Calculate the resistance of a cylindrical object to torsional deformation.
Last updated: March 2026 | By ForgeCalc Engineering
The polar moment of inertia, denoted as J, is a geometric property that quantifies how much a cross-section resists torsion (twisting) when a torque is applied. It is analogous to the area moment of inertia, which measures resistance to bending.
For circular shafts, the polar moment of inertia depends solely on the diameter. In mechanical engineering, it is a critical parameter for designing drive shafts, axles, and any component that transmits power through rotation.
Calculating J for a hollow drive shaft:
Calculation: J = (π · (100⁴ - 80⁴)) / 32
Final Answer: The polar moment of inertia is 5.7962e+6 mm⁴.
J is the polar moment of inertia (resistance to torsion), while I is the area moment of inertia (resistance to bending). For a circle, J = 2 × I.
It determines the shear stress in the shaft. Higher J values mean lower shear stress for the same applied torque.
No. For non-circular sections (like squares or rectangles), the calculation is much more complex and J is not simply (Ix + Iy).
Divide the mm⁴ value by 10¹² (1,000,000,000,000).
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