Beam Load Calculator — Deflection & Bending Moment

Deflection is how much a beam bends/sags under load. Excessive deflection can cause visible sagging, cracking in attached finishes (like ceilings or floors), or functional problems even if the beam isn't at risk of breaking. Building codes specify maximum allowable deflection (often as a fraction of span length, like L/360) for serviceability.

For a point load P at the center: Max Deflection = (P × L³) / (48 × E × I), where L is span length, E is the material's modulus of elasticity, and I is the beam's moment of inertia (a property of its cross-sectional shape). This formula applies specifically to a centered point load on a simply supported beam.

For a uniform load w (force per unit length) across the full span: Max Deflection = (5 × w × L⁴) / (384 × E × I). Maximum bending moment for this case is (w × L²) / 8, occurring at the beam's center.