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 length^4. 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