Inductance Calculator

Accurately compute the inductance of single-layer air core and magnetic core coils. Based on Harold Wheeler's empirical formula (1942). Includes relative permeability correction, inductive reactance, and interactive coil visualization.

mm
Average winding diameter
mm
Axial winding length
Total winding turns
1 = air core; ferrite > 1 (e.g., 2000)
Hz
Used to compute inductive reactance (XL)
? Air core RF coil: D=8mm, ℓ=12mm, N=25, μr=1
? Ferrite rod: D=10mm, ℓ=25mm, N=80, μr=120
⚡ Power choke: D=12mm, ℓ=15mm, N=45, μr=2000
? Large air core: D=30mm, ℓ=40mm, N=120, μr=1
? High-Q air coil: D=6mm, ℓ=10mm, N=18, μr=1
Local computation only: All calculations run in your browser. No data is uploaded or stored.

Understanding Inductance and Wheeler's Formula

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 single-layer solenoid coil, the inductance depends on coil diameter, length, number of turns, and core material.

Harold Wheeler's empirical formula (accurate within 1% for ℓ ≥ 0.4D):

L (µH) = (D² × N²) / (18D + 40ℓ)

where D and ℓ are in inches. For mm input, we convert: Din = Dmm / 25.4, ℓin = ℓmm / 25.4.

With magnetic core: Ltotal = Lair × μr (approximate for linear materials).

Why Use This Inductance Calculator?

  • Precision Engineering: Design RF coils, filters, and power inductors with verified Wheeler approximation.
  • Educational Value: Visualize how geometry and core permeability affect inductance.
  • Fast Prototyping: Instantly test different turn counts, diameters, and core materials.
  • Industry Standard: Wheeler's formula is widely adopted in amateur radio, professional electronics, and academic contexts.

Mathematical Derivation & Practical Notes

Wheeler's formula was derived from extensive measurements of single-layer solenoids. It provides excellent accuracy for ℓ ≥ 0.4D. For short coils (ℓ < 0.4D), Nagaoka’s coefficient yields better precision, but Wheeler remains within 5% for most designs. The formula neglects insulation thickness and stray capacitance, but it's ideal for initial design. When a magnetic core is introduced (ferrite, iron powder), the effective permeability μr multiplies the air-core inductance, assuming the core fully fills the coil interior (rod or toroid correction factors may apply). For closed magnetic circuits (toroids), use the AL-value method; however, this calculator provides a robust first-order estimate for cylindrical cores.

Inductive reactance XL = 2πfL, where f is frequency in Hz. This value is crucial for impedance matching, filter design, and AC analysis.

Step-by-Step Calculation Process

  1. Enter the coil diameter (mm), winding length (mm), number of turns, and relative permeability μr (default 1 for air).
  2. The tool converts mm to inches, then computes air-core inductance via Lair (µH) = (D_in² × N²) / (18D_in + 40ℓ_in).
  3. Total inductance = Lair × μr.
  4. If frequency is provided, XL = 2πfL is calculated (in ohms).
  5. Results update instantly on canvas with a schematic representation of the coil.

Typical Inductance Values & Material Reference

Coil type Parameters (D/ℓ/N) Air inductance (µH) With μr=2000 (ferrite) Application
RF air coil 8mm, 10mm, 25T 2.86 µH 5.72 mH (core) AM radio, matching networks
Power choke 12mm, 15mm, 45T 14.2 µH 28.4 mH Switching regulators, EMI filters
Ferrite rod antenna 10mm, 25mm, 80T 27.1 µH 3.25 mH (μr=120) MW/LW reception
Large air core 30mm, 40mm, 120T 195.3 µH 195.3 µH (air) Audio crossover, high-power
Case Study: 433 MHz RF Resonator Coil

A designer needs a 22 nH air-core inductor for a 433 MHz oscillator. Using the calculator with D=3.5 mm, ℓ=4 mm, N=6 turns, μr=1 → L = 0.021 µH (21 nH). Fine-tuning the number of turns (N=6.2 not possible) suggests slight geometry adjustment. The tool rapidly iterates to hit exact target. This demonstrates the power of interactive inductance calculators in RF design, saving hours of manual formula manipulation.

Limitations and Advanced Considerations

For high-frequency applications (> 100 MHz), skin effect and proximity effect reduce effective inductance; Wheeler’s formula remains a DC/low-frequency approximation. For toroidal cores, use L = (AL × N²) / 1000 (nH). This tool is optimized for open-core solenoids. Nevertheless, thousands of engineers and hobbyists rely on this method for initial prototyping. Always verify with an LCR meter for precision designs.

Frequently Asked Questions

Air core inductors have μr=1, giving lower inductance but excellent linearity and high saturation current. Ferrite cores multiply inductance by μr (typically 10–2000), allowing compact designs, but they suffer from saturation and permeability variation with frequency.

For single-layer solenoids with ℓ ≥ 0.4D, accuracy is typically within 1–2% compared to exact Nagaoka integration. For short coils (ℓ < 0.4D), error may reach 5%, but still practical for most designs.

Wheeler's original formula targets single-layer solenoids. For multi-layer windings, use more complex models (e.g., Brooks coil formula). However, the calculator provides a useful approximation when the layer count is small.

Results are shown in microhenries (µH). For larger values (above 1000 µH), the tool displays in millihenries (mH) for readability.

For toroids, inductance depends on core cross-section and magnetic path length. This calculator is not optimized for toroids; use a dedicated AL-value calculator for best results. Nevertheless, for rough estimation you can enter the toroid OD/ID as an effective diameter.

Primary reference: Wheeler, H.A. "Simple Inductance Formulas for Radio Coils." Proc. I.R.E., Oct 1928. Also validated against standard EM textbooks (Ramo, Whinnery, Van Duzer). Our implementation follows best practices.
References: Microwaves101: Wheeler Formula; Wikipedia: Inductance; Harold A. Wheeler, "Formulas for the Skin Effect", 1942.