Beam Deflection Calculator
How far a beam deflects under load — simply supported or cantilever, point load or distributed — with the span-to-deflection ratio builders actually check.
Deflection scales with the cube or fourth power of the span, which is why doubling a span is catastrophic rather than merely worse: a simply supported beam under a central point load deflects eight times as far when the span doubles.
How the beam deflection calculator works
Deflection scales with the cube or fourth power of the span, which is why doubling a span is catastrophic rather than merely worse: a simply supported beam under a central point load deflects eight times as far when the span doubles.
The practical check is the ratio: span over deflection. Building codes commonly want L/360 for floors under live load, and that ratio is usually the binding constraint long before the beam is anywhere near breaking.
Formula: δ = PL³/48EI (central point); δ = 5wL⁴/384EI (distributed)
Worked examples
| Inputs | Deflection (mm) | Note |
|---|---|---|
| 5 kN at mid-span over 4 m | 0.3922 | about 4.9 mm |
| A distributed load | 0.9804 | a different formula entirely |
| A cantilever | 6.2745 | sixteen times the deflection |
FAQFrequently asked questions
What is L/360?
A deflection limit: the beam may sag no more than the span divided by 360. It is the common requirement for floors under live load.
Why does span matter so much?
Deflection goes as the span cubed for a point load and the fourth power for a distributed one. Small increases in span cost a great deal of stiffness.
What is the second moment of area?
A measure of how the cross-section resists bending. It rises with the cube of depth, which is why beams are deep rather than wide.
Is deflection or strength the binding constraint?
For most floor beams, deflection. A beam stiff enough not to bounce is usually far stronger than it needs to be.
Does this account for the beam's own weight?
No. Add it to the distributed load — for long spans in steel or concrete it is a significant part of the total.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G, g₀, R, c
- NIST Special Publication 811 — Guide for the use of the International System of Units — unit conversions
- The Engineering ToolBox — material properties — specific heats, expansion coefficients, densities
- National Physical Laboratory — the UK's national measurement institute
Last checked: September 2026. Constants are the CODATA 2018 values; formulas are the standard textbook forms.