A solenoid is a coil of wire. When electric current passes through a solenoid, it generates a magnetic field. The strength of the magnetic field depends on how closely spaced the turns in the coil are, the amount of current passing through it, and the magnetic properties of the core material that the coil is wrapped around. Solenoids are used for a variety of purposes, including certain kinds of motors and automatic switching systems. Often solenoids are used in circuits as a kind of component called an inductor.
Divide the number of turns in the solenoid by its length in meters. This value is the "turn density," the number of turns per meter.
Multiply the relative permeability of the core by the magnetic constant, which is about 1.257 x 10^-6. The magnetic constant is the degree to which vacuum responds to a magnetic field. Relative permeability indicates how much a material amplifies the magnetic constant. The relative permeability of air is about 1, and the relative permeability of magnetic iron is about 200. The resulting calculation is the magnetic permeability of the core.
Multiply the turn density, permeability of the core and the current through the solenoid in amperes. The result is the strength of the magnetic field in the solenoid in units of Tesla.
Multiply the coil radius in meters by pi (3.14159265) to get the cross-sectional area of the solenoid.
Multiply the cross sectional area by the square of the number of turns in the solenoid and the magnetic permeability of the core, which you calculated above.
Divide the result by the length of the solenoid in centimeters. The result is the inductance of the solenoid in units of Henries.