Solenoid Inductance Calculator

A long, tightly-wound solenoid's self-inductance follows from combining Ampère's law and Faraday's law of induction: L = μ₀ × μᵣ × N² × A ÷ l, where N is the number of turns, A is the coil's cross-sectional area, l is its length, μ₀ is the vacuum permeability (1.25663706127×10⁻⁶ N/A², the CODATA 2022 value), and μᵣ is the core's relative permeability. Verified via web search against HyperPhysics's own 'Inductance of a Solenoid' derivation.

This is the standard long-solenoid approximation — accurate when the coil's length is much greater than its diameter and the winding is uniform; short, fat, or loosely-wound coils deviate from it. Core area and coil length get this page's metric/imperial toggle (mm²/in² and mm/in), converted to square meters and meters before the formula runs. Turn count and relative permeability are left as plain, un-toggled numbers, since a turn count is dimensionless and permeability is a ratio with nothing to convert.

Relative permeability defaults to 1 for an air core. Winding the same coil around a ferromagnetic core multiplies its inductance by that core material's relative permeability — a real, often large effect (iron cores commonly run in the hundreds to low thousands) — but the actual figure for a specific material is a fact you supply, since it varies by alloy and isn't something this calculator can invent.