Beam Load Calculator
Work out the forces in a loaded beam. Enter the span, the beam width and depth, the load case (simple or cantilever, point or uniform), the load and the material, and get the support reactions, the maximum shear and bending moment, the bending stress against the allowable, and the safe load the section can carry — with by-span and by-depth tables and a downloadable PDF.
| Span | Max moment | Stress | vs Fb |
|---|---|---|---|
| Enter a beam to compare | |||
| Depth | S (in³) | Stress | Safe load |
|---|---|---|---|
| Enter a beam to compare | |||
How to use the beam load calculator
Four quick steps turn a beam’s size and load into its forces — the support reactions, maximum shear and bending moment, the bending stress against the allowable, utilization, and the safe load the section can carry — with by-span and by-depth tables and a downloadable report.
Enter the beam
Span in feet, and the beam’s actual width and depth in inches.
Pick the load case
Simply supported or cantilever, with a point load or a uniform load.
Enter load & material
The load (total or per foot) and the material’s allowable bending stress Fb.
Read results & save a PDF
Get reactions, shear, moment, stress, utilization and safe load — then download a report.
The formulas behind the forces
The load case sets the reactions, shear and moment; the section modulus and the allowable stress decide whether the beam is adequate and how much it can safely carry.
▶ Worked example
A softwood beam 3.5 in wide × 9.25 in deep spans 12 ft (144 in), simply supported, carrying a uniform 100 lb/ft (1,200 lb total).
Each reaction is 600 lb, max shear 600 lb, and the moment is W L ÷ 8 = 1,800 lb-ft (21,600 lb-in). S is 3.5 × 9.25² ÷ 6 ≈ 49.9 in³.
σ = 21,600 ÷ 49.9 ≈ 433 psi vs Fb 900 — 48% utilized
The safe uniform load in bending is about 208 lb/ft (from Mallow = Fb × S).
Beam load quick reference
The reactions, shear and moment for each load case, the allowable bending stress of common materials, and the section modulus of common lumber sizes.
| Load case | Reactions | Max shear | Max moment |
|---|---|---|---|
| Simply supported, centre point | P ÷ 2 each | P ÷ 2 | P L ÷ 4 |
| Simply supported, uniform | W ÷ 2 each | W ÷ 2 | W L ÷ 8 |
| Cantilever, end point | P (fixed end) | P | P L |
| Cantilever, uniform | W (fixed end) | W | W L ÷ 2 |
P is a point load, W the total uniform load (load per foot × span), L the span in inches for the moment.
| Material | Allowable Fb (psi) |
|---|---|
| Softwood framing | 900 |
| Hardwood | 1,200 |
| LVL / engineered | 2,600 |
| A36 steel (0.6 × 36 ksi) | 21,600 |
Typical guide values. Use the published design Fb for your actual species, grade and product.
| Nominal | Actual b × h | S (in³) |
|---|---|---|
| 2×6 | 1.5 × 5.5 in | 7.56 |
| 2×8 | 1.5 × 7.25 in | 13.14 |
| 2×10 | 1.5 × 9.25 in | 21.39 |
| 2×12 | 1.5 × 11.25 in | 31.64 |
S = b·h²÷6. Because depth is squared, a deeper beam carries much more; doubling the width only doubles S.
Everything the calculator gives you
One beam and load produce a full force profile, not just a single number.
Beam load reference numbers
Built for anyone loading a beam
DIY builders, remodelers, and students all need to know the forces a loaded beam carries.
Checking whether a deck beam, door header or ridge can carry the load before building. A quick force check turns a guess into reactions, moment and a safe load.
- See the reactions each post or wall must carry
- Check the bending stress against the allowable
- Read the safe load the section can hold
Sizing beams and headers across a remodel and sanity-checking a member against the load before pulling a span table or calling the engineer.
- Test a span and section against the real load
- Compare softwood, hardwood, LVL or steel
- Hand the plan-check a clean PDF of the figures
Learning beam statics or running a fast first-pass check — reactions, shear, moment, stress and capacity — before a full design in the office software.
- See reactions, shear and moment worked out together
- Watch moment and stress climb with span and load
- Compare all four classic load cases quickly
Get a reliable load check
Small habits make a beam load estimate far more trustworthy.
Include dead and live load
Add the weight of the structure itself to the load it carries, or the forces will be too low.
Bending is one check
This checks bending stress only. Deflection, shear and bearing are separate checks a beam must also pass.
Use actual dimensions
A 2×10 is 1.5 × 9.25 in, not 2 × 10. Enter net sizes or the capacity will be too high.
Depth drives capacity
Section modulus rises with depth squared, so a deeper beam carries far more than a wider one.
Match the load case
A cantilever carries far more moment than a simple span. Model how the beam is really supported.
Pick the right Fb
Use the allowable stress for your actual species and grade, or the maker’s value for LVL and steel.
Confirm structural members
For anything load-bearing, have a licensed engineer or your building department confirm the design.
