Beam Deflection & Bending Moment Calculator
Calculate maximum deflection, bending moment, stress and reactions for simply supported and cantilever beams with point or uniform loads — rectangular sections in wood, steel or aluminum.
How to use
- 1Pick the support type and load type, then enter the span and load.
- 2Enter the beam's cross-section (width × depth) and material. Compare deflection with a limit like span/360.
How it's calculated
Simply supported: point load at center δ = PL³/48EI, M = PL/4; uniform load δ = 5wL⁴/384EI, M = wL²/8. Cantilever: end point load δ = PL³/3EI, M = PL; uniform δ = wL⁴/8EI, M = wL²/2. For a rectangle I = bd³/12 and bending stress σ = M·(d/2)/I.
Frequently asked questions
What deflection limit should I use?
Common limits are span/360 for floors (to avoid cracking finishes), span/240 for roofs, and span/180 for cantilevers. Check your local building code.
Is this enough to design a beam?
No — it's for estimates and learning. Real designs also check shear, bearing, buckling, load combinations and code safety factors. Consult an engineer for structural work.
Why does depth matter so much?
Stiffness grows with the cube of depth: doubling a beam's depth makes it 8 times stiffer, while doubling its width only doubles it.