How the beam deflection calculator works
Deflection is how far a beam sags under load. For a beam resting on supports at each end (simply supported), standard formulas from beam theory give the maximum deflection at mid-span.
Uniform load (total W): δ = 5 W L³ ÷ (384 E I) · Mmax = W L ÷ 8
E is the material's stiffness (about 29,000,000 psi for steel, 10,000,000 for aluminum and around 1,600,000 for typical structural lumber), and I is the section's moment of inertia, found in steel or lumber tables. Building codes limit live-load deflection of floors to about L/360 to avoid bouncy floors and cracked finishes. This tool checks stiffness only, not strength; have a licensed engineer design structural members.
Worked example
A steel beam with I = 100 in⁴ spans 120 in (10 ft) with a 1,000 lb load at mid-span. Deflection is 1,000 × 120³ ÷ (48 × 29,000,000 × 100) = 0.0124 in, or L/9,667, far within the L/360 limit of 0.333 in. Spread the same 1,000 lb evenly and deflection drops to 0.0078 in.
Frequently asked questions
What is the moment of inertia?
A property of the beam's cross-section that measures its resistance to bending. Taller sections have much larger I.
What is L/360?
A deflection limit equal to the span divided by 360, common for floors under live load.
What E value should I use for wood?
It depends on species and grade; about 1.6 million psi is typical for Douglas fir-larch No. 2. Check the NDS supplement.
Does this check if the beam will break?
No. It checks stiffness. Strength (bending and shear stress) needs a separate check.
Updated October 2026. Results are estimates for education, not financial or medical advice. All math runs in your browser; nothing you type is sent anywhere.