Engineering calculators

Steel Beam Calculator

Updated Sep 2, 2026 By Jehan Wadia
Rate Formulas
Global Configuration
Switching converts every entered value and every result.
Governing code: AISC 360-16, LRFD — load combinations per ASCE 7-16 §2.3.
A992 = modern rolled W-shapes. A36 = legacy / channels & S-shapes.
Beam Geometry
Strong Axis Bending (Ix)
Beam Section
Section Families to Search
Cross-Section Preview
PropertyValuePropertyValue
Applied Loads
Lateral Bracing
Choose "Yes" if the compression flange is braced at least every 2 ft (e.g. by a concrete slab or closely spaced joists).
Deflection Limits
Span / 360 = —
Typically L/360 for floors with plaster ceilings.
Span / 240 = —
Typically L/240 for general serviceability.
Span / 480 = —
Result Units
Beam Model — Supports, Spans, Loads & Bracing
Design Info Summary
ParameterValue
Utilization Ratio Dashboard
Detailed Results

Bending

Shear

Deflection

Step-by-Step Solution
Support Reactions
Load Case Reactions (unfactored)
Load Combination Reactions (factored)
Service Case Reactions (unfactored)
Structural Diagrams
Diagram Set
Shear Force Diagram
Bending Moment Diagram
Deflection Curve
Slope / Rotation Diagram
Calculation Breakdown
Beam Comparison
Print / Export Report

Introduction

This steel beam calculator checks whether a steel beam is strong enough to hold your loads. You pick a beam size, enter your spans and loads, and the tool runs the checks.

It checks three things: bending, shear, and deflection (how much the beam bends down). Each check gets a ratio. If the ratio is 1.00 or less, the beam works. If it is more than 1.00, the beam is too small and you need a bigger one.

You can work in imperial units (feet, inches, kips) or metric units (meters, millimeters, kN). The tool supports AISC 360-16 with LRFD or ASD, AISC ASD 9th Edition, and Eurocode 3 with UK or Irish National Annexes. It builds the right load combinations for the code you pick.

The section list holds W shapes, S shapes, and C channels. You can pick a shape yourself, or let the tool find the lightest shape that passes every check. You can also compare two beams side by side.

Results include support reactions, shear and moment diagrams, deflection and slope curves, and a step-by-step solution with code references. You can print or save a report with the parts you want.

Use this tool for quick design checks and early sizing. A licensed structural engineer should review any final design.

How to use our Steel Beam Calculator

Enter your beam span, supports, steel grade, section shape, loads, bracing, and deflection limits. The steel beam calculator then shows the beam size you need, bending, shear and deflection ratios, support reactions, shear and moment diagrams, and a full step-by-step check.

Unit System: Pick Imperial (ft, kip, ksi) or Metric (m, kN, MPa). All values you typed and all results change over for you.

Design Standard: Choose the code you design to. Options are AISC 360-16, AISC ASD 9th Edition, or Eurocode 3 with the UK or Irish National Annex.

Design Method: For AISC 360-16, pick LRFD or ASD. Other codes set this on their own.

Material Grade: Pick A992 for modern W-shapes, A36 for older steel and channels, or Custom to type your own values.

Yield Stress Fy and Tensile Fu: Type the steel strength if you chose Custom. The grade fills these in for you otherwise.

Minimum Yield Stress toggle: Quick buttons for 36,000 psi legacy steel or 50,000 psi modern steel.

Number of Spans: Choose 1 to 5 spans. Each span gets its own length box.

Span Length: Type the clear length of each span and pick the unit (ft, in, m, or mm).

Support Conditions: Set each support as pin, roller, or fixed. This changes the reactions and moments.

Bending Orientation: Press Rotate Beam to switch between strong axis (Ix) and weak axis (Iy) bending.

Selection Mode: Choose Auto-Select Lightest to let the tool find the lightest beam that works, or Manual Selection to pick one yourself.

