How to use this calculator

Enter the length from the fixed support to the free tip, the material stiffness E, the second moment of area I, and the loads. The end point load and the uniform load are solved as separate cases. The charts measure x from the fixed end, where the bending moment and shear are largest.

Formulas

For a prismatic cantilever of length L, fixed at x = 0 and free at x = L:

Point load P at the free end · tip deflection and slopeδ_max = PL³3 EI θ = PL²2 EI

Point load P · moment and reaction at the fixed endM_max = PL R = P

Uniform load w · tip deflection and slopeδ_max = wL⁴8 EI θ = wL³6 EI

Uniform load w · moment and reaction at the fixed endM_max = wL²2 R = wL

Deflection curves, x from the fixed endδ_P(x) = Px² (3L − x)6 EI δ_w(x) = wx² (6L² − 4Lx + x²)24 EI

The moment is hogging (tension on top) along the whole length: M(x) = −P(L − x) for the end load and −w(L − x)²/2 for the uniform load. The table reports its magnitude at the support.

Worked example

Steel cantilever, SI units (the calculator’s default values)

L = 1.5 m, E = 200 GPa, I = 800 cm⁴ = 8 × 10⁻⁶ m⁴, so EI = 1.6 × 10⁶ N·m². P = 1000 N, w = 500 N/m.

End load: δ_max = 1000 × 1.5³ / (3 × 1.6 × 10⁶) = 7.031 × 10⁻⁴ m = 0.703 mm; θ = 1000 × 1.5² / (2 × 1.6 × 10⁶) = 7.03 × 10⁻⁴ rad; M_max = 1000 × 1.5 = 1,500 N·m.
Uniform load: δ_max = 500 × 1.5⁴ / (8 × 1.6 × 10⁶) = 1.978 × 10⁻⁴ m = 0.198 mm; M_max = 500 × 1.5² / 2 = 562.5 N·m; R = 500 × 1.5 = 750 N.

The same 1000 N load on a 1.5 m simply supported span would deflect only 1/16 as much (PL³/48EI instead of PL³/3EI). Cantilevers are far more flexible for their length.

Combining loads

Both cases peak at the same places: deflection and slope at the free end, moment and reaction at the fixed end. Under linear elastic behavior you can add the two columns directly to get the result for both loads acting together.

Assumptions and limits

The fixed end is perfectly rigid: no rotation or settlement. Real connections rotate a little, which adds deflection.
Prismatic beam with constant E and I.
Linear elastic material, small deflections, shear deformation neglected (Euler–Bernoulli theory).
Self-weight is not included unless you add it to w.
No stress, buckling, fatigue or code check is performed.

Frequently asked questions

What deflection limit applies to a cantilever?

Limits are usually written in terms of span. A common approach is to treat a cantilever as a beam of twice its length, so an L/360 floor limit becomes 2L/360, or L/180 of the cantilever length. Check the standard your project uses.

Where is the bending stress highest?

At the fixed end, where the moment is largest. Stress there is σ = M_max c / I. Get c and I from the moment of inertia calculator.

Why is the moment shown as negative on the chart?

The chart uses the usual convention that sagging moment (tension on the bottom) is positive. A cantilever bends the other way, so its moment is hogging and plots below the axis.

Can I model a load partway along the cantilever?

Not in this version. A point load at distance a from the fixed end gives a tip deflection of P a² (3L − a) / 6EI, which you can compute by hand.

For education and preliminary checks only. Have a qualified engineer verify any design before it is built.