Coil Inductance Calculator

Accurately compute inductance for air‑core single‑layer coils (Wheeler's formula) and magnetic‑core inductors (AL value method).Includes inductive reactance, interactive coil visualization, and design guidelines — essential for power supplies, RF circuits, and filter design.

Hz
Calculate inductive reactance XL = 2πfL
Wheeler's empirical formula: L (µH) = (N² × D²) / (18D + 40ℓ) , where D and ℓ are in inches. Accurate for ℓ ≥ 0.8D.
?️ Air: D=12mm, ℓ=25mm, N=60 ? Air: D=0.5in, ℓ=1in, N=80 ? Ferrite: AL=2500, N=40 ⚙️ RF Core: AL=120, N=25
Trusted reference: Air core formula derived from H.A. Wheeler's 1928 paper. AL method standard in magnetics design. All calculations performed locally.
Coil Schematic Representation
Windings (conductors) Core (air / magnetic)
Illustration only – not to scale. Actual dimensions depend on D, ℓ, and N.

Understanding Coil Inductance: Principles & Formulas

Inductance is the property of an electrical conductor by which a change in current induces an electromotive force (EMF) in the same conductor (self‑inductance) or in a nearby conductor (mutual inductance). For a coil, inductance depends on geometry, number of turns, core material, and winding density.

Wheeler's Formula (Air Core Solenoid)

L (µH) = (N² × D²) / (18D + 40ℓ) , where D = coil diameter (inches), ℓ = coil length (inches), N = number of turns.

Valid for single‑layer air‑core coils with ℓ ≥ 0.8D. Accuracy within 1% for typical RF inductors. Developed by Harold A. Wheeler (NIST).

Frequency validity: Wheeler's formula assumes low frequencies where skin effect and distributed capacitance are negligible. For frequencies above 30 MHz, stray capacitance may reduce effective inductance. For magnetic cores, AL values are usually specified at 10–100 kHz; above 1 MHz core losses increase.
Magnetic Core Inductance (AL Method)

L = AL × N² , where AL is the core inductance factor (nH/turn²) provided by core manufacturers (e.g., Ferroxcube, TDK).

This method accounts for effective permeability, core area, and magnetic path length. Result can be expressed in µH, mH, or H.

Why Use This Calculator?

  • Engineering Precision: Trusted formulas validated by electromagnetic theory and practical measurements.
  • Interactive Visualization: Real‑time coil rendering helps beginners grasp winding geometry and core concepts.
  • Design Versatility: From air‑core RF chokes to high‑permeability ferrite inductors for switch‑mode power supplies (SMPS).
  • Educational Depth: Step‑by‑step derivation and industry references satisfy academic and professional needs.

Step‑by‑Step Calculation Procedure

  1. Select core type: Air Core (single‑layer solenoid) or Magnetic Core (AL value).
  2. For air core: input coil diameter, winding length, and number of turns. Choose mm or inches (automatic conversion).
  3. For magnetic core: provide AL value (nH/N²) and turns count.
  4. Enter optional frequency (Hz) to compute inductive reactance XL = 2πfL.
  5. Click calculate — the tool outputs inductance in convenient units (µH, mH or H) and reactance in ohms.

Real-World Applications & Case Studies

RF Filter Design

An engineer designing a 7‑MHz low‑pass filter needs a 2.2 µH air‑core inductor. Using the calculator with D = 8 mm, ℓ = 12 mm, N = 24 turns yields L ≈ 2.18 µH. The visualization helps verify mechanical feasibility on a small PCB.

Boost Converter Inductor

A power electronics designer selects a ferrite core with AL = 3200 nH/N². Target inductance: 100 µH at 50 turns. The calculator confirms L = 3200 × (50)² = 8,000,000 nH = 8 mH, allowing quick core selection without complex geometry.

From the workbench – RF engineer insight: “When winding air‑core coils, always add 2‑3% extra turns to compensate for parasitic lead inductance and manufacturing tolerances. For my 6‑turn 40‑m band filter, the measured inductance was 0.98× the calculated value – so I now design with a 2% safety margin.”

Frequently Asked Questions

Wheeler's formula yields inductance with an error typically less than 1% for coils where length ≥ 0.8 × diameter. It is widely used for RF and audio inductors.

Manufacturer datasheets (e.g., TDK, Ferroxcube, Magnetics) provide AL values in nH/N². For toroids and E-cores, AL is standard specification.

No. The tool focuses on low‑frequency inductance and reactance. For self‑resonant frequency (SRF), parasitic capacitance matters — a separate tool is recommended.

Wheeler's formula is optimized for single‑layer solenoids. For multilayer windings, refer to more advanced models (e.g., Nagaoka coefficient).

Wheeler's formula assumes negligible wire thickness. For thick wires or close spacing, effective diameter increases slightly. Use the inner diameter for a conservative estimate — actual inductance will be within 5% for typical enameled copper wire (AWG 18–30).

The AL method works perfectly for toroidal cores if you have the AL value. For air‑core toroids, this calculator does not apply; instead, use formulas specific to toroidal geometry (e.g., L = μ₀ × N² × h × ln(b/a) / (2π)).
Authoritative references: Wheeler, H.A., “Simple Inductance Formulas for Radio Coils”, 1928 | IEC 60205 (Magnetic cores) | TDK Ferrite Cores – AL values | Magnetics Inc. Design Guide.
GetZenQuery Tech team — validated May 2026.