Section Families: Tick the shapes to search: W wide flange, S standard beam, or C channel.

Section: In manual mode, pick the shape by depth, weight, and Ix. You can also press Suggest Lightest Shape for a quick pick.

Load Label and Load Type: Name each load and choose uniform, partial, point, or area load.

Preset Load Type and Tributary Width: For area loads, pick a preset like residential floor or roof, then type the width of floor the beam carries.

Position a and Length b: For point and partial loads, type where the load starts from the left support, and how long it runs.

Load Categories: Split each load into Dead (D), Live (L), Roof Live (Lr), Snow (S), and Wind (W). The tool builds the code load combinations from these.

Magnitude Unit: Pick the unit for that load, such as lb/ft, kN/m, kip, or psf.

Add Load: Press this to add more loads to the same beam.

Compression Flange Fully Braced: Choose Yes if a slab or close joists hold the top flange. Choose No to set the bracing yourself.

Unbraced Length Lb: Type the longest distance between brace points. Using the full span is safe but conservative.

Discrete Bracing Points: Type brace distances from the left support, split by commas. The tool uses the biggest gap as Lb.

Deflection Limits: Set the live load limit (often L/360), the total load limit (often L/240), and the dead load camber limit (often L/480).

Ponding Check: Tick this for roof beams to flag dead load sag that is over the camber limit.

Result Units: Choose the units for length, force, moment, and deflection in the results.

Diagram Set and Displayed Case: Pick load cases, load combinations, or service cases, then choose which one to plot.

Second Section to Compare: Pick another beam and press Add Beam to Compare to see both side by side.

Print Options and Generate Report: Tick the parts you want, then press Generate Report to print or save your steel beam design.

Calculate and Reset: Press Calculate to run the checks. Press Reset to go back to the default beam.

What Is a Steel Beam?

A steel beam is a straight piece of steel that carries weight across an open space. It holds up floors, roofs, and walls, then passes that weight down to columns, posts, or foundation walls. Builders use steel beams when a wood beam would be too weak, too deep, or too long.

Common Steel Beam Shapes

  • W-shape (wide flange), the most common beam today. It looks like a capital "H" turned on its side. Most are made from A992 steel with a yield strength of 50 ksi (345 MPa).
  • S-shape (American Standard beam), an older I-beam with narrow, sloped flanges. Usually A36 steel.
  • C-shape (channel), shaped like a "C" with one flat back. Often used for stair stringers, edges of floors, and lintels.

A name like W14X30 means a wide flange beam about 14 inches deep that weighs 30 pounds per foot.

The Three Checks Every Beam Must Pass

  1. Bending. The beam wants to sag and bend in the middle. Engineers compare the bending force (moment) to the beam's bending strength. Deeper beams are much stronger in bending.
  2. Shear. The load tries to slice the beam straight down, usually right next to the supports. The thin web in the middle of the beam carries this.
  3. Deflection. How far the beam sags. A beam can be strong but still bounce or crack the ceiling below. Common limits are span ÷ 360 for live load and span ÷ 240 for total load.

The result of each check is a utilization ratio. A ratio of 0.85 means the beam is using 85% of its strength. Anything over 1.00 means the beam is too small.

Loads on a Beam

Loads are sorted into groups because building codes multiply each group by a different safety factor:

  • Dead (D), the weight of the building itself: framing, flooring, drywall, roofing.
  • Live (L), people, furniture, and stored items.
  • Roof live (Lr), workers and tools on a roof.
  • Snow (S), snow piled on the roof.
  • Wind (W), push or pull from wind.

Loads can be spread evenly along the beam (pounds per foot), pushed at one spot (a point load from a post or another beam), or spread over an area (pounds per square foot times the tributary width the beam picks up).

