Beam Deflection Calculator

Learn more: beam deflection, loads, and design limits

Understanding deflection and L/360 limits

Beam deflection is the vertical sag that occurs when a load is applied. The L/360 limit means the maximum allowable deflection equals the beam span divided by 360. For a 3,600 mm (12-foot) span, the limit is 10 mm maximum sag under live load. This is the standard limit for floors in most building codes including BS 5950, AS/NZS 4600, and Eurocode. Exceeding L/360 can cause cracking in finishes, squeaking, or occupant discomfort even if the beam is structurally safe.

Carpentry span tables are built around the same L/360 limit, just worked backwards: instead of solving for deflection given a beam, they solve for the maximum span given a joist size. MyCarpentry's floor joist span table shows this in practice, cross-referencing lumber species and spacing against fixed live and dead load scenarios to find the longest allowable span under L/360.

Beam types: simply supported vs cantilever

A simply supported beam rests on supports at both ends, with the load applied between them. A cantilever beam is fixed at one end (built into a wall) and free at the other - like a diving board. Cantilevers deflect more than simply supported beams with the same load and span. The calculator handles both types and uses the appropriate deflection formulas: for UDL on a simply supported beam, deflection = 5WL3 / (384EI); for central point load: deflection = PL3 / (48EI).

Load types: UDL, point loads, and distributed patterns

A uniformly distributed load (UDL) spreads weight evenly along the beam - like flooring or ceiling. A single central point load concentrates the weight at one spot. Two point loads at the third-points represent common floor loading patterns. The calculator converts these patterns into deflection and bending moment using classic beam theory formulas, then shows results in millimeters, checking against L/360 and L/300 limits.

Material stiffness and section properties

Two factors control deflection: material stiffness (E, Young's modulus in GPa) and cross-section geometry (I, second moment of area in mm4). Steel has E=200 GPa while pine is only 8.5 GPa - steel is 23 times stiffer. For a rectangular beam, I = width × height cubed / 12 - making the beam deeper has a cubic effect on stiffness, so depth is far more important than width. Standard I-beam sizes are pre-loaded; you can also enter rectangular, circular, or custom section properties directly.

Why a cantilever deflects so much more than a supported beam

A cantilever and a simply supported beam under the same point load, span, and material do not deflect by comparable amounts. For a central point load, a simply supported beam deflects by WL3 / (48EI), while a cantilever carrying the same load at its free end deflects by WL3 / (3EI).

Working through those two formulas, the cantilever deflects sixteen times more than the supported beam for an identical load, span, and section. This is why an unsupported deck ledger or balcony overhang feels far bouncier than a joist spanning between two walls, even when both use the same size lumber.

Point loads vs. uniformly distributed loads at the same total weight

The formulas also show that how a load is spread across the span changes the result, even when the total weight is identical. A uniformly distributed load produces a simply supported beam deflection of 5WL3 / (384EI), while the same total weight applied as one central point load produces WL3 / (48EI).

Comparing those two coefficients, a central point load deflects about 1.6 times more than the same total weight spread evenly as a UDL. That is why a beam that comfortably carries an evenly loaded floor can still sag noticeably under one heavy, concentrated piece of furniture or equipment.

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Last reviewed: September 17, 2026