Cantilever Beam Deflection Calculator
A cantilever is a beam fixed rigidly at one end and free at the other, like a diving board or a balcony, and the deflection at its free end is a fundamental structural result. When a point load is applied at the free end, the tip droops by an amount that grows with the cube of the length and shrinks as the beam gets stiffer. Because length enters to the third power, a cantilever twice as long deflects eight times as much under the same load, which is why long overhangs need deep, stiff sections. This calculator takes the end point load, the length, the modulus of elasticity and the second moment of area, then returns the tip deflection in meters using consistent SI units. The result is shown with adaptive precision because the values are often very small. The formula assumes a prismatic, linearly elastic cantilever carrying a single concentrated load at the tip, the standard textbook case. Structural loading conventions and the related engineering standards are published by US federal agencies including the National Highway Traffic Safety Administration. Every figure is computed deterministically from the standard formula, shown below, with a worked example that reconciles exactly to the calculator so you can verify each step yourself.
Tip deflection of an end-loaded cantilever equals P L^3 / (3 E I). For a 2 m cantilever with a 1,000 N tip load, E of 200 GPa and I of 4.0e-6 m4, the deflection is 0.003333 m (about 3.33 mm). Deflection grows with the cube of length.
Cantilever deflection formula
delta = P L^3 / (3 E I)
delta = tip deflection (m)
P = end point load (N), L = length (m)
E = modulus of elasticity (Pa), I = second moment of area (m4)
The numerator P L^3 shows how the point load and length drive deflection, with length cubed. The denominator 3 E I represents the beam's bending stiffness. Keep all inputs in consistent SI units so the deflection comes out in meters.
Worked example
A steel cantilever 2 m long carries a 1,000 N point load at its free end. Steel has E = 200 GPa = 200,000,000,000 Pa and the section has I = 0.000004 m4.
- Numerator: 1,000 x 2^3 = 1,000 x 8 = 8,000
- Denominator: 3 x 200,000,000,000 x 0.000004 = 2,400,000
- Divide: delta = 8,000 / 2,400,000 = 0.003333 m
- That is about 3.33 mm of tip droop
So the free end deflects about 3.33 mm under the load. These are the calculator's default inputs, so the result above matches the widget exactly.
Cantilever Beam Deflection Calculator: frequently asked questions
How do you find a cantilever's tip deflection?
For a cantilever with a point load P at the free end, the tip deflection is P L^3 / (3 E I), where L is the length, E the modulus of elasticity and I the second moment of area. With consistent SI units the deflection comes out in meters.
Why does a cantilever deflect more than a simply supported beam?
A cantilever is supported at only one end, so the whole length acts as an unsupported overhang and the bending moments build up toward the fixed end. The coefficient in P L^3 / (3 E I) is far larger than for an equivalent supported beam, so a cantilever sags much more.
What if the load is distributed instead of a point load?
For a uniformly distributed load w over a cantilever, the tip deflection is w L^4 / (8 E I). This page covers the single end point load case; swap in that formula for a distributed load.
How can I reduce cantilever deflection?
Increase the section's second moment of area by using a deeper beam, choose a stiffer material with a higher modulus, or shorten the overhang. Because length is cubed, even a small reduction in length cuts deflection sharply.
What is the cantilever deflection formula?
For an end point load, the maximum tip deflection is delta = P L^3 / (3 E I).
Official sources
- Structural loading and engineering safety standards reference: US National Highway Traffic Safety Administration (NHTSA). As at 25 June 2026.
Reviewed by the CalculatorHub team, edited by James Graham, 25 June 2026. See our methodology. This is general information, not financial, tax, legal or investment advice.