Structural calculator

Beam Deflection Calculator

Calculate elastic deflection, support reactions, bending moment, slope, and serviceability ratio for common beam cases.

Use calculator View formulas FAQ

Interactive calculator

Enter beam values

Choose a beam case, set units, and use the live diagram to inspect the elastic deflected shape and moment profile.

Elastic beam

Result

Interactive diagram

Deflected shape and moment profile

The deflection curve is visually exaggerated so the shape is readable. Use the numeric result for actual deflection.

Enter values to check serviceability

About this calculator

How it works

The beam deflection calculator uses standard Euler-Bernoulli elastic beam formulas for common simply supported and cantilever cases. It is intended for quick serviceability checks, structural coursework, preliminary member sizing, and comparison of span, stiffness, load, and section inertia.

Formulas

Common maximum deflection formulas

Simply supported, center point load

delta max = P L^3 / (48 E I)

Simply supported, uniform load

delta max = 5 W L^3 / (384 E I)

Cantilever, end point load

delta max = P L^3 / (3 E I)

Cantilever, uniform load

delta max = W L^3 / (8 E I)

Worked example

Example calculation

Inputs

A 4 m simply supported steel beam with a 10 kN center load, E = 200 GPa, and I = 8e-6 m4.

Maximum deflection

delta = P L^3 / (48 E I) = 0.00833 m, or 8.33 mm.

Guide

How to use this calculator

Select the support and load case that best matches the beam.
Enter the load, span, elastic modulus, and second moment of area.
Use the material preset buttons when you want a quick elastic modulus value.
Enter a deflection limit such as L/360 to compare the result with a serviceability target.
Use the diagram for shape intuition and the table for numeric design checks.

Reference

What the results mean

Maximum deflection

The largest elastic displacement predicted by the selected closed-form beam equation.

L/deflection ratio

Span divided by maximum deflection. Larger values mean a stiffer beam relative to its span.

Maximum moment

The largest bending moment for the selected support and load condition.

Slope

The rotation of the beam tangent at the support or end, depending on the selected case.

Assumptions and limits

Before using the result

Formulas assume small deflection, linear elastic behavior, constant E and I, and ideal support conditions.
Uniform load input is total load over the full span, not load per meter.
Final design should also check strength, shear, bearing, buckling, vibration, lateral-torsional stability, connections, load combinations, and code requirements.

FAQ