Inductor Calculator helps you calculate inductance — free, instant, in your browser. Fill in Number of Turns, Cross-section Area (m²) and Coil Length (m) on Inductor and read your answer immediately. Inductor ties each output to its formula. Inductor suits budgeting and planning checks. You can disconnect once Inductor has loaded; the arithmetic runs locally. Inductor sits in the Engineering section next to free online inductor calculator and free inductor calculator. Inductor shows formula, assumptions and result together. Inductor stays bookmarked for next time.
What the defaults give
50 turns over a 0.001 m² cross-section and 0.05 m length gives 62.85 μH.
The core is assumed to be air, so μ₀ = 1.257 × 10⁻⁶ H/m is used unchanged.
The formula
L = μ₀ × N² × A ÷ l
μ₀ = 4π × 10⁻⁷ ≈ 1.257 × 10⁻⁶ H/m
L is inductance in henries, N is the number of turns, A is the cross-sectional area of the coil in square metres, and l is its length in metres. This is the ideal solenoid formula: it assumes a long, tightly wound coil with a uniform field and no fringing at the ends.
Worked examples
50 turns, 0.001 m², 0.05 m → 62.85 μH
100 turns, same geometry → N² is 4× larger → 251.4 μH
25 turns, same geometry → 15.71 μH
50 turns, 0.002 m², 0.05 m → 125.7 μH
50 turns, 0.001 m², 0.10 m → 31.43 μH
200 turns, 0.001 m², 0.05 m → 1.006 mH
Turns are the lever, length is the brake
Inductance scales with the square of the turn count, so the cheapest way to add inductance is more turns — but each turn also makes the coil longer if the wire stays the same, and length sits in the denominator. The two effects partly cancel, which is why a real design usually adds turns while packing them tighter rather than simply winding more wire onto the same former.
Area in the numerator is the cross-section the flux passes through, not the surface area of the former. A wider bobbin raises inductance linearly, and so does a longer magnetic path only if it increases area, which it normally does not.
What the ideal formula misses
Air-core coils in real circuits have a parasitic capacitance between adjacent turns, which sets a self-resonant frequency above which the part stops behaving as an inductor at all. Tight winding raises both inductance and capacitance, so more turns is not free at high frequency.
Adding a magnetic core multiplies L by the core relative permeability, which can be hundreds or thousands — far more than any practical change in winding. That is why a ferrite core the size of a fingernail can replace a large air coil. Core saturation, temperature drift and the manufacturer tolerance all sit outside this calculation, so treat the result as a geometry estimate and check the datasheet for anything going into production.
Frequently Asked Questions
What is the inductance of a 50-turn air coil?
62.85 μH with a 0.001 m² cross-section and 0.05 m length, from L = μ₀N²A/l.
How does turn count affect inductance?
It scales with turns squared. Doubling 50 turns to 100 quadruples inductance to 251.4 μH, before accounting for the longer winding.
What happens if I double the coil length?
Inductance halves, because length is in the denominator. At 0.10 m the same 50 turns give 31.43 μH instead of 62.85.
Does this formula work for cored inductors?
Only as a baseline. A magnetic core multiplies inductance by its relative permeability, which can be hundreds or thousands, so use the core datasheet.
Why does a real coil behave differently at high frequency?
Parasitic capacitance between turns creates self-resonance. Above that frequency the part behaves capacitively, and the ideal solenoid model no longer applies.
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