This beam deflection calculator finds the deflection of a solid rectangular beam and the section’s moment of inertia. Enter the beam width, height, span, load, and material modulus above to get the stiffness and deflection.
How is deflection calculated?
First the section stiffness, then the deflection for your support case:
Moment of inertia I = b × h³ ÷ 12 Simply supported, central point load: δ = P L³ ÷ (48 E I) Cantilever, point load at end: δ = P L³ ÷ (3 E I)
- b — width, h — height (depth), L — span
- E — modulus of elasticity of the material
Example calculation
A 2″ × 6″ wood beam, span 120″, central load 1,000 lb, E = 1,600,000 psi:
- I = 2 × 6³ ÷ 12 = 36 in⁴
- δ = 1,000 × 120³ ÷ (48 × 1,600,000 × 36) = 0.63 in
Compare deflection to the allowable limit (often span/360) and verify final designs with an engineer.
Related calculators
Frequently Asked Questions
How do I find the moment of inertia of a rectangular beam?
For a solid rectangle it is the width times the height cubed, divided by 12 (b·h^3 / 12). Height matters far more than width because it is cubed.
What is the deflection formula for a simply supported beam?
For a central point load it is the load times span cubed, divided by 48 times the modulus times the moment of inertia (PL^3 / 48EI).
Why does beam depth matter so much?
Because the moment of inertia depends on height cubed. Doubling a beam’s depth increases its stiffness eightfold, while doubling width only doubles it.