Hand-wound air-core coils are used in radio tuners, filters and Tesla coils. Wheeler’s classic formula estimates their inductance within about 1%, and Medhurst’s gives the stray capacitance that limits the highest useful frequency.
How to use the Helical Coil Calculator
- Coil diameter D (mean)
- Wire diameter d
- Number of turns N
- Spacing between turns s
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Enter the coil (mean) diameter, wire diameter, number of turns and spacing between turns.
Inputs explained
| Field | What to enter |
|---|---|
| Coil diameter D (mean) | Units: mm, cm, m, in, µm |
| Wire diameter d | Units: mm, cm, m, in, µm |
| Number of turns N | A number |
| Spacing between turns s | Units: mm, cm, m, in, µm |
What each result means
- Coil height (length) = [Number of turns N]×([Wire diameter d] + [Spacing between turns s])
- Wire length = [Number of turns N]×sqrt((pi×[Coil diameter D (mean)])^2 + ([Wire diameter d] + [Spacing between turns s])^2)
- Inductance (Wheeler) = ([Coil diameter D (mean)]÷0.0254)^2×[Number of turns N]^2÷(18×[Coil diameter D (mean)]÷0.0254 + 40×[Number of turns N]×([Wire diameter d] + [Spacing between turns s])÷0.0254)
- Self-capacitance (Medhurst) = [Coil diameter D (mean)]×100×(0.1126×[Number of turns N]×([Wire diameter d] + [Spacing between turns s])÷[Coil diameter D (mean)] + 0.08 + 0.27÷sqrt([Number of turns N]×([Wire diameter d] + [Spacing between turns s])÷[Coil diameter D (mean)]))
- Self-resonant frequency = 1÷(2×pi×sqrt([Inductance (Wheeler)]×1e-6×[Self-capacitance (Medhurst)]×1e-12))
Example values
How the main result changes when Coil diameter D changes and everything else stays at the example values above:
| Coil diameter D (mean) (mm) | Inductance (Wheeler) (µH) |
|---|---|
| 10 | 1.1412 |
| 15 | 2.4104 |
| 20 | 4.038 |
| 25 | 5.9652 |
| 30 | 8.1455 |
| 40 | 13.1234 |
Formula
ℓ = N·(d + s), wire = N·√((πD)² + (d + s)²), L(µH) = D²N²/(18D + 40ℓ) (inches, D = coil diameter)
C(pF) = D(cm)·(0.1126·ℓ/D + 0.08 + 0.27/√(ℓ/D)), f_SRF = 1/(2π√(LC))
Worked example
Inputs — Coil diameter D (mean): 20 mm; Wire diameter d: 1 mm; Number of turns N: 20; Spacing between turns s: 0.5 mm.
Results — Coil height (length) = 30 mm; Wire length = 1.257 m; Inductance (Wheeler) = 4.03796 µH; Self-capacitance (Medhurst) = 0.9387 pF; Self-resonant frequency = 81.74741 MHz.
Key terms
- Self-capacitance
- Stray capacitance between turns.
Frequently asked questions
How accurate is Wheeler's formula?
About 1% for coils longer than 0.4 × their diameter.
What is the self-resonant frequency?
Above it, the coil behaves like a capacitor.
How do I increase inductance?
More turns, a larger diameter or closer spacing.
Does wire thickness matter?
Mainly through the coil length and Q factor.