🔩 Polar Moment of Inertia Calculator
Calculate the polar moment of inertia for a solid or hollow circular shaft cross-section, used in torsion and shaft design calculations.
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What polar moment of inertia is
The polar moment of inertia (J) describes a circular shaft’s resistance to twisting (torsion). It is a purely geometric property based on the shaft’s cross-sectional shape and is used to calculate torsional stiffness and shear stress under torque.
The formula
For a solid circular shaft, J = (π/32) × D⁴, where D is the outer diameter. For a hollow circular shaft, J = (π/32) × (Do⁴ – Di⁴), where Do and Di are the outer and inner diameters.
These are standard mechanics of materials formulas for circular cross-sections; non-circular shafts use different, more complex formulas.
Last reviewed August 2026