This cantilever beam calculator finds the deflection, slope, and bending moment of a beam fixed at one end and free at the other. Enter the load, span, and beam stiffness (EI) above for point, distributed, or moment loading.
Key formulas
Point load P at the free end (length L):
Max deflection δ = P L³ ÷ (3 E I) Max slope θ = P L² ÷ (2 E I) Max moment M = P L (at the fixed end)
Uniformly distributed load w (per unit length):
δ = w L&sup4; ÷ (8 E I) M = w L² ÷ 2
- E — modulus of elasticity, I — moment of inertia of the section
Example calculation
Point load P = 500 lb, length L = 72 in, steel section I = 100 in⁴, E = 29,000,000 psi:
- δ = 500 × 72³ ÷ (3 × 29,000,000 × 100) = 0.021 in
- M = 500 × 72 = 36,000 lb·in (3,000 lb·ft) at the wall
These are elastic estimates. For final structural design, confirm with a licensed engineer and your governing code.
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Frequently Asked Questions
How do you calculate cantilever beam deflection?
For a point load at the free end, maximum deflection equals the load times length cubed, divided by three times the modulus times the moment of inertia (PL^3 / 3EI).
Where is the maximum moment in a cantilever?
At the fixed (wall) end. For a point load at the free end it equals load times length; for a uniform load it is w times length squared divided by two.
What load cases does this cover?
Point load at the free end, a uniformly distributed load, and an applied moment — the most common cantilever cases in structural work.