Shaft Deflection Calculator

Inputs

Load case

How the shaft is supported and loaded — this selects the beam-bending formula.

Shaft diameter (d)

Diameter of the round solid shaft. The area moment of inertia is I = π·d⁴/64.

Span / length (L)

Span between supports (simply supported) or the free length from the fixed end (cantilever).

Load (F)

Single point load applied at mid-span (simply supported) or at the free end (cantilever).

Young's modulus (E)

Steel ≈ 200 GPa, aluminium ≈ 69 GPa.

GPa

Default result

Max deflection(δ)

0.6791mm

δ = F·L³ / (48·E·I)

Largest bending deflection (at mid-span or the free end).

Also computed

Max bending stress(σ)81.49MPa

σ = M·c/I with M = F·L/4 and c = d/2.

σ = M·c/I at the outer fibre. Compare with the allowable stress.

Area moment of inertia(I)1.917cm⁴

I = π·d⁴/64 for a round solid section.

Method notes 4 notes

Modelled as simply supported with a central point load: δ = F·L³ / (48·E·I), with M = F·L/4 the max bending moment.
Area moment of inertia of the round solid section is I = π·d⁴/64; max bending stress σ = M·c/I uses the outer fibre c = d/2.
Elastic, small-deflection beam theory (Euler–Bernoulli): a single point load on a prismatic, constant-section shaft, self-weight ignored.
Real shafts with steps, keyways, fillets, press-fits and bearing supports differ — check against both an allowable stress and a deflection limit.