus tw) h cubed] divided by 12, where h is the clear web depth. That is exact for square corners; a real rolled shape has fillets that add about 1 to 2%.
Does the IRC have a table for steel beams?: No. There is no prescriptive table for hot-rolled steel beams in dwellings anywhere in the IRC. Such a beam is an engineered member designed under AISC 360, and most jurisdictions will ask for that design at permit.
What does W8x18 mean?: W is wide flange, 8 is the nominal depth in inches, and 18 is the weight in pounds per linear foot. Only the weight is exact: a W8x18 is actually 8.14 in deep, and sections in the same nominal group can differ by inches.
How much does a steel beam weigh per foot?: Cross-sectional area in square inches times 12 times 0.2836, the density of steel in pounds per cubic inch. A 5.02 sq in section is about 17 lb per foot. The weight in the section name is that figure rounded.
What is section modulus used for?: Bending stress is moment divided by section modulus, so S is the property that governs bending. It is 2I/d for a symmetric section, and it is why depth is worth more than width: doubling depth roughly quadruples I and doubles S.
Is bending stress enough to check a beam?: No. Capacity also depends on the steel grade, the unbraced length of the compression flange, and local buckling of the flange and web. AISC 360 handles all of it. A bare stress figure is where the check starts.
Why do my numbers differ slightly from the AISC tables?: Fillets. A rolled shape has a curved transition between web and flange that adds a small amount of area and inertia. On a W8x18 the published inertia is 61.9 against 60.9 for square corners, about 1.6%. Use the AISC shapes database for real sections.

Check these numbers yourself

AISC Shapes DatabaseAmerican Institute of Steel Construction. Published dimensions and section properties for every rolled shape, including the fillet effects this page's square-cornered geometry omits. Free download.
AISC 360, Specification for Structural Steel BuildingsAmerican Institute of Steel Construction. The standard a steel beam in a dwelling is designed under, since the IRC has no prescriptive table. Free PDF.
IRC R301.7 allowable deflectionInternational Code Council. Deflection limits apply to a steel beam as much as a wood one.

How every figure here is verified: Sources & Method. Who builds this: About. Found something wrong? Tell us and it gets fixed or removed.

Figures on this page last checked against the source documents on 2026-09-08. Codes are amended locally; confirm against the edition your jurisdiction enforces.

Related calculators

Geometry, not a design. The IRC has no prescriptive steel beam table for dwellings, so a steel beam in a house is an engineered member under AISC 360. These properties are exact for a square-cornered I-shape; real rolled sections have fillets and published values run slightly higher. Bending stress here is a demand, not a capacity check.