Cantilever Deflection Calculator NZ

This calculator finds the tip deflection of a cantilever beam carrying a point load at its free end, one of the most common cases in structural and mechanical engineering. A cantilever is a beam fixed rigidly at one end and free at the other, like a diving board, a balcony, or a bracket projecting from a wall. When a load is applied at the free end, the beam bends, and the tip drops by an amount that depends on the load, how far it projects, and the beam's stiffness. Controlling this deflection is essential: a cantilever strong enough not to break can still sag too much, causing problems with appearance, function or attached components. This calculator computes it. You enter the point load at the end, the length of the cantilever, the modulus of elasticity of the material, and the second moment of area of the cross-section, and the calculator returns the tip deflection, the value in millimetres, the maximum bending moment, and the load for reference. The results update as you type. Use it for engineering study, for checking a cantilever or bracket, or to understand how its stiffness depends on length and section. The tip deflection of an end-loaded cantilever is the load times the length cubed, divided by three times the modulus times the second moment of area. The maximum bending moment, which occurs at the fixed end, is simply the load times the length. The dependence on the length cubed is striking: doubling the length of a cantilever increases its tip deflection eightfold for the same load, which is why long cantilevers deflect so dramatically and need much deeper or stiffer sections. A larger modulus, from a stiffer material, or a larger second moment of area, from a deeper section, both reduce the deflection. This is an educational estimate of elastic deflection; real designs must follow the relevant code and proper engineering analysis.

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0.833 mm
tip deflection
In metres8.33e-4 m
Max bending moment1,000 N·m
End load500 N

End-loaded cantilever: deflection = P L³ / (3 E I). Max moment = P L, at the fixed end. Deflection grows with the cube of length. An educational estimate; follow the code.

How it works

For a cantilever with a point load at its free end, the tip deflection is the load times the length cubed, divided by three times the modulus of elasticity times the second moment of area. The maximum bending moment occurs at the fixed support and equals the load times the length.

Worked example

A 500 newton load at the end of a 2 metre steel cantilever, with a modulus of 200 billion pascals and a second moment of area of 8 times 10 to the minus 6, deflects by 500 times 8, divided by 3 times 200 billion times 0.000008. That is about 0.000833 metres, or 0.833 millimetres, with a maximum bending moment of 1,000 newton metres at the fixed end.

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Frequently asked questions

How is cantilever deflection calculated?

For a point load at the free end, the tip deflection is the load times the length cubed, divided by three times the modulus of elasticity times the second moment of area. This calculator applies that formula and also gives the maximum bending moment.

Why does length matter so much?

Tip deflection grows with the cube of the cantilever's length, so doubling the length increases the deflection eightfold for the same load. This is why long cantilevers sag dramatically and need much deeper or stiffer sections to control the movement.

Where is the bending moment greatest?

At the fixed end, where the cantilever is attached. The maximum bending moment there is the load times the length. This is also where bending stress is highest, so it is the critical location for checking the strength of a cantilever.