Polar Moment of Inertia, J, for Circular Cross-sections

The Polar Moment of Inertia is a geometric property of a cross section. The units of J are mm⁴ or in⁴.

Cross-section	Polar Moment of Inertia, J	Cross-section
Solid Circular Shaft	Jsolid = pR4 2
Hollow (Thick-walled) Shaft	Jthick = p(Ro4 Ri4) 2
Thin-Walled Shaft, t<<R	Jthin = 2pt(Rave)3 ; Rave = Ro + Ri 2