Cantilever Beam Calculator: Deflection, Stress, and Bending Moment

Cantilever Beam Formulas

For a Point Load (P) at the Free End:

• Maximum Deflection (δ) = (P × L³) / (3 × E × I)
• Maximum Bending Moment (M) = P × L

For a Uniformly Distributed Load (w) along the entire length:

• Maximum Deflection (δ) = (w × L⁴) / (8 × E × I)
• Maximum Bending Moment (M) = (w × L²) / 2

Where:

• P = Point Load (N or lbs)
• w = Uniformly Distributed Load (N/m or lbs/ft)
• L = Beam Length (m or ft)
• E = Modulus of Elasticity (Pa or psi)
• I = Area Moment of Inertia (m⁴ or in⁴)
• δ = Maximum Deflection (m or ft)
• M = Maximum Bending Moment (N·m or ft·lbs)