Cantilever Beam Deflection Calculator
Calculate the deflection of a cantilevered beam under a uniform load from its length, load, modulus of elasticity, and moment of inertia.
How this calculator works
A cantilever beam is fixed at one end and hangs free at the other, like a deck ledger, balcony, or overhang. Because there’s no support at the free end, this type of beam bends differently — and generally more — than a beam supported at both ends. This calculator takes the cantilever’s length, the uniform load it carries, the material’s stiffness, and the beam’s cross-sectional shape, and returns how far the free end deflects.
That deflection at the tip is what you check against a limit like L/180 to decide whether the beam is stiff enough for the job.
Formula: For a cantilever beam (fixed at one end, free at the other) with a uniform load, deflection at the free end = (w × L⁴) ÷ (8 × E × I), where w is load in lb per inch, L is length in inches, E is modulus of elasticity in psi, and I is moment of inertia in in⁴. A common deflection limit for cantilevers is L/180.
Worked example
A 6 ft cantilever carrying a 100 lb/ft load:
- Length: 6 ft = 72 in
- Load: 100 lb/ft ≈ 8.33 lb/in
- E = 1,600,000 psi, I = 100 in⁴
- Deflection at the free end ≈ 0.175 in
Notes
A cantilever deflects far more than a simply supported beam of the same length and load because the load isn’t shared between two supports — the entire beam has to resist bending through just one fixed end. This is why deck ledgers, balconies, and overhangs are usually kept short, or built with a much stiffer (deeper) beam than an equivalent simple span would need.
How to use
Enter the length of the cantilever, the uniform load it carries per foot, the modulus of elasticity for the beam material, and the moment of inertia for the beam’s cross-section. The calculator returns the deflection at the free end so you can compare it against your deflection limit, such as L/180.
This is a planning estimate using standard beam-deflection mechanics, not a substitute for engineering design. Confirm actual beam size, material, and deflection limits with a structural engineer and your local building code.
Frequently asked questions
What is a cantilever beam?
A cantilever beam is fixed at one end and free at the other, with no support holding up the far end. Deck ledgers that extend past a beam, balconies, and roof overhangs are common cantilever examples. Because only one end is held, the beam has to resist the entire load through that single fixed connection, which makes cantilevers behave very differently from beams supported at both ends.
Why is L/180 used instead of L/360 for cantilevers?
L/180 is a common deflection limit for cantilevers, looser than the L/360 often used for simply supported spans. Cantilevers naturally deflect more for the same length and load, so a stricter limit like L/360 would be very hard to meet in practice. L/180 still keeps movement in check while accounting for how cantilevers behave.
Why does a cantilever deflect so much more than a simple span?
A simply supported beam shares its load between two supports, which limits how far any point can move. A cantilever has only one fixed end, so the free end has nothing holding it up directly — it has to rely entirely on the stiffness of the beam itself. That's why the same length and load produce far more movement at a cantilever's free end than at the center of a simple span.
How can I reduce deflection in a cantilever?
Since deflection grows with the fourth power of length, shortening the cantilever has an outsized effect on reducing sag. Increasing the beam's depth also helps a great deal, since a deeper beam has much higher resistance to bending. Using a stiffer material raises the modulus of elasticity, which also reduces deflection, though length and depth typically matter more in practice.
Estimates only. Verify quantities with your supplier before purchasing.