Why Lateral Bracing Matters

When a beam bends, its top flange gets squeezed. If nothing holds that flange sideways, it can twist and buckle sideways before it ever reaches full strength. This is called lateral-torsional buckling (LTB). The distance between points that hold the flange steady is the unbraced length, Lb. A concrete slab or closely spaced joists usually brace the flange the whole way, so full strength is available. A long bare beam with no bracing can lose a large part of its strength.

Spans and Supports

A simple span sits on two supports and sags the most in the middle. A continuous beam runs over three or more supports; it sags less but gets negative bending over the middle supports. Support types change the answer too:

  • Pin, holds up and sideways, but can rotate.
  • Roller, holds up only, and can rotate and slide.
  • Fixed, holds up and stops rotation, like a beam cast into concrete.

Design Codes

In the United States, steel beams are designed with AISC 360, using either LRFD (loads are increased, strength is multiplied by φ = 0.90 for bending) or ASD (strength is divided by Ω = 1.67). Older jobs may use the AISC ASD 9th Edition allowable stress method. In the UK and Ireland, beams follow Eurocode 3 (EN 1993-1-1) with its National Annex, using partial factors and a χLT reduction for buckling.

Quick Tips

  • Depth wins. Going deeper adds far more stiffness than going heavier at the same depth.
  • Long spans are usually controlled by deflection, not strength.
  • Short, heavily loaded spans are often controlled by shear.
  • Bend a beam about its strong axis (Ix) whenever you can. Weak axis bending is many times weaker.
  • Always have a licensed structural engineer review a beam before it is built. Real projects also need checks for bearing, web crippling, connections, holes, and fire protection.

Formulas used

Plastic moment capacity
M_p = F_y Z
Limiting unbraced lengths for lateral-torsional buckling (AISC F2-5, F2-6)
L_p = 1.76\, r_y \sqrt{\frac{E}{F_y}}, \qquad L_r = 1.95\, r_{ts} \frac{E}{0.7F_y} \sqrt{\frac{Jc}{S_x h_o} + \sqrt{\left(\frac{Jc}{S_x h_o}\right)^2 + 6.76\left(\frac{0.7F_y}{E}\right)^2}}
Nominal flexural strength — inelastic and elastic LTB (AISC F2-2, F2-3/F2-4)
M_n = C_b\left[M_p - (M_p - 0.7F_yS_x)\frac{L_b - L_p}{L_r - L_p}\right] \le M_p, \qquad F_{cr} = \frac{C_b \pi^2 E}{(L_b/r_{ts})^2}\sqrt{1 + 0.078\frac{Jc}{S_x h_o}\left(\frac{L_b}{r_{ts}}\right)^2}, \quad M_n = F_{cr} S_x
Moment gradient factor (AISC F1-1)
C_b = \frac{12.5\,M_{max}}{2.5\,M_{max} + 3M_A + 4M_B + 3M_C} \le 3.0
Nominal shear strength (AISC G2-1)
V_n = 0.6\, F_y A_w C_v, \qquad A_w = d\, t_w
Design capacities — LRFD and ASD
\text{LRFD: } \phi_b M_n = 0.90 M_n,\ \ \phi_v V_n \qquad \text{ASD: } \frac{M_n}{\Omega_b} = \frac{M_n}{1.67},\ \ \frac{V_n}{\Omega_v}
Eurocode 3 LTB reduction factor and design moment
\bar{\lambda}_{LT} = \sqrt{\frac{M_p}{M_{cr}}},\quad \Phi = 0.5\left[1 + \alpha(\bar{\lambda}_{LT} - 0.4) + 0.75\bar{\lambda}_{LT}^2\right],\quad \chi_{LT} = \min\left(\frac{1}{\Phi + \sqrt{\Phi^2 - 0.75\bar{\lambda}_{LT}^2}},\, 1.0,\, \frac{1}{\bar{\lambda}_{LT}^2}\right),\quad M_{b,Rd} = \chi_{LT} M_p
Utilization ratios and deflection limits
\text{Ratio}_M = \frac{M_{max}}{M_{cap}},\quad \text{Ratio}_V = \frac{V_{max}}{V_{cap}},\quad \Delta_{allow} = \frac{L}{n},\quad \text{Ratio}_\Delta = \frac{\Delta_{max}}{\Delta_{allow}}

Frequently asked questions

What size steel beam do I need for a 20 foot span?

