By Zencalcy Editorial TeamLast reviewed About us
Deflection matters as much as strength: a beam that carries the load but sags visibly will crack finishes and feel unsafe. The classic cases are a central point load and a uniform load; both depend on span to the fourth power, so doubling the span multiplies deflection sixteen times.
Maximum deflection of a simply supported or cantilever beam.
Point: δ = P L³ ÷ (48 E I) Uniform: δ = 5 w L⁴ ÷ (384 E I)
Keep units consistent: convert span to inches, load to pounds, E to psi (steel 29,000,000; wood 1,600,000) and I to inches to the fourth. The result is inches. L/360 is the common floor limit; L/240 is used for roofs.
| Symbol | Meaning |
|---|---|
| P, w | Point load or uniform load per unit length. |
| L | Span. |
| E, I | Modulus of elasticity and moment of inertia. |
δ = 2,000 × 120³ ÷ (48 × 29,000,000 × 100) = 0.025 in, well inside L/360 = 0.33 in.
Continue with the Beam Load Calculator, Bending Stress Calculator, Wood Beam Span Calculator, or the Floor Joist Calculator — or browse more structural & workshop and all construction calculators.
L/360 for floors with plaster or tile, L/240 for roofs and general framing, L/480 where finishes are sensitive.
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