Beam Deflection Calculator
Estimate the maximum deflection of a simply supported beam carrying a single point load at midspan. Enter the load, span, the material's Young's modulus and the section's moment of inertia, and the calculator returns the maximum mid-span deflection using δ = PL³ / (48EI).
Formula
δ_max = P·L³ / (48·E·I) (simply supported beam, central point load)
- P is the point load applied at midspan, L the span between supports.
- E is Young's modulus (entered in GPa, converted to Pa) and I the second moment of area (entered in cm⁴, converted to m⁴).
- Maximum deflection for a central point load on a simply supported beam is δ = PL³ / (48EI), occurring at midspan.
- For a uniformly distributed load the formula differs (δ = 5wL⁴ / 384EI) — this calculator covers the central point-load case.
- Deflection should usually stay within a serviceability limit such as L/360; check the span/deflection ratio against your code.
- This is an elastic estimate for a single span and ignores shear deflection and self-weight.
5 kN load on a 4 m steel beam, I = 5000 cm⁴
Inputs
- Point Load P: 5000 N
- Span L: 4 m
- Young's Modulus E: 200 GPa
- Moment of Inertia I: 5000 cm⁴
E = 200 GPa, I = 5000 cm⁴ = 5×10⁻⁵ m⁴. δ = (5000 × 4³) / (48 × 200×10⁹ × 5×10⁻⁵) ≈ 0.000667 m ≈ 0.67 mm, a span/deflection ratio of about L/6000 — well within limits.
Frequently asked questions
What does this calculator find?
The maximum mid-span deflection of a simply supported beam carrying a single point load at the centre, using δ = PL³ / (48EI).
What units should I use?
Load in newtons, span in metres, Young's modulus in GPa and the moment of inertia in cm⁴. The calculator converts E and I internally to SI units.
What is a safe deflection limit?
A common serviceability rule is that deflection should not exceed span/360 for floors. Always check the limit specified by your design code.
Does this work for a distributed load?
No — this assumes a central point load. A uniformly distributed load uses δ = 5wL⁴ / 384EI instead.