Estimate the allowable load on a simply supported rectangular beam, based on a basic bending stress calculation. For educational and rough planning use only, see the important note below.
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This calculator computes the beam's section modulus (S = width × depth² ÷ 6 for a rectangular cross-section), multiplies it by your allowable bending stress to get an allowable bending moment, then solves for the maximum load that would produce that moment: for a uniformly distributed load, max load = 8 × moment ÷ span²; for a center point load, max load = 4 × moment ÷ span, both standard formulas for a simply supported beam.
This calculator checks bending stress only. It does not check deflection limits (a beam can meet bending strength but still sag more than acceptable), shear capacity, buckling, load duration factors, connection design, or any other requirement that matters for a safe, code-compliant structure. Actual beam sizing for any real construction project must be verified by a licensed structural engineer against your local building code, do not use this calculator as the sole basis for a real structural decision.
For a beam 1.5 in wide, 9.25 in deep, spanning 12 ft, with an allowable bending stress of 1,000 psi, under a uniformly distributed load: section modulus = (1.5 × 9.25²) ÷ 6 ≈ 21.39 in³. Allowable moment = (1,000 × 21.39) ÷ 12 ≈ 1,782.6 ft-lb. Max distributed load = (8 × 1,782.6) ÷ 12² ≈ 99.0 lb per ft, or a max total of about 1,188.4 lb across the full 12 ft span. For the same beam under a center point load instead, max point load = (4 × 1,782.6) ÷ 12 ≈ 594.2 lb, notably less than the 1,188.4 lb total the same beam can carry when that weight is spread evenly, since a concentrated point load creates a higher peak bending moment than the same total weight distributed across the span.
Using this calculator's result as the basis for an actual construction decision, it checks bending stress only and skips deflection, shear, buckling, load duration and connection design entirely, any real beam supporting a structure must be sized by a licensed structural engineer against local building code, not estimated with this tool.
Guessing at the allowable bending stress value, this figure varies enormously by material and grade (roughly 700-1500 psi for common softwood lumber vs around 22,000 psi for A36 structural steel), using the wrong value produces a load capacity estimate that's wrong by a large factor.
Treating the distributed-load and point-load results as interchangeable, a beam can typically carry meaningfully more total weight as a load spread evenly across its span than as the same total weight concentrated at the center, mixing these up overstates real capacity for a point-loaded scenario.
This varies significantly by material and grade, common softwood construction lumber is often in the 700-1500 psi range, structural steel (A36) is often around 22,000 psi allowable. Use the published allowable stress for your specific material and grade, or consult an engineer, this calculator doesn't include built-in material presets since the correct value depends heavily on your specific material grade and application.
A point load at the center of a span creates a higher peak bending moment than the same total weight spread evenly across the span, so a beam can typically support more total weight as a distributed load than as an equivalent single point load, which is why this calculator handles the two cases with different formulas.
No, use this only to build intuition about how beam dimensions and span relate to load capacity. Any beam supporting a real structure, a deck, floor, or roof, must be sized by a qualified professional accounting for all relevant load types, code requirements and safety factors.
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