Beam Deflection Calculator (Cantilever)
Find the maximum deflection of a cantilever beam under a point load at the free end or a uniformly distributed load.
🏗️ What is Cantilever Beam Deflection?
Cantilever beam deflection is the amount a beam bends, or displaces vertically, when it is fixed rigidly at one end and completely free at the other. Unlike a simply supported beam, a cantilever has no support at all restraining the far end, so it must resist bending and rotation entirely through the fixed connection. Maximum deflection always occurs at the free tip, the point farthest from the support.
Cantilevers appear throughout structural and civil engineering. Balcony slabs, canopy roofs, diving boards, aircraft wings, and retaining wall stems all behave as cantilevers under load. Crane jibs and traffic sign gantries are cantilevered so they can project outward from a single mounting point. In every one of these cases, the fixed end must supply both the shear force and the bending moment that a second support would otherwise share.
A common misconception is that a cantilever with the same span, load, and stiffness as a simply supported beam will deflect a similar amount. It does not. Because only one end is restrained, a cantilever under a point load at its free end deflects 16 times more than an equivalent simply supported beam with the same point load at midspan, since the deflection formula's denominator is 3EI rather than 48EI.
This calculator computes the maximum deflection of a cantilever beam under either a point load at the free end or a uniformly distributed load, using standard Euler-Bernoulli beam formulas, and shows the deflected shape along the full unsupported length as an interactive chart.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Steel Cantilever Under a Point Load at the Free End
A 3 m steel cantilever (E = 200 GPa, I = 80,000,000 mm⁴) carrying a 10 kN point load at the free end
Example 2 — Same Steel Cantilever Under a Uniformly Distributed Load
The same 3 m steel cantilever carrying a 12 kN/m distributed load across the full unsupported length
Example 3 — Timber Cantilever Under a Point Load at the Free End
A 2 m timber cantilever (E = 11 GPa, I = 60,000,000 mm⁴) carrying a 2 kN point load at the free end
❓ Frequently Asked Questions
🔗 Related Calculators
What is the formula for cantilever beam deflection under a point load at the free end?
For a cantilever fixed at one end with a point load P at the free end, maximum deflection is delta_max = PL^3/(3EI), occurring at the free end (x = L). P is the load, L the unsupported length, E the modulus of elasticity, and I the second moment of area.
What is the formula for cantilever beam deflection under a uniformly distributed load?
For a cantilever under a uniformly distributed load w (force per unit length) over the full span, maximum deflection is delta_max = wL^4/(8EI), also occurring at the free end. This is smaller than the equivalent total point load case because the load is spread across the span.
Why does a cantilever deflect more than a simply supported beam?
A cantilever is restrained at only one end, so the free end has no support resisting rotation or displacement. For the same P, L, E, and I, a cantilever with a point load at the free end deflects 16 times more than a simply supported beam with the same point load at midspan (denominator 3EI versus 48EI).
What units should I use for E and I in this calculator?
Enter the modulus of elasticity E in gigapascals (GPa) and the second moment of area I in millimeters to the fourth power (mm^4), the same units used across every beam deflection calculator on this site. The tool converts to SI base units (Pa and m^4) internally before reporting the free-end deflection in millimeters.
What is a typical deflection limit for a cantilever beam?
A common serviceability limit for cantilevers is span/180 (L/180), more lenient than the L/360 typically used for simply supported spans, since only one end of a cantilever is restrained. For a 3 m cantilever, L/180 is about 16.7 mm.
Where does maximum deflection occur on a cantilever beam?
For both a point load at the free end and a uniformly distributed load, maximum deflection on a cantilever occurs at the free end (x = L), the point farthest from the fixed support.
How does unsupported length affect cantilever deflection?
Deflection is extremely sensitive to unsupported length. Under a point load at the free end, deflection scales with L^3 (doubling the length increases deflection 8x). Under a uniformly distributed load, deflection scales with L^4 (doubling the length increases deflection 16x).
What is the difference between a point load and a uniformly distributed load on a cantilever?
A point load (P) is a single concentrated force applied at the free end in this calculator. A uniformly distributed load (w) is spread evenly across the entire unsupported length in force-per-unit-length units (kN/m), such as the self-weight of a balcony slab or an overhanging canopy.
Does increasing the modulus of elasticity always reduce cantilever deflection?
Yes, deflection is inversely proportional to E, so a stiffer material (higher E) under the same load and geometry deflects less. Steel (E is about 200 GPa) deflects roughly 18 times less than an equivalent timber cantilever (E is about 11 GPa) for identical length and section.
What assumptions does this cantilever deflection formula make?
This calculator uses classical Euler-Bernoulli beam theory, which assumes linear-elastic material behavior, small deflections relative to the length, a prismatic (constant cross-section) beam, and a rigid fixed support that prevents both displacement and rotation at x = 0.
Can this calculator be used for simply supported or fixed-fixed beams?
No, this calculator specifically applies cantilever formulas, fixed at one end and completely free at the other. Simply supported and fixed-fixed beams use different boundary conditions and different deflection formulas, and would give incorrect results here.