Beam Deflection Calculator
Calculate beam deflection step by step: Simply supported: PL³/48EI (centre point), 5wL⁴/384EI (uniform).
In short
Formula: Simply supported: PL³/48EI (centre point), 5wL⁴/384EI (uniform). Cantilever: PL³/3EI (end point), wL⁴/8EI (uniform).
Maximum deflection
1.4062 mm
- Span ÷ deflection
- L/2,133
- EI
- 2,000,000 N·m²
What this calculator does
Calculate beam deflection step by step: Simply supported: PL³/48EI (centre point), 5wL⁴/384EI (uniform). Worked example, questions and limitations included.
Use it to turn Beam and load, Load (P in N, or w in N/m), Span length, Young's modulus E, and the other shown inputs into a checked result you can compare, copy, or rerun with different assumptions.
The page shows the formula, a numeric worked example, and the assumptions that affect this mechanical calculation.
Inputs and what they mean
- Beam and load
- — choice value.
- Load (P in N, or w in N/m)
- — number value.
- Span length
- — number value.
- Young's modulus E
- — number value.
- Second moment of area I
- — number value.
How to use it
- Enter each value in the unit shown next to the box (use the unit converter first if your numbers are in other units).
- Check the breakdown to see every intermediate step.
- Read the limitations before relying on the result.
Formula
Standard Euler–Bernoulli beam formulas from structural mechanics tables.
I in cm⁴ is converted to m⁴ (× 10⁻⁸); E in GPa to Pa.
Small deflections, linear elastic, prismatic beam; self-weight is not added unless you include it in w.
Simply supported: PL³/48EI (centre point), 5wL⁴/384EI (uniform). Cantilever: PL³/3EI (end point), wL⁴/8EI (uniform).
Inputs used: Beam and load, Load (P in N, or w in N/m), Span length, Young's modulus E, Second moment of area I.
Worked example
5 kN at centre of a 3 m steel beam
- EI = 200 × 10⁹ × 1,000 × 10⁻⁸ = 2 × 10⁶ N·m².
- δ = 5,000 × 27 ÷ (48 × 2 × 10⁶) = 0.00141 m = 1.41 mm.
Reading the result
The headline figure is the main answer. Any breakdown underneath shows the parts that make it up, so you can check the working and see what changes when you adjust an input.
Limitations and assumptions
- Four standard cases only.
- Linear elastic, small-deflection theory.
- Shear deformation neglected (fine for slender beams).
- Results are estimates for planning and learning. Real designs, installations and bids must be checked by a qualified, licensed professional against the codes that apply where you work.
- The result depends on the values you enter for this beam deflection calculator; it does not supply missing rates, rules, prices, dates, or assumptions for you.
Common questions
What deflection limit should I use?
Codes often express limits as span ÷ a number, such as L/360 for floors. The breakdown shows your L/ ratio to compare with your code.
Where do I find I?
From section tables for standard shapes, or I = b·h³/12 for a solid rectangle. Check the formula, example, and limitations on this page before using the result for a real mechanical decision.
Does it include the beam's own weight?
Only if you add it into the uniform load w. Check the formula, example, and limitations on this page before using the result for a real mechanical decision.
How do I use the Beam Deflection Calculator?
Enter the required values for Beam and load, Load (P in N, or w in N/m), Span length, Young's modulus E, Second moment of area I. The calculator applies the formula on this page and shows the main result with any supporting breakdown so you can check the arithmetic.
What formula does the Beam Deflection Calculator use?
Simply supported: PL³/48EI (centre point), 5wL⁴/384EI (uniform). Cantilever: PL³/3EI (end point), wL⁴/8EI (uniform). The visible formula section above lists the calculation path and the edge cases the page handles, so the result can be checked without relying on the form alone.
Can the Beam Deflection Calculator be used for exact decisions?
Use it as a calculation aid, not as a substitute for checking the underlying rule, contract, policy, or professional advice that applies to your situation. When a result depends on local rules, personal details, prices, or dates, enter those values yourself and confirm them before acting.
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