Calculator
Example data table
| Case | Coil type | Key inputs | Computed inductance | Notes |
|---|---|---|---|---|
| A | Solenoid | N=120, length=50 mm, diameter=25 mm, μr=1 | ≈ 1.48×10⁻⁴ H (148 µH) | Long-solenoid model, no correction. |
| B | Toroid | N=50, Di=12.7 mm, Do=25.4 mm, height=10 mm, μr=2000 | ≈ 0.014 H (14 mH) | Rectangular cross-section approximation. |
| C | Air-core (Wheeler) | N=30, length=25 mm, diameter=20 mm | ≈ 3.5×10⁻⁵ H (35 µH) | Useful for single-layer air-core coils. |
Formula used
Solenoid
L = μ0 μr N² A / l
A = πr², μ0 = 4π×10⁻⁷ H/m. Optional short-coil factor: K ≈ 1/(1 + 0.45(D/l) + 0.2(D/l)²).
Toroid
L = μ0 μr N² A / (2π r̄)
Rectangular core: A ≈ height × thickness, r̄ is mean radius. Custom mode accepts A and r̄ directly.
Wheeler air-core
L(µH) = (r²N²)/(9r + 10l)
r and l must be in inches. The calculator converts your inputs automatically.
Circular loop
L ≈ μ0 μr N² r [ln(8r/a) − 2]
r is loop radius, a is wire radius. Works best when wire is thin versus loop radius.
Derived quantities
Reactance: XL = 2πfL
Energy: E = ½LI²
Resonance: f = 1/(2π√(LC))
How to use this calculator
- Select the coil type that matches your geometry.
- Enter turns and dimensions using your preferred units.
- Set relative permeability for the core material if needed.
- Optionally enter frequency, current, or capacitance for extra outputs.
- Press Calculate to show results above the form.
- Use the export buttons to download CSV or PDF.
FAQs
1) Which coil type should I choose?
Pick solenoid for long cylindrical windings, toroid for ring cores, Wheeler for single-layer air coils, and loop for one or more circular turns.
2) Why does measured inductance differ from the estimate?
Real coils include spacing, fringing fields, lead length, core tolerance, temperature drift, and frequency effects. These formulas estimate geometry-driven inductance only.
3) What does relative permeability mean?
μr scales magnetic flux versus air. Air is near 1. Ferrites and powdered iron raise μr, increasing inductance for the same turns and geometry.
4) When should I enable the short-coil correction?
If your solenoid diameter is not small compared with its length, long-solenoid assumptions overestimate L. The correction reduces L for short, wide coils.
5) Is Wheeler accurate for multilayer coils?
Wheeler’s classic form targets single-layer air-core coils. Multilayer windings and coil formers can shift inductance, so treat results as a starting estimate.
6) How is toroid area computed in standard mode?
Standard mode assumes a rectangular cross-section: area equals core height times radial thickness. If your core is not rectangular, use custom inputs.
7) What capacitance should I use for resonance?
Use your known parallel capacitance if you have it. For self-resonant frequency, you need parasitic capacitance, which depends on winding, insulation, and layout.
8) Are results valid at high frequency?
At high frequency, skin effect, proximity effect, and core losses matter. Inductance can change and Q drops. Use these outputs for initial sizing, then measure.