# Rectangle Loop Inductance Calculator

## This calculator helps you compute the inductance of a rectangle loop.

### Output

### Overview

This tool is designed to calculate the inductance of a square loop of wire given its dimensions (width, height and diameter of the wire used). To use this calculator, just enter the required values and press the "calculate" button. You can specify which unit of measurement to use for the width, height and wire diameter. Most square loops have air as substrate so a relative permeability of 1 is often used.

### Equations

\[\begin{align*}

L_{rec}=\frac{\mu _{o}\mu _{r}}{\pi }\left [ -2\left ( W+H \right )+2\sqrt{H^{2}+W^{2}}-H\ln \left ( \frac{H+\sqrt{H^{2}+W^{2}}}{W} \right )\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ -W\ln \left ( \frac{W+\sqrt{H^{2}+W^{2}}}{H} \right)+H \ln \left ( \frac{2H}{\frac{d}{2}} \right )+W \ln \left ( \frac{2W}{\frac{d}{2}} \right )\right]

\end{align*}\]

$$W$$ = width of the loop

$$H$$ = height of the loop

$$d$$ = diameter of the wire

$$\mu_{r}$$ = relative permeability

$$\mu_{0}$$ = permeability of free space = 4π x 10-7

### Applications

Loop inductors find themselves in many applications. Loop antennas are fairly common and are often used as TV antennas mainly due to their low price. Although they can also be used as transmit antennas, loop antennas have low radiation resistance and high reactance which makes it difficult to match them with the impedance of transmitters.

Loop inductors are also found inside metal detectors. When a metallic object comes in contact with the magnetic field generated by the loop inductor, a current is induced. A more modern use of loop inductors is in hearing aids where one or more loops are used and are placed near areas where a hearing aid user would be.

2 CommentsHow to calculate if the shape is cut by 2 mm in the middle at height 20 mm?

The value of number of turns is missing in the formula. There is a N^2 term . For the single loop of wire this formula holds good though 1^2 = 1