The Torsion Constant, also known as the Polar Moment of Inertia (or Second Polar Moment of Area) is a geometric property of an object representing its resistance to twisting in response to an applied torque.

The units are length4. The torsion constant is the second moment of area calculated along the z axis. The torsion constant is dependant on the shape - see Torsion Constant for Common Shapes.

Consider the cylinder below where the x axis and y axis are a cross section of the cylinder making a circle and z axis is going through the centre of the cylinder:

The torsion constant is calculated by adding the Second Moment of Area about the x and y axis as follows.

For a circle the second moment of area in both the x and y axis is given by:

Hence the torsion constant of a cylinder is:

The torsion constant along with the Shear Modulus can be used to calculate the angle of rotation given a torque applied at a distance from a fixed point.

See also: Crossarm parameter: Torsion Constant