Inductance Calculator
Calculate the inductance of a solenoid.
Solenoid Inductance Formula
$$L = \mu_0 \mu_r \frac{N^2 A}{l}$$
Where $\mu_0$ (permeability of free space) is $4\pi \times 10^{-7} \, \text{H/m}$.
Input Parameters
Calculated Inductance
Enter values and click ‘Calculate’ to see the result.
What is Inductance?
Inductance ($L$) is a property of an electric conductor or circuit that causes an electromotive force (EMF) to be generated in the conductor when the current flow through it changes. In simple terms, it’s the electrical inertia that opposes changes in current. The unit of inductance is the Henry ($\text{H}$).
This tool specifically calculates the inductance of a long solenoid, which is a coil of wire commonly used in electrical engineering.
Usage Guide
- Number of Turns ($N$): Enter the total number of times the wire is wrapped around the coil form. This must be an integer (e.g., $100$).
- Cross-sectional Area ($A$): Enter the area of the coil’s inner loop in square meters ($\text{m}^2$). If you have the radius ($r$), use the formula $A = \pi r^2$.
- Length of Coil ($l$): Enter the physical length of the solenoid in meters ($\text{m}$). The calculation assumes $l$ is much greater than the radius.
- Relative Permeability ($\mu_r$): Enter the relative permeability of the core material inside the coil. For air or vacuum, use $\mu_r = 1$. For materials like iron or ferrite, $\mu_r$ will be much higher.
- Calculate: Click the ‘Calculate Inductance ($L$)’ button. The result for $L$ in Henries will be displayed below, formatted to two decimal places.
Key Constants and Terms
- $\mathbf{L}$: Inductance, measured in Henries ($\text{H}$).
- $\mathbf{\mu_0}$: Permeability of Free Space. $$\mu_0 = 4\pi \times 10^{-7} \, \frac{\text{H}}{\text{m}}$$
- $\mathbf{\mu_r}$: Relative Permeability (unitless). This is a factor by which the permeability of the core material increases compared to a vacuum.
