By Zencalcy Editorial TeamLast reviewed About us
Bending stress is the moment divided by the section modulus. For a rectangular section the modulus is bd²/6, so depth matters twice as much as width — which is why joists are stood on edge rather than laid flat.
Stress in a beam from moment and section modulus.
σ = M ÷ S Rectangular S = b × d² ÷ 6
Moment must be in pound-inches for psi output; multiply pound-feet by 12. Allowable bending stress is roughly 1,000–1,500 psi for dimensional lumber, 20,000 for mild steel with a safety factor and 2,000–3,000 for reinforced concrete.
| Symbol | Meaning |
|---|---|
| M | Bending moment. |
| S | Section modulus. |
| σ | Bending stress. |
S = 1.5 × 9.25² ÷ 6 = 21.4 in³, so σ = 12,000 ÷ 21.4 = 561 psi — well under the 1,000 psi allowable for many species.
Continue with the Beam Deflection Calculator, Beam Load Calculator, Wood Beam Span Calculator, or the Floor Joist Calculator — or browse more structural & workshop and all construction calculators.
The geometric property I/c that converts a moment into a surface stress. For a rectangle it is bd²/6.
Results use standard construction estimating arithmetic: volumes from measured area and depth, unit weights from published material densities, and code-referenced spans or clearances where the page names a code. Quantities are rounded up to whole saleable units and include the stated waste allowance. These tools are planning aids, not structural design, and do not replace a licensed engineer, a local code check, or a contractor's site measurement.
Reference material used to build and check this calculator:
Last reviewed: September 2026. See how we build and check every tool on the about page.
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Content updated: September 2026