How to use the cantilever beam calculator
A cantilever is fixed at one end and free at the other, which describes balconies, canopies, shelf brackets, and crane support arms. Enter the load type and magnitude, the projecting length, the rectangular section size, and the material to get the free-end deflection, the fixed-end moment, and the peak bending stress immediately.
For a point load at the free end, deflection is d = PL³/(3EI) and the fixed-end moment is M = PL. For a uniform load, deflection is d = wL⁴/(8EI) and the moment is M = wL²/2. Bending stress comes from s = M/S, where a rectangular section has S = bh²/6 and I = bh³/12.
Length dominates the answer. Deflection scales with the cube of length under a point load and the fourth power under a uniform load, so trimming the projection is the most effective fix. On the section side, depth is far more valuable than width because moment of inertia is cubic in depth.
These formulas assume elastic behavior, a prismatic rectangular section, and a truly rigid support. Real designs also need allowable stress checks for the specific material, lateral torsional buckling, connection stiffness at the fixed end, and vibration serviceability. Have a licensed structural engineer confirm the section before it is built.
Frequently asked questions
Deflection peaks at the unsupported free end, while bending moment and bending stress peak at the fixed support. The two critical locations differ, so each has to be checked separately.
A free-end point load gives deflection proportional to length cubed and a uniform load to length to the fourth power, so doubling the length multiplies deflection by 8 and 16 respectively.
Moment of inertia is linear in width but cubic in depth, so adding depth is far more effective. Lateral torsional buckling and constructability still have to be checked.