The formula and equation for the area moment of inertia of a hollow or solid cylinder, also known as the polar moment of inertia (second moment of area) of a solid or hollow cylinder, is below. The formula is the same for movement about its axis or about its end or diameter:

, where:

I = Area Moment of Inertia of Cylinder (m^4) (expressed as j or I)

r_{o} = Outer Radius (m)

, where:

I = Area Moment of Inertia about the y-axis (m^4)

z = Distance from the y-axis (m)

A = Elemental Area (m^2)

, where:

I = Area Moment of Inertia of Circle (m^4)

r = Radius (m)

, where:

I = Area Moment of Inertia about x-axis (m^4)

b = Length about x-axis (m)

y = Length about y-axis (m)

The Jourawsky Formula for shear stress (formula di jourawski), as derived from the shear stress formula, has many real world examples:

, where:

= Shear Stress (Pa)

V = Shear Force (N)

Q = First Moment of Area (m^3)

I = Area Moment of Inertia (m^4)

t = Thickness (m)