How this calculator works
Inductance relates linked magnetic flux to current. In a long solenoid, the approximately uniform field makes flux proportional to turn density, current and core permeability. Linking that flux through every turn gives a turns-squared dependence. End fringing, widely spaced turns, core saturation and frequency-dependent losses are omitted. A calculated non-integer number of turns is a design target to round and recheck.
Formula
L = mu0 mur N² A/l; A = pi r²; N = sqrt(Ll/(mu0 mur A)).
Worked example
A 100-turn air-core solenoid with area 0.001 m² and length 1 m has L = 12.5663706 microhenries. Solving back from that inductance gives 100 turns.
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Frequently asked questions
How long must the coil be?
The approximation improves when length is much greater than diameter. Short coils need a finite-length correction or a different model.
Does an iron core always multiply inductance by a fixed value?
No. Effective permeability depends on geometry, air gaps, field level and frequency.
Can the calculated turn count be fractional?
It is a mathematical target. Choose a practical winding count and recalculate the result.