# Helical Coil Calculator

URL: https://speedycalculator.com/calculators/physics/helical-coil/
Last updated: 2026-10-30

> The helical coil calculator finds the height, wire length, inductance (Wheeler's formula), self-capacitance (Medhurst) and self-resonant frequency of a single-layer air-core coil.

## Inputs

- Coil diameter D (mean) (mm, cm, m, in, µm)
- Wire diameter d (mm, cm, m, in, µm)
- Number of turns N
- Spacing between turns s (mm, cm, m, in, µm)

## Results

- Coil height (length)
- Wire length
- Inductance (Wheeler)
- Self-capacitance (Medhurst)
- Self-resonant frequency

## 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))
```

## Explanation

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

FieldWhat to enterCoil diameter D (mean)Units: mm, cm, m, in, µmWire diameter dUnits: mm, cm, m, in, µmNumber of turns NA numberSpacing between turns sUnits: 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)101.1412152.4104204.038255.9652308.14554013.1234

## 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.

## FAQ

**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.


## Sources

- [OpenStax – University Physics Volume 2](https://openstax.org/details/books/university-physics-volume-2)
- [HyperPhysics (Georgia State University)](http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html)