This calculator is used to calculate the polar moment of inertia (J) and polar section modulus (Zp) for common shapes such as circular, rectangular, and hollow circular sections. The polar moment of inertia is a measure of a cross-section's resistance to torsion, while the polar section modulus is a measure of a beam's resistance to torsion.

To use the calculator, select the shape type from the dropdown menu and enter the appropriate dimensions for the shape. The calculator will then calculate and display the polar moment of inertia and polar section modulus based on the entered dimensions.

For circular shapes, the polar moment of inertia is calculated using the formula J = (π/32) * D^4, where D is the outer diameter of the circle. The polar section modulus is calculated using the formula Zp = (π/16) * D^3.

For rectangular shapes, the polar moment of inertia is calculated using the formula J = (1/12) * W * H^3, where W is the width and H is the height of the rectangle. The polar section modulus is calculated using the formula Zp = (W * H^2) / 4.

For hollow circular shapes, the polar moment of inertia is calculated using the formula J = (π/32) * (D^4 - d^4), where D is the outer diameter and d is the inner diameter of the hollow circle. The polar section modulus is calculated using the formula Zp = (π/16) * (D^4 - d^4) / D.