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), d1 is the inner diameter (in inches), and d2 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), r1 is the inner radius (in cm), and r2 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.