This inductance calculator estimates a solenoid coil’s inductance from its turns, core material, cross-section and length — plus the magnetic energy it stores at a given current.
Formula: L = µ₀µᵣN²A ÷ ℓ — the ideal long-solenoid approximation (real short coils run 10–40% lower; end effects leak flux). Turns dominate: doubling N quadruples L, because each turn links the flux of all the others — inductance is a team statistic.
L = µ₀µᵣN²A ÷ ℓ
Four levers, one squared: turns N enters as N² (each new turn both creates flux and links it), area and permeability scale linearly, length dilutes. Energy storage U = ½LI² mirrors the capacitor’s ½CV² — inductors bank energy in magnetic fields as capacitors do in electric ones. Part of our Physics Calculators collection.
Worked Example (Verified)
- 500 turns, 1 cm² section, 10 cm long, air core (defaults): L = 4π×10⁻⁷ × 250,000 × 10⁻⁴ ÷ 0.1 = 314 µH — a classic RF-coil value; at 2 A it stores 0.63 mJ
- Swap in a power ferrite (µᵣ 125): the same winding becomes 39 mH — cores are inductance multipliers, which is why a pea-sized ferrite inductor replaces a bucket of air-core wire
- The N² law in practice: rewinding 500 → 1,000 turns on the same former quadruples inductance but also roughly quadruples resistance (more wire) and lowers self-resonant frequency — engineering is the art of which penalty you accept
- Saturation honesty: iron’s µᵣ 5,000 holds only until the core saturates (~1–2 T); past that, inductance collapses toward the air-core value — the calculator’s number is the small-signal truth
Related Tools
- LC Resonance Calculator — inductors paired with capacitors
- Capacitance Calculator — the electric-field counterpart
- Physics Calculators — the full collection
Frequently Asked Questions
How do you calculate a coil’s inductance?
For a solenoid: L = µ₀µᵣN²A/ℓ — permeability of free space (× core µᵣ), turns squared, cross-sectional area, divided by coil length, all in SI units. 500 turns over 10 cm at 1 cm² on air gives ≈ 314 µH. Short, fat coils measure somewhat below the ideal formula.
Why do turns count squared?
Each turn contributes flux proportional to N (all turns’ currents add), and that flux links all N turns — the two factors multiply. It’s why a modest rewind changes an inductor’s character entirely, and why inductance per turn grows with coil size rather than staying constant.
What does an inductor store energy in?
Its magnetic field: U = ½LI². Interrupt the current suddenly and the field’s collapse drives the energy back out — as a voltage spike (V = L·dI/dt) if no path is provided, which is the spark in every relay and ignition coil ever built.
Air core vs ferrite vs iron?
Air: perfectly linear, no saturation or core loss, but tiny inductance per size. Ferrite: µᵣ tens to thousands, low loss at RF/power frequencies, saturates ~0.3–0.5 T. Iron/steel: highest µ, but lossy above audio frequencies (eddy currents — hence laminated cores in transformers).
What is self-resonance?
Real windings have inter-turn capacitance; at the self-resonant frequency the “inductor” behaves capacitively above it. More turns (bigger L) with more winding capacitance pushes SRF down — one reason RF design prefers many small tricks over one giant coil.
Is this inductance calculator free?
Yes — free, instant, no sign-up. An ideal-solenoid estimator; precision design uses Wheeler/Nagaoka corrections or measurement.