Beam Deflection Calculator

Inputs

Load case

Support and load condition. Uniform-load options use the total load over the span.

Span / length (L)

Support span or cantilever free length.

Load (P or W)

Point load P, or total uniformly distributed load W over the full span.

Young's modulus (E)

Steel ≈ 200 GPa, aluminum ≈ 69 GPa.

GPa

Area moment of inertia (I)

Second moment of area about the bending axis.

cm⁴

Section modulus (S)

Section modulus about the bending axis, used for sigma = M/S.

cm³

Default result

Max deflection(delta)

0.1042mm

Pass

delta = P*L^3/(48*E*I)

Elastic small-deflection beam result.

Also computed

Max bending moment(M)250N·m

M = P*L/4

Reported as N*m or lbf*ft; formula uses N*mm internally.

Bending stress(sigma)25MPa

sigma = M/S using section modulus about the bending axis.

sigma = M/S.

Span / deflection(L/delta)9,600

Higher is stiffer; compare to your deflection limit.

Method notes 3 notes

Modelled as simply supported beam with a central point load: delta = P*L^3/(48*E*I), with M = P*L/4 for the maximum bending moment.
Uniform-load cases treat the entered load as the total load W over the span. If you have line load w, enter W = w*L.
Euler-Bernoulli small-deflection theory for prismatic members. Shear deflection, local stress concentrations, holes, tapered sections, self-weight unless entered as load, and dynamic effects are not included.