Beam Deflection & Bending

How much will this beam sag? Pick a support and load type and see the deflected shape, maximum deflection, and peak bending moment update live.

Beam Deflection & BendingLive

Euler-Bernoulli beam theory

Controls

Presets

Span L (m)

Load P (kN)

Flexural rigidity EI (kN·m²)

Euler-Bernoulli theory relates a beam's deflection and internal moment to its load, span, and flexural rigidity EI. Deflection grows with the cube or fourth power of span, which is why doubling a span is far worse than doubling the load. Educational tool — not a substitute for a stamped structural design.

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Data Inspector

Max deflection1.30 mm

Max moment12.5 kN·m

Span/deflectionL/3840

Governing equation

δ = \frac{P L ^{3}}{48 E I} = \frac{10 \cdot 5 ^{3}}{48 \cdot 20000} = 1.30 mm

Reading this result: At L/3840 this beam clears the usual L/360 serviceability limit, so strength (not deflection) is likely to govern the design.

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How it works

Euler-Bernoulli beam theory relates deflection and internal bending moment to the load, span, and flexural rigidity EI. Because deflection scales with the cube or fourth power of the span, small changes in length dominate the result. Educational tool — not a substitute for a stamped structural design.

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Frequently asked questions

Is this beam deflection calculator tool really free?▾

Yes. Beam Deflection & Bending runs entirely in your browser using your device's own compute, so local use is free forever. You only pay Compute Tokens if you scale a job to the cloud.

Do I need to install anything?▾

No. Everything runs client-side in a modern browser — no downloads, no license, no account required to start.

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How accurate are the results?▾

The solver uses established numerical methods, but results are for research and educational purposes and should be validated against experiment or professional review before you rely on them.