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Solenoid Inductance Calculator

Find the inductance of a coil or solenoid.

How it is calculated

The inductance of a long, tightly wound solenoid is L = μ0 · μr · N² · A ÷ l. N is the number of turns, A the cross-section area of the core and l the winding length. The tool takes A in cm² and l in cm and converts them to m² and m, uses μ0 = 4π × 10⁻⁷ H/m, and treats μr (relative permeability of the core) as 1 if it is left empty or is not positive. Turns, area and length must be above zero. The result is shown in microhenries (µH) and millihenries (mH). Inductance grows with the square of the turns. The formula assumes the length is much larger than the diameter.

Worked example

A coil has 200 turns, a cross-section of 2 cm², a length of 10 cm and an air core (μr = 1). In SI units the area is 2×10⁻⁴ m² and the length is 0.1 m. Then L = 4π×10⁻⁷ × 200² × 2×10⁻⁴ ÷ 0.1, which is about 1.0053×10⁻⁴ H. That is 100.53 µH, or 0.1005 mH.

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Common mistakes

  • Entering area in mm² or m² and length in mm or m. The tool expects cm² and cm.
  • Using the wire length instead of the winding length along the axis.
  • Entering the core diameter where the cross-section area is needed. Area is π × (d ÷ 2)².
  • Doubling the turns and expecting double the inductance. Doubling N multiplies L by four.
  • Putting a ferrite or iron μr on a short, fat coil. The result is an ideal estimate and assumes the field is mostly inside a long core.

About this calculator

This calculator finds the inductance of a solenoid (coil): L = μ0 · μr · N² · A / l, where μ0 is the permeability of free space, μr is the relative permeability of the core material, N is the number of turns, A is the cross-sectional area, and l is the coil's length. Inductance grows with the square of the turn count, so doubling the turns quadruples it, and a ferromagnetic core (high μr) can boost inductance dramatically over an air core.

Electronics engineers and hobbyists use it when winding custom coils or inductors for filters, transformers, chokes, and RF circuits, to predict how a design's turns, geometry, and core material will affect its inductance before building it. Enter the turns, area, length, and core permeability to get the inductance.

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