Cantilever Beam Calculator
Estimate fixed-end shear, moment, tip slope, and tip deflection for a cantilever beam with an end point load and/or a full-span uniformly distributed load (UDL).
V = P + wL
M = PL + wL²/2
θ = PL²/(2EI) + wL³/(6EI)
δ = PL³/(3EI) + wL⁴/(8EI)
What is a cantilever beam?
A cantilever beam is fixed at one end and free at the other. Because one end is restrained against rotation and translation, the fixed support carries the highest internal forces. This beam type appears in balconies, sign brackets, aircraft wings, crane booms, and many machine components.
In practical design, engineers check several items: maximum shear force, maximum bending moment at the fixed end, acceptable tip deflection, and allowable stress. This calculator gives fast first-pass values for those checks.
How this cantilever calculator works
Load cases included
- Point load at free end (P): concentrated load acting downward at the tip.
- Full-span UDL (w): evenly distributed load along the beam length.
- Combined loading: both loads applied together using linear elastic superposition.
Outputs provided
- Fixed-end reaction shear, V (kN)
- Fixed-end reaction moment, M (kN·m)
- Tip slope, θ (radians and degrees)
- Tip deflection, δ (mm)
- Maximum bending stress, σ = M/Z (MPa), if section modulus is entered
Step-by-step usage
- Enter beam length L in meters.
- Enter material stiffness E in GPa.
- Enter section stiffness I in cm⁴.
- Enter tip point load P in kN (or 0).
- Enter UDL w in kN/m (or 0).
- Optionally enter section modulus Z in cm³ for stress.
- Click Calculate.
Worked example
Suppose a steel cantilever has length 2 m, E = 200 GPa, I = 5000 cm⁴, end load P = 5 kN, and UDL w = 1.5 kN/m. The tool computes the support shear and moment, then determines slope and deflection from standard beam equations. Because deflection scales with L³ and L⁴, even modest length increases can cause much larger displacement.
Engineering notes and assumptions
Assumptions behind the formulas
- Linear elastic behavior (Hooke’s law).
- Small deflection theory (Euler-Bernoulli beam).
- Constant E and I along the beam.
- Loads are static and applied in one principal bending direction.
When to use a more advanced model
- Large deflections or nonlinear material response.
- Variable cross-section or variable stiffness members.
- Dynamic, impact, fatigue, or thermal loading.
- Complex boundary conditions or partial-span loads.
Unit consistency tips
Most beam mistakes come from unit mismatch. This page handles unit conversion internally: GPa to Pa, cm⁴ to m⁴, and kN to N. Still, ensure your input values are realistic for your chosen section and material.
Quick FAQ
Is this suitable for final structural sign-off?
No. Use it for conceptual sizing and checks. Final design should be reviewed by a qualified engineer under applicable codes.
What if I only have one load type?
Set the other load to zero. The calculator will automatically reduce to the correct single-load formulas.
Why is my deflection high?
Deflection is very sensitive to span and stiffness. Increasing section inertia I, shortening L, or reducing load typically has the biggest impact.