By Zencalcy Editorial TeamLast reviewed About us
A simply supported beam with a symmetric load has equal reactions of half the total load. The maximum bending moment sits at midspan and equals wL²/8 for a uniform load or PL/4 for a central point load. Those two numbers — reaction and moment — are what you take to a beam table.
Reactions, moment and shear for a simply supported beam.
Uniform: R = wL/2, M = wL²/8 Point: R = P/2, M = PL/4
Span must be in feet and load in pounds or pounds per foot. The moment is in pound-feet; divide by the section modulus in cubic inches to get bending stress in psi. This assumes simple supports, not fixed ends.
| Symbol | Meaning |
|---|---|
| P, w | Total load or load per unit length. |
| L | Span. |
| M | Maximum bending moment at midspan. |
Total load 480 lb, each reaction 240 lb, maximum moment 720 lb·ft and maximum shear 240 lb.
Continue with the Beam Deflection Calculator, Bending Stress Calculator, Wood Beam Span Calculator, or the Floor Joist Calculator — or browse more structural & workshop and all construction calculators.
PL/4 at midspan for a central point load. That is double the moment of the same total load spread uniformly.
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.
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Last reviewed: September 2026. See how we build and check every tool on the about page.
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Content updated: September 2026