By Zencalcy Editorial TeamLast reviewed About us
A beam's allowable span is limited by bending stress and by deflection, and the smaller of the two governs. For a uniform load, bending gives L = √(8 Fb S / w), while deflection gives L = ∜(384 E I / 5 w). This calculator reports both.
How far a wood beam can span for a given load.
Bending: L = √(8 Fb S ÷ w) Deflection: L = ∜(384 E I ÷ 5 w)
w is in pounds per inch (divide lb/ft by 12), Fb in psi, S in in³, E in psi and I in in⁴. Common Fb: 1,000–1,500 psi for visually graded lumber, 1,800–2,400 for engineered lumber. Deflection is limited to L/360.
| Symbol | Meaning |
|---|---|
| Fb | Allowable bending stress. |
| S | Section modulus, bd²/6. |
| w | Uniform load per inch. |
S = 3.5 × 9.25² ÷ 6 = 49.9 in³, so bending allows about 22 ft; L/360 deflection limits the same beam to about 19 ft, and that governs.
Continue with the Beam Deflection Calculator, Beam Load Calculator, Bending Stress Calculator, or the Floor Joist Calculator — or browse more structural & workshop and all construction calculators.
A 4 × 12 or a laminated veneer lumber beam may work, but the answer depends on load, species and deflection. Use a span table or engineer.
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