Beam Load Calculator
Estimate the maximum load a simply supported beam can carry, from its span, section and material.
Reviewed by the ToolNestr Editorial Team — July 2026
How the beam load calculator works
This tool runs the flexure formula in reverse to find capacity instead of stress. Normally, σ = M ÷ S tells you the stress a given moment produces; rearranged, the maximum moment a beam can safely resist is the allowable bending stress (Fb) times its section modulus (S). For a simply supported beam under a uniform load, that maximum moment relates to the maximum total load by the standard beam equation M = wL² ÷ 8, which rearranges to w = 8M ÷ L².
Section modulus for a solid rectangular beam is width times depth squared, divided by 6 — depth matters far more than width because it's squared, which is why a beam standing on edge carries much more load than the same lumber laid flat. Allowable bending stress (Fb) is a published, material-specific value: for lumber it comes from the NDS Supplement based on species and grade, and for steel it comes from the material's yield strength with an appropriate safety factor applied.
This calculator checks bending strength only — whether the beam would break under load. It does not check deflection, the amount the beam sags under a load that may be safely below its breaking point but still excessive for comfort or code (commonly limited to span/360). A beam can pass this strength check and still fail a deflection check, so both need to be verified independently, and any real load-bearing beam needs full engineering verification beyond this estimate.
The flexure formula and section modulus calculations follow the National Design Specification (NDS) for Wood Construction.
Enter span & section
Span in feet, width and depth in inches.
Set allowable stress
From your material's published Fb value.
Check deflection too
This is a strength check only, not the full design.
The formula explained
Section modulus
S = b·d² ÷ 6. A 1.5×9.25 in section: 1.5×9.25² ÷ 6 = 21.39 in³.
Max moment
Mₓ = Fb × S. At 900 psi: 900 × 21.39 = 19,251 lb·in.
Max uniform load
wₓ = 8·Mₓ ÷ L² (L in inches) = 8×19,251 ÷ 120² ≈ 10.7 lb/in → 1,283 lb total.
Worked example
A 2×10 (1.5×9.25 in), 10 ft span, Fb = 900 psi.
Real-world context
A 2×6 (1.5×5.5 in) joist-grade beam spanning 8 ft at Fb = 1,000 psi computes a section modulus of 7.56 in³, a max moment of 7,562.5 lb·in, and a total strength-limit load of about 630 lb — a reminder that dimensional lumber this shallow is really only suited to light-duty spans like a small deck ledger or a garden shed header, not a load-bearing floor beam.
Step up to a rough-sawn 4×8 timber (3.5×7.25 in) at 12 ft with Fb = 1,200 psi, typical of a higher-grade Douglas fir timber, and the numbers change dramatically: S = 30.66 in³, max moment = 36,794 lb·in, and a strength-limit capacity around 2,044 lb — over three times the 2×6's capacity despite the span growing 50%, illustrating how much depth (squared in the section modulus formula) outweighs a longer span.
Engineered lumber pushes further still. A 1.75×11.25 in LVL (laminated veneer lumber) beam, rated for Fb around 2,600 psi, spanning 16 ft computes S = 36.91 in³, max moment = 95,977 lb·in, and a strength-limit total load near 3,999 lb — nearly double the 4×8 timber's capacity on a third again as much span, which is exactly why LVL and similar engineered products dominate long-span residential floor and garage-door headers where solid-sawn lumber would need an impractically deep section.
Common misconceptions
"If a beam passes this load check, it's safe to install." This checks strength only, not deflection or real-world safety factors. A beam can carry its calculated maximum load without breaking and still sag well past the L/360 comfort and code limit — deflection has to be checked separately, and a real installation needs a licensed engineer's sign-off, not just a strength calculation.
"Doubling the width doubles the beam's capacity, same as doubling the depth." Depth matters far more because it's squared in the section modulus formula. Doubling width doubles capacity, but doubling depth roughly quadruples it — that's why beams are almost always oriented to stand on edge, with depth greater than width, rather than laid flat.
"Allowable stress values are the same for every piece of lumber of a given size." Fb depends on species and grade, not just dimension. A No. 1 Southern Pine 2×10 and a No. 2 Spruce-Pine-Fir 2×10 are physically identical in size but have different published allowable bending stresses — always pull Fb from the NDS Supplement table entry for the actual species and grade being used, not a generic number.
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Frequently asked questions
How do I calculate the maximum load a beam can hold?
Using the flexure formula in reverse: max moment = allowable stress × section modulus, then max uniform load = 8 × max moment ÷ span. A 2×10 (1.5×9.25 in) at 900 psi allowable stress over a 10 ft span can carry roughly 1,665 pounds total, distributed evenly.
What is section modulus?
Section modulus (S) measures how well a cross-section resists bending, combining shape and size into one number. For a solid rectangle, S = width × depth² ÷ 6. A deeper beam has a much higher section modulus than a wider one of the same area, since depth is squared.
What allowable stress should I use?
Allowable bending stress (Fb) depends on the wood species and grade, or steel grade, and is published in reference tables like the NDS Supplement for lumber. Common softwood dimensional lumber often uses around 700-1,000 psi; always use the value for your actual material.
Does this calculator check deflection too?
No — this only checks bending strength (whether the beam breaks), not deflection (whether it sags too much for comfort). A beam can pass a strength check and still deflect more than the L/360 serviceability limit; check deflection separately.
Sources & references
This tool uses standard formulas and reference values from:
- • American Concrete Institute — ACI 318, Building Code Requirements for Structural Concrete. concrete.org
- • ICC — International Residential Code (IRC), span, footing and framing tables. codes.iccsafe.org
- • APA – The Engineered Wood Association, allowable span and load guidance.
Estimates for planning only. Span, load and code values vary by jurisdiction — verify against your local adopted code and a licensed engineer before building.