Solenoid Inductance Calculator

Created by Miłosz Panfil, PhD
Reviewed by Bogna Szyk and Adena Benn
Last updated: Jan 30, 2023

The solenoid inductance calculator finds the self-inductance of a solenoid. Reading the text below, you will find out how a solenoid works in electric circuits and what its inductance is.

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 that resist a change in the current.

A change in the 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; and
  • 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 the 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 then computes the area, assuming a circular cross-section.

💡 You might also be interested in the helical coil calculator.

FAQ

What is a solenoid?

A solenoid is an electrical device composed of a round metal coil. These devices have a two-way functionality. A magnetic field is generated when an electrical current flows through the coil. On the contrary, an electric current is induced in the coil in the presence of a changing magnetic field. This is known as electromagnetic induction.

We use these devices to control electric circuits such as valve actuators, engine starters, and locking mechanisms, among other applications.

What's the formula for solenoid inductance?

The formula for solenoid inductance is:

L = µ_0 × N² × A / l

where:

  • L – Solenoid's inductance;
  • µ_0 – Vacuum permeability, with a value of 1.25664 × 10-6 T·m/A for air;
  • N – Number of turns;
  • A – Cross-sectional area; and
  • l – Solenoid's length.

What's the inductance of a solenoid with N=10turns/cm, D=8cm, and l=1.5m?

The inductance is L = 9475 µH. To get this value:

  1. Use the solenoid inductance formula:

    L = µ_0 × N² × A / l

    where:

    • µ_0 – Vacuum permeability, 1.25664 × 10-6 T·m/A;

    • N – Number of turns;

    • A – Cross-sectional area; and

    • l – Length.

  2. Calculate total number of turns:

    N = 10 turns/cm × 1.5 m × 100 cm/m

    N = 1500 turns

  3. Continue to replace all the values in the solenoid's inductance formula:

    L = µ_0 × (1500 turns)² × π(4 cm)² / 1.5 m

    L = 9475 µH

What is the unit of measurement for a solenoid’s inductance?

In the SI system, we measure a solenoid's inductance in henries (H), with 1 H = 1 Wb/A, where the magnetic flux is expressed in weber and the current in ampere. A solenoid's inductance typically ranges from 1 µH (10-6 H, micro) to 20 H.

Miłosz Panfil, PhD
Number of turns
Radius
m
Cross-sectional area
Length
m
Inductance
μH
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