Cantilever Beam Deflection Calculator

Estimate tip deflection, bending stress and end rotation for a rectangular cantilever under one free-end point load.

Model: prismatic rectangular cantilever, fixed at one end, with one transverse point load at the free end.

Tip deflection0.4 mm0.0157 in
Maximum bending stress12 MPa1.74 ksi
Free-end rotation0.034°0.0006 rad
Second moment of area (I)4,166,666.667 mm⁴Rectangular section about strong axis

Important: this is a small-deflection, linear-elastic beam estimate. It excludes self-weight, distributed loads, shear deflection, large-deflection effects, local buckling, lateral-torsional buckling, stress concentrations and connection flexibility.

Method

For a prismatic rectangular cantilever with a tip load, I = bh3/12, δ = PL3/(3EI), σmax = PL(h/2)/I and θ = PL2/(2EI).

Worked example

A 1 kN load on a 1 m steel cantilever with a 50 mm × 100 mm section gives about 0.4 mm tip deflection and 12 MPa maximum bending stress under this idealized model.

Important limits

This is not a beam-design or code-compliance check. It applies only to a fixed-free beam with a single tip load and small elastic deflection. Assess strength, stability, connections, shear and serviceability under the applicable standard separately.

References

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