Inductance Solenoid Calculator
Calculate the inductance of a solenoid from its number of turns, cross-sectional area, and length, using the permeability of free space.
Inductance Solenoid Calculator
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Formula: L = μ₀N²A/l
Worked example — 12.57 mH
Formula
L = μ₀N²A/l
Inductance of a solenoid. μ₀ = 4π×10⁻⁷ H/m.
Worked Examples
Example 1: 1000-turn solenoid
Problem:N=1000, A=0.001m², l=0.1m
Solution:L=4π×10⁻⁷×10⁶×0.001/0.1=12.57 mH
Result:12.57 mH
Frequently Asked Questions
What is inductance and why does it matter?
Inductance (L) measures a coil's ability to store energy in a magnetic field and oppose changes in current. It is measured in Henries (H). Inductors are key components in filters, transformers, and oscillators.
How do you calculate solenoid inductance?
Use L = μ₀N²A/l, where μ₀ = 4π×10⁻⁷ H/m is the permeability of free space, N is the number of turns, A is the cross-sectional area in m², and l is the solenoid length in meters.
What SI units are used for inductance calculation inputs?
Number of turns N is dimensionless, cross-sectional area A is in square metres (m²), solenoid length l is in metres (m), and the result L is in Henries (H). Practical values are often in millihenries (mH) or microhenries (μH).
How does adding an iron core affect inductance?
Inserting a ferromagnetic core multiplies inductance by the relative permeability μᵣ of the material: L_core = μᵣ × L_air. Iron has μᵣ ≈ 200–5000, so a 1 mH air-core solenoid becomes up to 5 H with an iron core.
Why does inductance grow with the square of the number of turns?
The field inside a solenoid is B = mu-zero x N x I / l, so it already scales with N. The flux linkage is then the flux through one turn multiplied by all N turns, which introduces a second factor of N. Since L is flux linkage per amp, L ends up proportional to N-squared. Doubling the turns while keeping the same length and cross-section therefore quadruples the inductance, not merely doubles it.
How much energy does a solenoid store, and why does that cause inductive kick?
Stored energy is U = 0.5 x L x I-squared, held in the magnetic field rather than in the wire. A 12.57 mH coil carrying 2 A stores 0.5 x 0.01257 x 4 = 0.0251 J, about 25 mJ. If the current is interrupted abruptly that energy has nowhere to go, and the coil generates a large reverse voltage spike. This is why relays and solenoid valves are fitted with a flyback diode across the coil.
What back-EMF appears when the current through a solenoid changes?
Faraday's law gives V = -L x dI/dt, so the induced voltage depends on the rate of change of current, not on the current itself. Collapsing 2 A to zero in 1 ms through a 12.57 mH coil produces about 0.01257 x 2/0.001 = 25 V. Shorten the switching time tenfold and the spike grows tenfold, which is what damages switch contacts and transistors in unprotected inductive circuits.
How does a coil's inductive reactance depend on frequency?
In an AC circuit the opposition an inductor presents is X_L = 2 x pi x f x L, measured in ohms. A 12.57 mH solenoid shows about 3.95 ohms at 50 Hz but roughly 790 ohms at 10 kHz. Because reactance rises linearly with frequency, inductors pass DC and low frequencies while blocking high ones - the basis of low-pass filters, chokes and power-supply smoothing.
How accurate is L = mu-zero N-squared A / l for a short, fat coil?
The formula assumes an ideal long solenoid, where length far exceeds diameter so the interior field is uniform and end effects are negligible. Real coils leak flux at the ends, so the true inductance is lower. Engineers apply a Nagaoka correction factor, always less than one and falling as the length-to-diameter ratio shrinks. Treat the calculator's value as an upper bound whenever the coil is not several diameters long.
What is the difference between self-inductance and mutual inductance?
Self-inductance L describes flux from a coil's own current linking back through itself, and is what Inductance Solenoid Calculator returns. Mutual inductance M describes flux from one coil linking a second, producing an EMF of M x dI/dt in the neighbour. The two are related by M = k x sqrt(L1 x L2), where the coupling coefficient k lies between 0 and 1. Transformers use a shared magnetic core to push k close to 1.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator · Editorial policy
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