Beam Deflection Calculator
Work out beam deflection instantly with clear inputs, formula shown and shareable results.
About Beam Deflection Calculator
A simply supported beam with a central point load deflects PL^3/(48EI) at mid-span. The cube on span is what makes long beams so floppy: doubling the span multiplies deflection eightfold at the same load. 5 kN on a 3 m span with EI = 2 MN m2 deflects 1.4 mm, a span-to-deflection ratio well inside the usual L/360 serviceability limit.
Formulas
Central point load
delta = P L^3 / (48 E I)
Serviceability check
typical limit is span / 360
Worked example
With the default values below, Beam Deflection Calculator returns Mid-Span Deflection of 1.4063. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Central point loadminimum 0 N
- 5,000 N
- Span between supportsminimum 0 m
- 3 m
- Young's modulusminimum 0 GPa
- 200 GPa
- Second moment of areaminimum 0 m4
- 0.00001 m4
Results
- Mid-Span Deflection
- 1.4063 mm
- Same Deflection In Metres
- 1.40625 × 10⁻³
- Span-To-Deflection Ratio
- 2,133.3
- Stiffness
- 3,555.556 N/mm
Step by step
- 1Values used
- 2Central point load
- 3Serviceability check
- 4Mid-Span Deflection= 1.4063 mm
- 5Same Deflection In Metres= 0.00141
- 6Span-To-Deflection Ratio= 2,133.3
- 7Stiffness= 3,555.556 N/mm
Assumptions and limits
- The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax or compounding frequency into account.
- Figures are rounded for display to 5 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
Why does depth matter so much more than width?
Because the second moment of area goes with depth cubed. Turning a joist on edge is far more effective than making it wider.
What about a uniformly distributed load?
The coefficient changes to 5wL^4/(384EI). This calculator covers the central point load case only.