Frequently asked questions
Common questions about beam loads, reactions, bending moment, and safe capacity.
The load a beam can carry depends on its span, its cross-section and the material. The method is to work out the maximum bending moment the load creates, then check the bending stress that moment causes against the material’s allowable stress.
The maximum moment depends on how the beam is supported and loaded. A simply supported beam with a uniform load has a maximum moment of the total load times the span divided by 8; with a central point load it is the load times the span divided by 4.
Enter the span, the width and depth, the load case, the load and the material, and this calculator returns the reactions, the maximum shear and bending moment, the bending stress, and the safe load the section can carry.
The reactions are the upward forces the supports provide to hold the beam and its load in balance. For a beam resting on two supports, they add up to the total load on the beam.
For a simply supported beam with the load centred or spread evenly, the two reactions are equal, each carrying half the total load. For a cantilever, which is fixed at one end, that single support carries the whole load plus a fixed-end moment that resists the rotation.
For example, a 12-foot beam carrying 100 pounds per foot has a total load of 1,200 pounds, so each of two supports carries 600 pounds. This calculator works out the reactions for every load case.
The maximum bending moment is the greatest internal bending the load produces, and it sets where the beam is most likely to fail. It depends on the load, the span and how the beam is supported.
For a simply supported beam, a uniform load gives a maximum moment of the total load times the span over 8, at mid-span; a central point load gives the load times the span over 4. A cantilever is worse: a point load at the free end gives the load times the full length, at the fixed end.
For example, 100 pounds per foot over a 12-foot simple span gives 1,200 times 12 over 8, which is 1,800 pound-feet. This calculator reports the maximum moment and where each load case puts it.
Work out the maximum bending stress and compare it with the material’s allowable bending stress, Fb. The stress is the maximum moment divided by the section modulus (S), and the beam is adequate in bending when that stays at or below Fb.
Utilization expresses how close you are — the actual stress divided by Fb, as a percentage. At 100 percent the beam is right at its allowable; below that you have margin.
For example, a moment of 21,600 pound-inches on a section with S of 49.9 cubic inches gives a stress of about 433 psi, which against a softwood Fb of 900 is about 48 percent utilized. This calculator shows the stress, the allowable and the utilization together.
The allowable bending stress (Fb) is the stress a material can safely carry in bending, in pounds per square inch. Typical values are about 900 psi for softwood framing lumber, 1,200 for hardwoods, 2,600 for engineered lumber like LVL, and about 21,600 for A36 structural steel.
The steel figure is 0.6 times its 36,000 psi yield, a common allowable-stress basis. Wood values are far lower and depend heavily on the species, the grade, the member size and the service conditions.
Use the design value for your actual material from a span table or supplier rather than a round number. This calculator offers softwood, hardwood, LVL and steel so you can compare, but a real design uses the published Fb for the exact product.
The section modulus (S) measures how well a cross-section resists bending. For a rectangular beam it is the width times the depth squared, divided by 6 — written b times h squared over 6 — in cubic inches.
Because the depth is squared, it dominates: a 1.5-inch by 9.25-inch joist has a section modulus of about 21.4 cubic inches, while the same width at 5.5 inches deep has only about 7.6. That is why deeper beams carry much more.
The bending stress is the moment divided by S, so a larger section modulus means lower stress for the same load. This calculator works out S from the width and depth you enter and uses it for the stress and safe-load figures.
Beam load — strength — is about whether the beam can carry the force without overstressing: the reactions, shear, bending moment and stress against the allowable. Beam deflection is about stiffness: how far the beam sags under load, checked against a limit like L/360.
A beam has to pass both. It can be strong enough in bending yet still too bouncy, or stiff enough yet overstressed, because strength depends on the section modulus and deflection on the moment of inertia and the modulus of elasticity.
This calculator covers the strength (load) side — reactions, shear, moment, stress and safe load. For the deflection side, use a beam deflection calculator, and confirm any structural member with an engineer.
The safe load is the load that brings the bending stress up to the allowable Fb. Set the maximum moment equal to Fb times the section modulus, then solve back for the load using the formula for your support case.
For a simply supported beam with a uniform load, the safe load per foot is 8 times Fb times S, divided by the span in inches, divided by the span in feet. A deeper or wider section raises S and so raises the safe load.
For example, a softwood 3.5 by 9.25 beam on a 12-foot simple span has a safe uniform load of about 208 pounds per foot in bending. This calculator reports the safe load for your section, span and material — but remember it is a bending check only.
Disclaimer: US units (feet, inches, pounds, psi). Statics for a rectangular section: S = b × h² ÷ 6, bending stress = M ÷ S, safe load from M = Fb × S. This checks bending only against the allowable Fb — it does not check deflection, horizontal shear, bearing, lateral stability, connections, duration of load or combined loads. Allowable Fb values are typical and vary with species, grade, size and conditions. Real framing must follow the building code and span tables; have a licensed engineer or your building department confirm the design.