🏗️ Beam Deflection Calculator
Calculate the maximum deflection of a cantilever beam with a point load at the free end.
🏗️ Beam Deflection Calculator
Calculate the maximum deflection of a cantilever beam with a point load at the free end.
✅ Calculation Result
Beam Deflection Diagram
Calculator Description
The beam-deflection calculator finds the maximum deflection of a cantilever beam — fixed at one end with a point load at the free end. Deflection is a serviceability measure: too much of it causes cracks, sticking doors/frames and objectionable vibration.
What this calculator finds
Enter the point load P, beam length L, modulus of elasticity E and area moment of inertia I to obtain the maximum free-end deflection δ.
Why it matters
- Checking serviceability against deflection limits (e.g. L/250, L/360)
- Sizing stiffness of architectural and machine-support beams (formwork, pipe supports)
- Comparing how section shape (I) and material (E) affect deflection
Formula
Cantilever Beam Deflection
For a cantilever with point load P at the free end, maximum deflection is proportional to the cube of the length. With consistent units the formula is identical in SI and US customary systems.
- δ — Maximum deflection [mm (Metric) or in (Imperial)]
- P — Point load [kN (Metric) or kip (Imperial)]
- L — Beam length [m (Metric) or ft (Imperial)]
- E — Modulus of Elasticity (steel ≈ 200 GPa or 29 Mpsi)
- I — Area moment of inertia [cm⁴ (Metric) or in⁴ (Imperial)]
How the formula works
- Deflection δ scales with L³, so doubling the span increases deflection eightfold.
- A larger moment of inertia I (deeper/thicker section) reduces deflection — the key to stiffness.
- Higher modulus E (steel > aluminium > timber) gives less deflection.
- Larger load P increases deflection linearly.
Worked example
For a steel cantilever with L = 5 m, P = 10 kN, E = 200 GPa (=200,000,000 kN/m²), I = 8000 cm⁴ (=8×10⁻⁴ m⁴): δ = 10×5³/(3×200,000,000×8×10⁻⁴) = 1250/480,000 ≈ 0.00260 m = 2.6 mm, well under the L/250 = 20 mm limit.
Useful Tips
Practical tips
- To cut deflection, shorten the span or increase section depth (raising I) — more effective than just reducing load.
- For a uniform load w use δ = wL⁴/(8EI); other load cases have different coefficients — identify the load type.
- Deflection limits vary by use (roof L/240, ceiling L/360, etc.); check the design code.
Limitations & cautions
- This formula applies only to small elastic deflections of an ideal cantilever (fixed-free).
- Real frames with continuous/simply-supported/ cantilever segments have different boundary conditions and need other formulas.
- Do not mix units — E, I, P and L must be in one consistent system (SI or US).