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Beam Deflection Calculator

Compute the maximum deflection and slope of a simply-supported, cantilever, or fixed-fixed beam under a point or uniformly distributed load.

Pick support and load type, enter span, modulus E, and moment of inertia I. Results are elastic small-deflection values.

About this tool

The Beam Deflection Calculator is a free, in-browser structural tool that returns the maximum deflection and slope of a single-span beam using the closed-form Euler-Bernoulli solutions. Pick the support condition (simply-supported, cantilever, or fixed-fixed), the load type (a central point load P or a uniformly distributed load w), and enter the span L, the modulus of elasticity E, and the area moment of inertia I. Everything is computed locally in your browser, so nothing you type is uploaded.

Each case uses its standard formula. Simply-supported with a central point load gives maximum deflection δ = PL³/(48EI) and end slope θ = PL²/(16EI); with a UDL it is δ = 5wL⁴/(384EI) and θ = wL³/(24EI). A cantilever with an end point load gives δ = PL³/(3EI) and θ = PL²/(2EI); with a UDL, δ = wL⁴/(8EI) and θ = wL³/(6EI). Fixed-fixed beams are stiffer: δ = PL³/(192EI) for a central point load and δ = wL⁴/(384EI) for a UDL. The flexural rigidity EI drives every result, so the tool also reports it. Choose SI (metres, GPa, mm⁴, newtons) or imperial (inches, psi, in⁴, lbf) and the units convert consistently.

As a worked example, a simply-supported steel beam (E = 200 GPa, I = 10,000,000 mm⁴) spanning 3 m under a 10,000 N central load has EI = 2,000,000 N·m² and a maximum deflection of PL³/(48EI) = 10,000 × 27 / (48 × 2,000,000) ≈ 0.00281 m, or about 2.81 mm, with an end slope near 0.16°. These are elastic, small-deflection results for a prismatic beam of constant EI and should be checked against a stiffness or serviceability limit such as L/360.

Frequently asked questions

How is maximum beam deflection calculated?
It uses the closed-form Euler-Bernoulli case for the chosen support and load. For a simply-supported beam with a central point load, δ = PL³/(48EI); for a uniformly distributed load, δ = 5wL⁴/(384EI). E is the elastic modulus and I is the area moment of inertia.
What support and load cases are covered?
Simply-supported, cantilever, and fixed-fixed beams, each with either a central point load or a uniformly distributed load (UDL). Fixed-fixed beams are the stiffest — δ = PL³/(192EI) for a point load — while a cantilever end load deflects the most at δ = PL³/(3EI).
Which units should I enter?
In SI mode enter span in metres, E in GPa, I in mm⁴, point load in N and UDL in N/m; deflection is reported in mm. In imperial mode use inches, psi, in⁴, lbf and lbf/in, with deflection in inches. The tool keeps the units consistent internally.
Why does the slope show for some cases but not others?
The tool reports the standard maximum slope for simply-supported and cantilever cases. For fixed-fixed beams the slope is zero at both built-in ends and at mid-span by symmetry, so no single representative slope is shown — only the deflection and flexural rigidity EI.

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