Coil inductance: how many turns, on what, for how many microhenries
You can buy inductors, but for a crystal set, an antenna tuner, a filter or a choke you often wind your own. The inductance of a coil depends on its turns squared, its diameter, its length and whatever is inside it. This calculator uses Wheeler's formulas for single-layer and multi-layer air coils, good to about 1%, and L = AL n² for any ferrite or iron-powder core, and turns the question round: how many turns for the inductance you want.
How to use the coil inductance calculator
- Pick the type: a single layer on an air former, several layers, or a core with an AL value.
- Type the turns and, for an air coil, the former's diameter and the winding length in millimetres (plus the winding depth for multi-layer); for a core, its AL from the data sheet or the list.
- Optional: the wire diameter (or pick an AWG) for the wire length, the DC resistance and whether the turns fit in one layer; a target inductance gives the turns to wind, one click to use them.
- The drawing shows the coil with its dimensions and the turns; the panel has the formula with your numbers, the fit bar and the wire. The Turns table lists the same form with other turn counts.
Single-layer air coils
L (µH) = d² n² / (457 d + 1016 l) (d, l in mm; 18 d + 40 l in inches)
Harold Wheeler's 1928 formula for a solenoid: d is the diameter of the turns (the former's outside), l the length the winding occupies and n the turns. It is within 1% of the exact result for any coil at least 0.4 diameters long, which covers nearly every practical coil; shorter, flatter coils read a few percent high. Inductance goes with n², nearly with d², and falls as the coil is stretched: the same turns spread over twice the length give roughly half the inductance.
Multi-layer air coils
L (µH) = 0.8 a² n² / (6a + 9b + 10c) (inches: a mean radius, b length, c depth)
Wheeler's other formula, for the squat, deep coils of chokes, relay coils and loudspeaker crossovers. The mean radius is the former's radius plus half the winding depth. It is good to a few percent when the three dimensions are of the same order; for a very thin or very long winding use the single-layer formula instead.
Coils on cores
L = AL × n²
A ferrite or iron-powder core multiplies the inductance by its effective permeability, and the maker folds that together with the core's size into one number, AL, in nanohenries per turn² (the same figure as millihenries per 1000 turns). Ten turns on a core of 523 nH is 52.3 µH; a hundred turns is 5.23 mH. Iron powder (low AL, 2–100 nH) is for RF and high currents; ferrite (hundreds to thousands) for chokes, transformers and EMI; a gapped ferrite sits between. Tolerances are ±20–25%, and ferrite drifts with temperature, so wind a few turns extra and measure.
| Core | AL | 10 turns | Turns for 100 µH |
|---|---|---|---|
| T37-2 iron powder (red) | 4 nH/n² | 400 nH | 159 |
| T50-6 iron powder (yellow) | 4.6 nH/n² | 460 nH | 148 |
| T68-2 iron powder (red) | 5.7 nH/n² | 570 nH | 133 |
| FT37-43 ferrite | 350 nH/n² | 35 µH | 17 |
| FT50-43 ferrite | 523 nH/n² | 52.3 µH | 14 |
| FT82-43 ferrite | 557 nH/n² | 55.7 µH | 14 |
| FT114-43 ferrite | 603 nH/n² | 60.3 µH | 13 |
| ETD29 3C90 (gapped 0.5 mm) | 160 nH/n² | 16 µH | 25 |
| Ungapped ETD29 3C90 | 2200 nH/n² | 220 µH | 7 |
Wire and resistance
The wire length is π × mean diameter × turns, and the DC resistance follows from copper's resistivity and the wire's cross-section. For a single layer the turns that fit close-wound are the length divided by the wire diameter; more turns than that need a longer former, thinner wire or a second layer. Thicker wire means less resistance (higher Q, less heating) but fewer turns in the space. At radio frequencies the current crowds to the wire's surface and the effective resistance rises, so Q is what matters there, not the DC ohms.
Winding tips
Wind on something round and non-metallic: PVC pipe, a pill bottle, a cardboard tube. Keep the turns tight and even; close-wound enamelled wire is the easiest to make repeatable. Leave the ends long. Fix the winding with tape or a dab of glue before measuring, because loose turns shift. For a tunable coil, leave the turns spaced and slide them, or push a ferrite slug (raises L) or a brass slug (lowers L) into the former. Keep other metal a diameter away: it lowers the inductance and the Q.
Your coil, step by step
- Inductance: Single-layer air coil, 30 turns on 20 mm × 25 mm = 10.42 µH.
- Wire: 1.96 m, 67.2 mΩ DC; 31 turns fit a layer.
- Sensitivity: one turn more gives 11.13 µH, twice the turns 41.69 µH.
Worked example: 30 turns on a 20 mm former, 25 mm long
d = 20 mm, l = 25 mm, n = 30: L = 20² × 30² / (457 × 20 + 1016 × 25) = 360 000 / 34 540 = 10.42 µH. The coil is 1.25 diameters long, well inside Wheeler's 1% band. With 0.8 mm wire the turns need 24 mm of the 25 mm available, so they fit in one layer; the wire is 1.96 m long and 67.2 mΩ. For 20 µH on the same former you would wind √(20 / 0.0) × 30 ≈ 41.6 turns, which no longer fit in 25 mm of 0.8 mm wire: thinner wire or a longer former.
Questions
Does the wire gauge change the inductance?
Only slightly, through the mean diameter and the length the turns occupy. It decides the resistance, the current the coil can carry and how many turns fit.
How accurate is this for a real coil?
Air coils: a percent or two if you measure the dimensions carefully. Cores: the AL tolerance, ±20–25%. Either way, wind a turn or two extra and trim while measuring with an LC meter.
What about a coil on a nail or a bolt?
Steel raises the inductance by an unpredictable amount, saturates early and is lossy at anything above mains frequency. Use a proper ferrite or iron-powder core with a known AL, or air.
Can I use this for a planar or PCB spiral coil?
No: flat spirals follow different formulas (Wheeler also published one). This calculator is for wound solenoids, multi-layer bobbins and toroids.