Solenoid Inductance Calculator
Calculate solenoid inductance from number of turns, coil area, length, and core permeability using L = mu*N^2*A/l.
What Is Solenoid Inductance?
A solenoid is a coil of wire that stores magnetic energy when current flows. Its inductance depends on the number of turns, cross-sectional area, coil length, and the permeability of the core material.
Solenoid Inductance Formula
$$L = \frac{\mu_0 \mu_r N^2 A}{l}$$\(N\) is the number of turns, \(A\) is the cross-sectional area, \(l\) is the coil length, and \(\mu = \mu_0 \mu_r\) is absolute permeability. Inductance grows with the square of turns and linearly with area and permeability.
Design Considerations
More turns increase inductance but also raise resistance. A ferromagnetic core (\(\mu_r \gg 1\)) greatly boosts inductance compared to an air-core coil. Coil length in the denominator means longer solenoids have lower inductance.
Related tools: Inductor Calculator and Helical Coil Calculator.
Frequently Asked Questions
When is the solenoid formula accurate?
It applies to long, tightly wound coils where the length is much greater than the diameter and the field is fairly uniform inside.
How does core material affect inductance?
Ferromagnetic cores multiply inductance by \(\mu_r\). Iron powder and ferrite cores are common choices for RF and power applications.
Why does inductance scale with N squared?
Each turn contributes to the magnetic flux, and flux linkage depends on both the number of turns and the flux per turn, giving an \(N^2\) dependence.
What units should I use?
Use SI units internally: area in square meters, length in meters, and inductance in henries. This calculator accepts common metric area and length units.
Does wire gauge affect inductance?
Wire gauge mainly affects resistance and packing density. The ideal formula assumes a uniform current sheet; real coils differ slightly from the ideal model.
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