It depends on the load, not just the span. A common house example: a floor beam that picks up 10 ft of floor with 10 psf dead load and 40 psf live load carries about 500 lb per foot.

For that case over 20 ft, a W10x22 or W12x19 usually works. Deflection controls, so the beam needs roughly 75 in⁴ of moment of inertia to stay under L/360.

Change the tributary width, add a wall or post above, and the answer changes fast. Always check bending, shear, and deflection for your own numbers.

How much weight can a steel I-beam hold?

There is no single number. The same beam holds far more over a short span than a long one, because bending force grows with the square of the span.

Example: a W12x26 in A992 steel, fully braced, on a 20 ft simple span. Bending strength alone would allow about 2.8 kip per foot. But keeping sag under L/240 cuts it to about 1,600 lb per foot.

Double the span to 40 ft and that same beam drops to a few hundred pounds per foot.

What is the rule of thumb for steel beam depth?

A quick starting guess is depth = span ÷ 20 for floor beams and span ÷ 24 for roof beams, using the same units.

A 20 ft (240 in) floor span gives 240 ÷ 20 = 12 in, so start with a W12. A 30 ft span gives 18 in, so start with a W18.

This is only a first guess. You still have to run the real bending, shear, and deflection checks.

How do I calculate the maximum bending moment on a beam?

For a simple span with two supports:

  • Even load across the whole beam: M = wL² ÷ 8
  • One point load at midspan: M = PL ÷ 4

Here w is load per foot, P is the point load, and L is the span in feet. The answer comes out in kip-ft or lb-ft.

Example: 500 lb/ft over 20 ft gives M = 500 × 400 ÷ 8 = 25,000 lb-ft, or 25 kip-ft.

What is tributary width and how do I find it?

Tributary width is the strip of floor or roof that one beam carries. It is half the distance to the framing on each side.

If joists span 12 ft on one side of the beam and 8 ft on the other, the tributary width is 6 + 4 = 10 ft.

Multiply that width by the area load in psf to get the load per foot on the beam. So 50 psf × 10 ft = 500 lb per foot.

What does L/360 mean for deflection?

L/360 means the beam may sag no more than the span divided by 360. Use the span in inches.

  • 20 ft span = 240 in ÷ 360 = 0.67 in
  • 30 ft span = 360 in ÷ 360 = 1.0 in

L/360 is the usual live load limit for floors with plaster or drywall ceilings. L/240 is the common total load limit. Tighter limits like L/480 are used where tile or brittle finishes could crack.

Why does a beam pass the strength check but fail deflection?

Strength and stiffness are two different things. Strength depends on section modulus, but sag depends on the moment of inertia and on the span raised to the fourth power.

Double the span and the load stays the same, but the sag goes up 16 times. That is why long, lightly loaded beams almost always fail deflection first.

The fix is a deeper beam, not a heavier one at the same depth.

What is the difference between A36 and A992 steel?

They are two steel grades with different strengths.

  • A36: yield 36 ksi (250 MPa). Older steel, still used for channels, angles, and plates.
  • A992: yield 50 ksi (345 MPa), tensile 65 ksi. The standard grade for W-shapes made today.

A992 is about 39% stronger in bending, so it usually allows a lighter beam. If you are checking an old building, assume A36 unless the mill papers say otherwise.

Is it better to use a deeper beam or a heavier beam?

Deeper almost always wins. Stiffness grows with the cube of the depth, so a small gain in depth beats a big gain in weight.

Compare two beams that weigh the same: a W12x26 has I = 204 in⁴, but a W16x26 has I = 301 in⁴. That is 48% stiffer for the same pounds per foot.

