Inductance Calculator

In L = μ₀μᵣN²A/l, the number of turns N appears squared, while cross-sectional area A and length l each appear only to the first power (and length is in the denominator). That means doubling the turn count quadruples inductance, while doubling the area only doubles it and doubling the length actually halves it — turns are by far the most powerful lever in this formula.

The relative permeability μᵣ multiplies directly into the inductance formula, so it scales the result linearly. An air or vacuum core uses μᵣ = 1 as a baseline, while iron cores (roughly 200-5,000) or ferrite cores (roughly 1,000-10,000) can multiply that same coil's inductance by two to four orders of magnitude — which is exactly why real inductors and transformers use magnetic cores instead of air.

Reactance is computed as X_L = 2πfL, so for a fixed inductance it scales directly with frequency. Since 1 kHz is roughly 16.7 times higher than 60 Hz, the reactance at 1 kHz comes out proportionally higher too — this is the basic reason inductors block high-frequency AC signals far more strongly than low-frequency ones.

The L = μ₀μᵣN²A/l formula assumes an idealized long solenoid — one whose length is much greater than its diameter, with perfectly uniform winding and no flux leakage at the ends. A short, fat coil doesn't meet that assumption: field lines fringe and leak out near the open ends rather than staying confined along the coil's axis, so its measured inductance will typically come in lower than this ideal formula's result.