Beam Deflection Calculator
Screen elastic deflection for a simply supported beam under either a full-span UDL or a mid-span point load.
Use the Beam Deflection Calculator
Screen elastic deflection for a simply supported beam under either a full-span UDL or a mid-span point load.
Calculations and transformations happen locally in your browser. ToolLott does not send these inputs to a server for this tool.
Preliminary engineering screening only. It does not replace project-specific design, applicable codes/standards, load combinations, manufacturer data, professional review or independent verification.
How to use it
Start with the worked example, replace it with your real inputs, inspect the result and supporting details, then copy only after you have checked the assumptions or transformed output.
How the Beam Deflection Calculator works
Screen elastic deflection for a simply supported beam under either a full-span UDL or a mid-span point load. The methodology below exposes the production equation, a QA-verified worked example and the boundary between this screen and detailed design.
Calculation breakdown
ToolLott will explain the current inputs and displayed result here.
Simply supported beam elastic deflection
The production engine evaluates UDL: delta_max = 5 w L^4/(384 E I); midspan point: delta_max = P L^3/(48 E I). It begins by convert E from GPa to Pa and I from cm4 to m4., then choose the equation for uniformly distributed load or a mid-span point load., and finally calculate maximum elastic deflection and convert metres to millimetres. This keeps the calculation auditable instead of hiding design assumptions behind a single number.
UDL: delta_max = 5 w L^4/(384 E I); midspan point: delta_max = P L^3/(48 E I)ToolLott evaluates the relationship using the entered units and full numeric precision before display rounding.
| Symbol / input | Meaning | Unit |
|---|---|---|
loadCase | Load case | user input |
span | Beam span (m) | user input |
load | Service load | user input |
elasticModulus | Elastic modulus E (GPa) | user input |
inertia | Second moment of area I (cm4) | user input |
Step-by-step method
- Convert E from GPa to Pa and I from cm4 to m4.
- Choose the equation for uniformly distributed load or a mid-span point load.
- Calculate maximum elastic deflection and convert metres to millimetres.
Worked example
Aisha, a project engineer, A structural engineer is screening a simply supported 4.0 m beam carrying an 8 kN/m service UDL; E is 200 GPa and the trial section has I = 8,500 cm4, so the immediate question is the elastic deflection before a fuller member check.
Example inputs
- Load case: udl
- Beam span (m): 4
- Service load: 8
- Elastic modulus E (GPa): 200
- Second moment of area I (cm4): 8500
Calculation / processing
For UDL, w = 8 kN/m = 8,000 N/m; L = 4 m.E = 200 GPa and I = 8,500 cm4 = 8.5e-5 m4.delta = 5 x 8000 x 4^4 /(384 x E x I) = 0.001569 m = 1.569 mm.
Use the result as a screening or quantity-planning value and compare it with the project criteria, manufacturer data and applicable engineering requirements before making a design or procurement decision.
Assumptions
- The entered values are representative of the condition being screened and use the units shown on the page.
- The equation models only the stated relationship; omitted system effects are not silently estimated.
Limitations
- This page is not engineering certification and does not replace applicable standards, design loads, manufacturer data, site investigation or competent professional review.
- Results can change materially when real geometry, losses, transients, material properties, duty cycles, safety factors or regulatory criteria differ from the simplified inputs.
Common questions
Is this a final engineering design?
No. It is a transparent screening calculation using the entered assumptions and the stated equation.
Why does the page show assumptions and limitations?
Engineering formulas are only valid within their modelling assumptions; exposing them helps users decide what additional design checks are required.
Should I use the rounded displayed value in later design work?
Use suitable calculation precision and the governing project/standard requirements rather than relying on display rounding alone.
Methodology sources
Related ToolLott tools
A realistic way Aisha could use this tool
Aisha is a project engineer.
A structural engineer is screening a simply supported 4.0 m beam carrying an 8 kN/m service UDL; E is 200 GPa and the trial section has I = 8,500 cm4, so the immediate question is the elastic deflection before a fuller member check.
For this case the entered data is load case = “udl”; span = 4; load = 8; elastic modulus = 200; inertia = 8500. The page evaluates that exact set and reports Estimated maximum deflection: 1.569 mm; the example therefore demonstrates the method with real values rather than describing a vague before-and-after story.
This produces Estimated maximum deflection: 1.569 mm. In practical terms, Aisha can screen elastic deflection for a simply supported beam under either a full-span UDL or a mid-span point load using a result tied to the shown inputs instead of an unexplained recommendation. The page also keeps this limitation explicit: Preliminary structural/engineering screening only; final design remains subject to governing standards, load combinations, member stability, detailing, site criteria and professional verification.
Fictional scenario using realistic example data. For Ready tools, the worked result is tied to the tested example shown in the tool. Replace the figures with your own inputs and independently verify important professional, financial, legal, health or safety decisions.
What this calculator is for
Use it to calculate elastic beam deflection for a simply supported beam under a full-span UDL or mid-span point load.
It sits within ToolLott’s Structural collection, where you can also check beam deflection, beam reactions, column capacity, live loads, steel weight and wind loads for structural screening calculations.