Enter the number of turns, cross-sectional area, radius to the centerline, and permeability into the calculator to determine the toroid inductance.

Toroid Inductance Formula

The following formula is used to calculate the inductance of a toroid. 

L = ( u * N^2 * A ) / (2*pi*r)
  • Where L is the inductance (henries)
  • u is the permeability of the core
  • N is the number of turns
  • A is the cross-sectional area (cm^2)
  • r is the radius to the center line of the toroid (cm)

Toroid Definition

What is a toroid?

In general terms a toroid is a ssurface of revolution with a hole through the center.

In electrionics, the term toroid is used to describe transformers and inductors that use magentic cores in the toroid shape. These components are known as passive electronic components.

Toroid transformers and inductors are superior to square devices and have a better electrical performance.

Example Problem

How to calculate toroid inductance?

The following example problem will outline the steps required to solve for the inductance of an electrical toroid.

First, determine the total number of turns the toroid will have. In many cases toroids can have 100s of turns, but for this example to keep the calculation more simple the toroid has only 12 turns.

Next, determine the cross sectional area. For this example, the cross-sectional area is found to be 50 cm^2.

Next, determine the radius to the core centerline. Measuring the toroid in this example yields a radius of 6 cm.

Next, determine the permiability of the material. This is a property that is determined by the material the toroid is made of. In this case, the permeabitlity is found to be .45.

Finally, calculate the inductance of the toroid using the formul above:

L = ( u * N^2 * A ) / (2*pi*r)

L = ( .45 * 12^2 * 50 ) / (2*3.14159*6)

L = 85.943 henries.