# Coil Inductance

Calculate the Inductance of a Coil

## Coil Inductance Calculator

### Inputs

Number of Turns
N
Loop Diameter
D
Wire Diameter
d
Relative Permeability
μR

### Outputs

Inductance:

#### Introduction

A coil inductance formula is based upon the basic loop inductance. Inductance is the ability to store energy in a magnetic field, and coils are a very common way to create inductance. Many magnetic field coupling circuits, like chokes and transformers take advantage of a coil’s magnetic storage properties.

#### Wire Loop Inductance Description

The inductance of a wire loop is a common example of a circuit with inductance. The variables used in this tool are the diameter of the wire conductor and the diameter of the wire loop, number of turns, and the relative permeability. Coil inductance is related to individual loop inductance by the square of the number of turns.

#### Coil Inductance Model.

The inductance of the wire a coil is:

L_{loop}\approx N^{2}\mu _{o}\mu _{r}\left ( \frac{D}{2} \right )\cdot \left ( \ln\left ( \frac{8\cdot D}{d} \right )-2 \right )