Beam Deflection Calculator
Estimate the maximum deflection of a simply supported beam under a point load or a uniformly distributed load.
What is Beam Deflection?
Beam deflection is how much a beam bends downward under load. Engineers check deflection against span-to-deflection limits (commonly L/360 for floors) to make sure a structure feels stiff and doesn’t sag noticeably.
The Formulas
For a simply supported beam with a point load at the center: δ = PL³ ÷ (48EI). For a uniformly distributed load across the full span: δ = 5wL⁴ ÷ (384EI), which is equivalent to 5PL³ ÷ (384EI) when P is the total load. Here P is the load, L is the span, E is the material’s modulus of elasticity, and I is the cross-section’s moment of inertia.
- E for steel: about 29,000,000 psi
- E for typical softwood lumber: about 1,200,000 – 1,900,000 psi
This calculator assumes a simply supported (pin-pin) beam and is for general planning and educational purposes — final structural designs should be verified by a qualified structural engineer.