Go deeper whenever your ceiling height and headroom allow it. It saves steel and money.

What is the difference between Sx and Zx?

Both describe how well a shape resists bending, but they use different assumptions.

  • Sx (elastic section modulus): used when only the outer fibers reach yield. Sx = I ÷ c.
  • Zx (plastic section modulus): used when the whole section yields. Zx is bigger, usually 10% to 20% more than Sx for a W-shape.

Modern AISC design uses Mp = Fy × Zx for compact, braced beams. Older allowable stress design used Fb × Sx.

Do I need to include the beam's own weight in the load?

Yes. Add it to the dead load. A beam name tells you the weight: a W14x30 weighs 30 lb per foot.

On most beams this is only 2% to 5% of the total load, so it rarely changes the size. On long span roof beams with light loads it can matter more.

The simple fix is to guess a beam, add its weight, then re-check once you pick the final size.

How far apart should lateral bracing be on a steel beam?

Close enough that the top flange cannot twist sideways. The key number is Lp, the length below which the beam reaches full plastic strength.

For A992 W-shapes, Lp is often about 3 to 9 ft. A W12x26 has Lp near 5.3 ft; a W21x62 near 6.3 ft.

A concrete slab or joists at 16 to 24 in on center brace the flange the whole way. A bare beam in a basement with only end connections has an unbraced length equal to the full span, which can cut strength by half or more.

What is Cb in steel beam design?

Cb is the moment gradient factor. It rewards beams whose bending moment is not constant along the unbraced length.

Cb = 1.0 is the safe base value and applies to constant moment. A simple span with a uniform load and braced ends gives about 1.14. Some patterns reach 1.3 to 1.7. The code caps it at 3.0.

A higher Cb raises buckling strength, so it only helps when the beam is not fully braced.

How much bearing length does a steel beam need at each end?

Codes normally ask for at least 3 inches of bearing on masonry or concrete, and 1.5 inches on steel or a column cap.

The real length depends on the reaction. Short bearing on a thin web can cause web crippling or local yielding, where the web folds right above the support.

Heavy beams often need a steel bearing plate to spread the load over the wall, plus web stiffeners when the reaction is large.

What is camber on a steel beam?

Camber is a slight upward curve rolled or heated into the beam at the shop. When the dead load goes on, the beam settles down to nearly flat.

Fabricators usually camber for 60% to 100% of the dead load sag, and skip anything under about 3/4 in. It is common on spans over 25 ft, especially under wet concrete slabs.

Camber does not add strength. It only hides dead load sag, so live load deflection still has to be checked.

What is roof ponding and why is it dangerous?

Ponding is when a flat roof sags, water collects in the low spot, the extra water makes it sag more, and more water flows in. The cycle can keep going until the roof fails.

It is why roof beams get tighter deflection limits, often L/480 for dead load, and why roofs need slope and working drains.

Check ponding on any flat or nearly flat roof, especially long span steel framing.

Is LRFD or ASD more conservative?

It depends on the ratio of live load to dead load.

  • Live load less than 3× dead load: LRFD usually gives the slightly smaller beam. This covers most buildings.
  • Live load more than 3× dead load: ASD gives the smaller beam.

At exactly 3 to 1 the two methods match. Both are in AISC 360 and both are accepted, so pick one method and stay with it through the whole job.

How do I size a steel beam to remove a load bearing wall?

Work out everything the wall holds up, then design a beam for that load.

  1. Find the tributary width of floor and roof each side of the wall.
  2. Add dead load, live load, and snow, plus the weight of any wall above.
  3. Add point loads from posts, girders, or stair headers landing on the wall.
  4. Check bending, shear, and deflection, then design the posts and footings that carry the new beam ends.

The new posts push a lot of weight into a small area, so the footings below often need to be enlarged. This work needs a permit and a licensed structural engineer.

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