Beam Deflection Calculator
Pick a beam type, enter the span and load, choose your cross-section and material - see how much it bends and whether it passes the standard limits. Everything runs in your browser, nothing uploaded.
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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.
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.
FAQ
What is L/360 deflection limit?
L/360 means the maximum allowable sag equals the beam span divided by 360. For a 3,600 mm span, the limit is 10 mm. This is the standard live-load deflection limit for floors in most building codes.
What is the deflection formula for a simply supported beam with a UDL?
For a simply supported beam with a uniformly distributed load W over span L, midspan deflection = 5WL3 / (384EI), where E is the elastic modulus of the material and I is the second moment of area of the cross-section.
What does E and I mean in beam calculations?
E is Young's modulus (elastic modulus) - a material property measuring stiffness. Steel is 200 GPa, oak is 11 GPa. I is the second moment of area - a cross-section property. A deeper beam has a much higher I. Together, EI defines how stiff a beam is against bending.