Utilize our free Polar Moment of Inertia Calculator to determine the torsional rigidity of circular shafts quickly and accurately. This essential tool helps mechanical engineers and designers assess a shaft's resistance to twisting, crucial for preventing failure under torsional loads. Calculate for both solid and hollow circular sections with ease.
Formula:
Formulas for Polar Moment of Inertia
The polar moment of inertia (J), also known as the second polar moment of area, quantifies an object's resistance to twisting or torsion. It is a critical parameter in the design of shafts and other components subjected to torsional loads.
- For a Solid Circular Shaft:
- For a Hollow Circular Shaft:
J = (π/32) * D4
J = (π/32) * (Do4 - Di4)
Where:
J= Polar Moment of Inertia (e.g., mm4, in4)π= Pi (approximately 3.14159)D= Diameter of the solid circular shaftDo= Outer diameter of the hollow circular shaftDi= Inner diameter of the hollow circular shaft