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| Load Case | Reaction / Moment / Shear | Slope / Deflection (max, at free end unless noted) |
|---|---|---|
| Point load at free end | Ra=P, Ma=PL, Vmax=P, Mmax=PL | θ=PL²/2EI, δ=PL³/3EI |
| Point load at position a | Ra=P, Ma=Pa, Vmax=P, Mmax=Pa | θ(L)=Pa²/2EI, δ(L)=Pa²(3L-a)/6EI, δ(a)=Pa³/3EI |
| Uniform distributed load | Ra=wL, Ma=wL²/2, Vmax=wL, Mmax=wL²/2 | θ=wL³/6EI, δ=wL⁴/8EI |
| Triangular load (max at fixed end) | Ra=w0L/2, Ma=w0L²/6, Vmax=w0L/2, Mmax=w0L²/6 | θ=w0L³/24EI, δ=w0L⁴/30EI (verified) |
A Cantilever Beam Calculator helps you find beam loads, bend, slope, and deflection. A cantilever beam has one fixed end and one free end. Think of a diving board fixed to a pool deck. The free end bends when you add weight.
Our online Cantilever Beam Calculator makes these checks easy. Enter your beam size, load, and material data. The tool then works out key results. Use them to check a beam before you build or change it.
The right formula depends on the load type. Here, L means beam length, P means point load, and w means load per unit length. E is Young's modulus. I is the second moment of area.
Max bending moment = P × L
Max slope = P × L² / (2 × E × I)
Max deflection = P × L³ / (3 × E × I)
Let a be the load's distance from the fixed end.
Max bending moment = P × a
Free-end deflection = P × a² × (3L − a) / (6 × E × I)
For a uniform load across the full beam:
Max bending moment = w × L² / 2
Max slope = w × L³ / (6 × E × I)
Max deflection = w × L⁴ / (8 × E × I)
This case has the highest load at the fixed end. The load drops to zero at the free end.
Max bending moment = w₀ × L² / 6
Max slope = w₀ × L³ / (24 × E × I)
Max deflection = 11 × w₀ × L⁴ / (120 × E × I)
Choose a load type. Pick a tip load, a point load, a uniform load, or a triangular load.
Enter the beam length. Choose a unit, such as m, mm, ft, or in.
Enter the load. For a point load inside the beam, add its distance from the fixed end.
Add material and section data. Enter Young's modulus and the second moment of area.
Click Calculate. Review the support reaction, shear, moment, slope, and deflection. Add section data if you need bending stress.
Say a steel beam is 2 m long. A 1,000 N load acts at its free end. Use E = 200 GPa and I = 8 × 10⁻⁶ m⁴.
First, find the support reaction.
Reaction = P = 1,000 N
Next, find the max bending moment.
Moment = P × L = 1,000 × 2 = 2,000 N·m
Now, find the max slope.
Slope = P × L² / (2EI) = 0.00125 rad
Last, find the max deflection.
Deflection = P × L³ / (3EI) = 0.001667 m
That equals about 1.67 mm. These results assume a straight, elastic beam with small deflection.
A Cantilever Beam Calculator gives fast results for common beam loads. It helps with early design checks and basic learning. But a quick result cannot prove that a beam is safe. Check stress, buckling, support details, load limits, and local building codes before you rely on a design.
It finds support reactions, shear force, bending moment, slope, and beam deflection.
For a point load at the free end, use P × L³ / (3EI). For a full-length uniform load, use w × L⁴ / (8EI).
Yes, if the tool converts all inputs to one consistent unit system before it solves the formulas.
No. It uses an ideal beam model. A qualified engineer must check the full design and the rules that apply to the project.