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Solenoid Inductance Calculator

Find the inductance of a solenoid coil.

How it is calculated

The tool applies the long-solenoid formula L = μ₀ · N² · A ÷ l. Here μ₀ = 4π × 10−7 H/m (air or vacuum core), N is the number of turns, A is the cross-sectional area of the coil in m² and l is the coil length in metres. The turn count is rounded to the nearest whole number and must be at least 1; area and length must be greater than zero. The answer is given in millihenries with four decimals and in henries with six. There is no core permeability input, so a ferrite or iron core would multiply the real value by the core's relative permeability. The formula assumes a coil much longer than its diameter and ignores end effects.

Worked example

A coil of 500 turns has a core 2 cm in diameter, so A = π × 0.01² ≈ 0.000314 m², and it is 0.05 m (5 cm) long. First N² = 250,000. Then μ₀ × N² = 1.2566 × 10−6 × 250,000 = 0.31416. Multiply by A: 0.31416 × 0.000314 ≈ 9.865 × 10−5. Divide by l: 9.865 × 10−5 ÷ 0.05 ≈ 0.001973 H, which the tool shows as 1.9729 mH.

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Common mistakes

  • Entering the area in cm² or mm² and the length in cm; both fields are in SI units, m² and m.
  • Using the wire diameter or the coil's outer size instead of the cross-section area of the core the flux passes through.
  • Forgetting that a ferrite or iron core raises inductance far above this air-core value.
  • Using the formula for a short, fat coil (length similar to diameter), where the real inductance is lower than the long-solenoid result.
  • Expecting the inductance to double when you double the turns; it grows with the square, so it quadruples.

About this calculator

This calculator finds a solenoid's inductance using L = μ₀·N²·A/l, where μ₀ is the permeability of free space, N is the number of turns, A is the coil's cross-sectional area, and l is its length — inductance scales with the square of the turn count because each turn both generates magnetic flux and links with the flux from every other turn.

Electronics hobbyists winding custom coils for radio-frequency circuits, filters, or transformers, electrical engineering students verifying inductor design formulas, and RF engineers prototyping antenna or matching-network components use this. Enter the number of turns, cross-sectional area, and coil length to get the inductance.

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