Solenoid Inductance Calculator
Inductance of an air-core or iron-core solenoid from turns, length, coil diameter and core permeability, with stored energy at a given current.
How it works
L = μᵣ μ₀ N² A ÷ l · E = ½ L I² · B = μᵣ μ₀ N I ÷ l
A solenoid’s inductance grows with the square of the turn count and with the core’s permeability, and shrinks as the coil gets longer for the same turns. The textbook formula assumes a coil much longer than its diameter; Wheeler’s correction handles short air coils. Iron and ferrite multiply inductance enormously but saturate at high current, so μr is only valid at low fields.
Worked example
500 turns, 10 cm long, 2 cm diameter, air core: 4π × 10⁻⁷ × 500² × 3.14 × 10⁻⁴ ÷ 0.1 = 0.99 mH.
Frequently asked questions
How do I get more inductance without more turns?
Add a ferrite core, shorten the coil, or increase the diameter — inductance scales with area.
What about a toroid?
L = μᵣ μ₀ N² A ÷ (2π r) with r the mean radius; toroids confine the field and follow the formula more closely.
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This calculator is for educational purposes. Double-check important results before acting on them.