# How To Calculate Toroidal Transformers

A toroidal transformer is a transformer shaped like a doughnut. It has a round iron core with a coil of insulated wire wrapped around it. The iron core with the coil of wire is also called the "winding." Once powered, the winding generates a magnetic field and stores energy. The amount of energy is measured in units of inductance. As with most transformers, toroidal transformers have both a primary and secondary inductive winding, which is used to step down or step up the input voltage applied to the primary winding.

### Step 1

Determine the number of turns in the primary winding of the transformer. Call this value "N." Refer to the transformer specifications. As an example, assume N is 300 turns.

### Step 2

Find the radius of the transformer. Refer to transformer specifications. As an example, assume radius is 0.030 meters.

### Step 3

Calculate the area using the formula A = π * r² where π is 3.1415. Continuing with the example:

A = 3.1415 * (0.030)(0.030) = 0.0028 square meters

### Step 4

Calculate the inductance of the primary winding using the formula L = (μ0 **N²** A) / 2 **π** r, where μ0 is the relative permeability of space with a value of 4 **π** 10^-7 T m/A. Continuing with the example:

μ0 = 4 **π** 10^-7 = 4 **3.1415** 10^-7 = 12.56 * 10^-7.

L = [(12.56 * 10^-7)(300^2)(0.0028)] / [(2)(3.1415)(0.030)] = 0.000316 / 0.188 = 0.00168 henries or 1.68 millihenries.

### Cite This Article

#### MLA

Chestnut, Dwight. "How To Calculate Toroidal Transformers" *sciencing.com*, https://www.sciencing.com/how-8655759-calculate-toroidal-transformers/. 27 June 2011.

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Chestnut, Dwight. (2011, June 27). How To Calculate Toroidal Transformers. *sciencing.com*. Retrieved from https://www.sciencing.com/how-8655759-calculate-toroidal-transformers/

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Chestnut, Dwight. How To Calculate Toroidal Transformers last modified March 24, 2022. https://www.sciencing.com/how-8655759-calculate-toroidal-transformers/