What this calculator does
Deflection is what people notice. Too much and ceilings crack, glazing distorts and partitions bow, even when the member is comfortably strong. This calculator applies the textbook coefficient for your support and loading case and compares the result against the L/240 serviceability limit.
How to use it
- Choose the support and loading arrangement — the coefficient changes completely between a simply supported and a cantilever beam.
- Enter the span, the material E-modulus and the second moment of area.
- Enter either the uniform load or the central point load to match your case.
- The maximum moment is reported alongside the deflection so you can check strength with the same numbers.
Governing formula
δ = k · w L⁴ / (E I) or k · P L³ / (E I) Where:
-
k= Coefficient for the support/loading case [–] -
I= Second moment of area [mm⁴] -
E= Modulus of elasticity [MPa]
Derived Equations:
δ_limit = L / 240 δ_limit = L / 360 Worked example — 6 m simply supported beam, 10 kN/m
The figures below were produced by running this page's own engine with the example inputs (Support and loading case, Span (m), Uniform load (kN/m), Central point load (kN), Modulus of elasticity (MPa), Second moment of area (I) (mm⁴)). If the calculator returns something different for the same numbers, that is a bug, not a rounding difference.
| Maximum deflection | 9.85 mm |
|---|---|
| L/240 limit | 25 mm |
| Deflection / limit | 0.39 – |
| Maximum moment | 45 kN·m |
| Case | Simply supported — UDL |
| Assessment | Deflection 9.8 mm is within the 25 mm (L/240) serviceability limit. |
- For a simply supported beam under uniform load, δ = 5wL⁴ / 384EI.
- With I = 85.7 × 10⁶ mm⁴ the span is quite stiff relative to the load.
- The L/240 limit on a 6 m span is 25 mm — compare the calculated deflection against it.
Assumptions & limitations
Engineering calculation. Standard elastic beam-deflection coefficients for six common support and loading arrangements, with an L/240 serviceability limit.
- Elastic, small-deflection theory only — very deep or flexible members need large-deflection treatment.
- Assumes constant EI along the span and ignores self-weight unless you include it.
- Composite action, partial fixity at supports and propped cantilevers change the coefficients and are not modelled.
This tool supports professional engineering work; it does not replace a sealed design. Confirm every result against the applicable standard and a licensed engineer before it is built.
References & standards
- Eurocode 2 / EN 1993 — serviceability limit states for deflection.
- SCI P359 — deflection of beams.
- AISC Design Guide 3 — industrial buildings, deflection criteria.