# Solenoid Inductance Calculator

By Miłosz Panfil, PhD
Last updated: Aug 19, 2021

Solenoid Inductance Calculator finds the self-inductance of a solenoid. Reading the text below you will find out how does a solenoid work in electric circuits and what is its inductance.

If you want to learn about the effective resistance of a solenoid, we recommend checking our inductive reactance calculator.

## How does a solenoid work

Solenoids, and coils in general, are essential elements of electric circuits (try the RLC Circuit Calculator to see an inductive element in action). Their characteristic is an inductance `L`, and they act as inertial elements: coils resist a change in the current. A change in a current flowing through a coil results in a self-induced potential difference. The inductance `L` sets the ratio between the potential and the rate of change of the current

`V = - L * dI/dt`

The minus shows the resistive nature of the inductance; the potential difference is opposing the change in the current. The magnetic field inside of the solenoid causes this behavior. If we change the current, we are changing this magnetic field. In turn, it induces a potential difference in the solenoid. To learn more about the magnetic field inside the solenoid and the phenomena of inductance, check the Solenoid Magnetic Field Calculator and Faraday's Law Calculator.

## Inductance of a solenoid

A solenoid is a long, tightly wound coil. We can describe a solenoid using three parameters:

• number of turns `N`,
• length `l`,
• area of the cross-section `A`.

The inductance of solenoid follows then from the following equation

`L = µ₀ * N² * A/l`,

with the vacuum permeability `µ₀ = 1.25664 * 10^-6 T*m/A`. Using our Solenoid Inductance calculator you can easily find inductance of a solenoid for different configurations. Instead of specifying the area of the cross-section `A`, you can set the radius `r`. The calculator computes then the area assuming a circular cross-section.

Miłosz Panfil, PhD
Number of turns
m
Cross section area
Length
m
Inductance
μH
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