# First principle derivation for torsional constant

For torsional constant, analytical formulas are available for some standard steel sections as shown in this wiki page.

But what about arbitrary shapes? How can I obtain the formulas for torsional constants? If no such formulas are available, are there any first principles that I can use to deduce the approximate formulas or FEM calculation for torsional constant?

Note: a related question about the FEM formulation of torsional constant is being asked here.