Beam Deflection Calculator — Cantilever Beam Point Load Formulaδ = PL³ / 3EI
Use this free Beam Deflection Calculator to instantly compute the maximum deflection of a cantilever beam subjected to a concentrated point load at the free end. Based on the standard cantilever beam deflection formula used in structural engineering and mechanical design, this tool calculates vertical displacement (δ) using your input values for applied load (P), beam span length (L), modulus of elasticity (E), and second moment of area / moment of inertia (I). To analyze the forces acting on the beam before calculating deflection, you can also calculate force based on mass and acceleration.
This cantilever beam deflection calculator is widely used by civil engineers, structural engineers, and mechanical designers to verify that maximum beam deflection stays within permissible deflection limits — typically span/180 to span/360 as specified by AISC, Eurocode 3, ACI 318, and IS 456 standards. Ensuring deflection compliance is critical for preventing structural failure, cracking of finishes, serviceability issues, and long-term fatigue damage in both steel and reinforced concrete beams.
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Beam Deflection Calculator — How Much Your Structure Will Bend Under Load
Beam deflection is the vertical displacement of a beam under applied loads — a critical structural engineering parameter because excessive deflection causes cracking in finishes, misalignment of connected elements, and serviceability failures even when the beam has adequate strength. Building codes typically limit beam deflection to span/360 for live loads (about 8mm in a 3m span). A steel W-beam supporting a 20 kN/m distributed load over 5 meters may have the strength to carry the load but still fail the deflection limit — the calculator checks both simultaneously.
Deflection depends on the fourth power of span: doubling a beam's length increases deflection by 16 times for the same load. This non-linearity is why long-span structures require disproportionately heavier beams. It also explains why adding an intermediate support is so effective — cutting the effective span in half reduces deflection by 93.75%. The calculator covers simply supported, cantilever, fixed-fixed, and propped cantilever boundary conditions with point loads, distributed loads, and moment loads at arbitrary positions.
The moment of inertia I of the beam cross-section is the primary geometric parameter controlling deflection. Doubling I halves deflection. A wide-flange beam (W-shape) concentrates material far from the neutral axis to maximize I for a given weight — which is why structural steel is never solid rectangular bar. The calculator accepts standard steel section properties (W, S, C, L shapes) and allows custom I values for timber, concrete, or composite sections.