Polar Moment of Inertia Calculator

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Choose the cross-section that matches your shaft or beam. The polar moment of inertia formula changes with the shape.
Outer diameter of the solid circular cross-section.
mm
Polar moment of inertia (J)
613,592.3152

Resistance of the cross-section to torsion (twisting).

Unitmm⁴
Polar section modulus (Zp)24,543.6926
Unitmm³
Outer radius (R or c)25
J (polar moment)613,592.3152
Zp (section modulus)24,543.6926

Solid circular cross-section: J = 613592.32 mm⁴, Zp = 24543.69 mm³.

  • J = 613592.32 mm⁴: a larger value means the section resists twisting more strongly.
  • Zp = 24543.69 mm³: divide the applied torque (T) by Zp to get the maximum shear stress: τ = T / Zp.
  • Hollow circular sections achieve a higher J per unit area than solid circles, making them efficient for torsion-critical shafts.

Next stepUse J with the torsion formula τ = T × c / J (or equivalently T / Zp) to check whether the shear stress stays below the material's allowable limit.

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