ToolHub

Polar Moment of Inertia Calculator

Calculate the polar moment of inertia for different cross-sectional shapes including circular, annular, and rectangular sections. This tool helps analyze a structure’s resistance to torsion and rotational deformation in both SI and imperial units.

Formulas Used

  • Circular Shaft: J = (π r⁴) / 2
  • Annular Section: J = (π (rₒ⁴ − rᵢ⁴)) / 2
  • Rectangular Section: J = (w h (w² + h²)) / 12
  • Unit Conversion: 1 in = 0.0254 m

Use Cases

  • - Shaft and torsion analysis in mechanical engineering
  • - Structural design for beams and rotating components
  • - Mechanical system optimization and safety analysis
  • - Engineering assignments and lab calculations
  • - Stress and deformation analysis under torque

Calculation History