Polar Moment of Inertia

Calculate the polar second moment of area (J) for circular and rectangular sections.

Section Dimensions

Section Shape

Units

Outer Diameter (D)

Calculation Results

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Overview

The polar moment of inertia (J) is a quantity used to describe the resistance to torsional deformation (twisting) in cylindrical objects.

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Pro Tips

J is measured in length to the fourth power (e.g., m⁴, mm⁴, in⁴).
For a solid circle, J = πD⁴ / 32.
Increasing the diameter of a shaft significantly increases its torsional stiffness because of the power of 4.

Fun Facts

"Torsional stress is highest at the outer surface of a shaft and zero at the center."
"Hollow shafts are very efficient because they remove material from the center where it contributes least to torsional resistance."
"The perpendicular axis theorem states J = Ix + Iy."

Formula: J = π(D⁴ - d⁴)/32

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