# Toroid Inductor Formulas and Calculator

Toroids may be wound on a circular form as shown in the figure below:

The inductance for such a toroid can be calculated from the equation below:

where N is the number of turns, R is the mean radius of the form as shown in the figure (in cm), and a is the radius of the windings on the form as shown in the figure (in cm).

Another formula for the inductance of a circular cross section toroid is shown below:

where N is the number of turns, D is the mean diameter of the form as shown in the figure (in inches), and d is the diameter of the windings as shown in the figure (in inches).

They may also be wound on a rectangular form as shown in the figure below:

The inductance for a rectangular cross section toroid can be found from the following equation (Terman, Frederick E., __Radio Engineers Handbook__, McGraw-Hill, New York, 1943, p58.):

where N is the number of turns, h is the height of the winding (in inches), d_{1} is the inner diameter (in inches), and d_{2} is the outer diameter (in inches).

A second formula for a rectangular form toroid is shown below:

where N is the number of turns, h is the height of the winding (in cm), r_{1} is the inner radius (in cm), and r_{2} is the outer radius (in cm).

The calculators below can be used to determine the proper parameters for either a circular or square cross section Toroid inductor. Credit for the initial Javascript code used in the calculator is given to Ray Allen who has a number of similar useful calculators on his website, Pulsed Power Portal.