Beam Deflection Calculator

Beam deflection is the vertical displacement or sag that occurs when a load is applied to a beam. It is critical because excessive deflection can cause: cracked plaster and drywall, binding doors and windows, visible sagging floors, bouncy or uncomfortable floors, and structural damage over time. Building codes specify maximum allowable deflections - typically L/360 for floors (span/360), L/240 for roofs, and L/180 for ceiling joists with no plaster.

Beam deflection is most affected by: Span length (L⁴ - doubling span increases deflection 16×), Beam depth (d³ - doubling depth reduces deflection 8×), Load magnitude (directly proportional), Material stiffness (modulus of elasticity E), and support conditions (simply supported vs fixed vs cantilever). The beam depth is the most practical variable to adjust - a slightly deeper beam is the most effective way to reduce deflection.

Allowable stress design ensures the beam material does not exceed its safe stress limit. Deflection control ensures the beam does not sag excessively under service loads. Often, deflection limits are the governing factor for beam sizing, especially for longer spans. A beam may be strong enough (stress OK) but still too bouncy (deflection too high). Always check both criteria. For residential floors, L/360 live load deflection is typical; for sensitive floors like tile, L/480 is recommended.

Support conditions dramatically change deflection magnitude:<br>Simply supported (pinned both ends): Most deflection, used for typical beams<br>Cantilever (fixed one end, free other): 7.5× more deflection than simply supported for same load<br>Fixed both ends: Least deflection (60% less than simply supported)<br>Continuous over multiple supports: Deflection depends on span ratios<br>The calculator uses standard formulas for each support type. Choosing the correct support condition is essential for accurate results.