Cantilever Load Calculator | Deflection, Moment & Shear

Calculate cantilever beam shear, moment, slope, deflection, stress, or allowable point and distributed loads in metric or imperial units.

Cantilever Load Formula

For an ideal fixed-free beam with constant EI, the formula below gives tip deflection δ from a free-end point force P. For a uniform load w over the full span, δ = wL⁴/(8EI), where w is force per unit length.

δ = (P L³) / (3 E I)

Variables:

δ is the tip-deflection magnitude (m)
P is the load applied at the end of the beam (N)
L is the length of the beam (m)
E is the modulus of elasticity of the beam material (Pa)
I is the moment of inertia of the beam’s cross-sectional area (m^4)

For a point force, multiply P by the cube of span L and divide by 3EI to obtain tip deflection. To solve a point-load deflection limit, Pδ = 3EIδallow/L³; the bending-stress limit is Pσ = σallowS/L. For a full-span uniform load, wδ = 8EIδallow/L⁴ and wσ = 2σallowS/L². The planning modes choose the smaller of the two corresponding bounds, with section modulus S about the bending axis. These checks alone do not establish a safe structural load.

What is a Cantilever Load?

A cantilever load is a force that is applied to a structure, typically a beam or a pole, that extends horizontally and is only supported at one end. This type of load creates a bending effect on the structure, causing it to flex and potentially deform or break if the load is too heavy. The amount of load a cantilever can bear depends on the material’s strength and the length of the overhang.

How to Calculate Cantilever Load?

The following steps calculate tip deflection from a known tip point load. Choose a planning mode to apply allowable bending-stress and deflection limits instead.

First, determine the load applied at the end of the beam (P) in newtons (N).
Next, determine the length of the beam (L) in meters (m).
Next, determine the modulus of elasticity of the beam material (E) in pascals (Pa).
Next, determine the moment of inertia of the beam’s cross-sectional area (I) in meters to the power of 4 (m^4).
Finally, calculate tip deflection δ = PL³/(3EI). For a full-span uniform load, use δ = wL⁴/(8EI) instead.
After inserting the values of the variables and calculating the result, check your answer with the calculator above.

Example Problem:

Use the following variables as an example problem to test your knowledge:

Load applied at the end of the beam (P) = 500 N

Length of the beam (L) = 2 m

Modulus of elasticity of the beam material (E) = 2.1 x 10^11 Pa

Second moment of area I = 4.5 × 10⁻⁶ m⁴. These example values give δ = 500 × 2³ / (3 × 2.1 × 10¹¹ × 4.5 × 10⁻⁶) ≈ 0.00141093 m = 1.41093 mm. The model assumes linear elasticity, ideal fixity and small deflection; shear failure, buckling, connections, support flexibility, dynamics and code-required factors need separate design checks. See MIT’s beam displacement table and the University of Illinois bending reference.