Is this beam deflection calculator a substitute for a structural engineer?

No. It applies standard Euler-Bernoulli formulas for simple load cases and gives an estimate for early sizing or a sanity check, but a licensed structural engineer must verify beam sizing, combined loading, and code compliance before construction.

What deflection limit should I use?

L/360 (span divided by 360) under live load is a widely used limit for floor joists in many building codes, with L/240 under total load and L/180 sometimes used for roof members — but the exact limit depends on your local code and the beam's use, so check the governing standard for your project.

How much does it cost to get a beam deflection check verified by an engineer in the UK?

A chartered structural engineer in the UK typically charges around £220-£800 to review and sign off a single beam deflection calculation, with the fee depending on the load case, the beam material, and whether the report needs to be submitted to building control.

Beam Deflection Calculator (UK)

Beam Deflection Calculator: Euler-Bernoulli Formula for Sag Under Load

This calculator estimates how much a simply-supported or cantilever beam bends under a given load, using standard Euler-Bernoulli beam theory for common load cases (point, uniform, triangular, and moment loads). It is a quick serviceability check for students, tradespeople, and engineers sizing a beam early in a design — it is not a substitute for a licensed structural engineer's sign-off, and it does not check bending stress or shear, only deflection.

How to use the beam deflection calculator

Choose the support type (simply-supported or cantilever) and the load case that matches your beam — a point load, a uniform distributed load, or a moment at the support.
Enter the span length, the load magnitude, and the modulus of elasticity (E) for your material, or pick a material preset (steel, concrete, aluminum, or timber).
Pick the section shape (rectangle, circle, hollow circle, or a custom moment of inertia) and enter its dimensions.
Set the deflection limit denominator (e.g. 360 for L/360) to see whether the calculated deflection passes a typical serviceability check.

The beam deflection formula

For a simply-supported beam under a uniform distributed load w over span L, the maximum deflection at midspan is delta = 5wL^4 / (384EI), where E is the modulus of elasticity and I is the section's moment of inertia (for a rectangle, I = width x height^3 / 12).

Worked example: a 4 m timber joist (E = 11 GPa) with a 50 mm x 200 mm rectangular section carries a 2000 N/m uniform load. I = 0.05 x 0.2^3 / 12 = 3.33 x 10^-5 m^4, so EI = 11 x 10^9 x 3.33 x 10^-5 ~= 366,700 N.m^2. Deflection = 5 x 2000 x 4^4 / (384 x 366,700) ~= 0.0182 m, or about 18 mm. Checked against a common L/360 limit (4000 mm / 360 ~= 11 mm), this joist would fail — it would need a deeper section or a shorter span.

Tips

Common allowable-deflection limits are L/360 for floor joists under live load, L/240 under total load, and L/180 for roof members — but always confirm the limit that applies under your governing building code, since it varies by member type and use.

Beam depth matters far more than width: since I scales with height cubed, doubling a section's depth cuts deflection roughly eightfold, while doubling its width only halves it.

In the UK, a chartered structural engineer typically charges around £220-£800 to check and sign off a single beam deflection calculation like the worked example above, depending on the load case and whether calculations are needed for building control.