Air-core coil calculator: inductance, turns, self-resonance
For resonant circuits, filters and antenna matching: the tool calculates the inductance of single-layer coils precisely (Nagaoka coefficient after Lundin), multilayer coils after Wheeler, and conversely the turns for a desired inductance.
Free, no account needed
Abbreviations and symbols on this page (8)
- L
- Inductance of a coil, unit henry (H). Indicates how strongly the coil opposes a change in current.
- nH, µH, mH, H
- Nano-, micro-, millihenry and henry: 1 µH = 0.000001 H.
- Nagaoka coefficient K
- Correction factor for short coils (0 to 1): L = µ0 N² A K ÷ l. Calculated here with the approximation by Lundin (1985).
- SRF
- Self-resonant frequency: the frequency at which the coil resonates with its own capacitance. Above it, it no longer acts as a coil.
- Q
- Quality factor of a resonant circuit: 2π f L ÷ R. High = low losses, narrow resonance.
- X(Lp)
- Reactance of the primary coil at the operating frequency: X = 2π f Lp, in ohms.
- AWG
- American Wire Gauge: higher number = thinner wire. AWG 24 ≈ 0.51 mm.
- LCR meter
- Instrument for measuring inductance (L), capacitance (C) and resistance (R).
Turns side by side on a tube, close-wound or spaced.
| Inductance (Lundin) | 7.032 µH |
| Inductance (Wheeler) | 7.013 µH |
| Self-capacitance (Medhurst) | 1.444 pF |
| Self-resonance (SRF) | 49.95 MHz |
| Reactance at 7 MHz | 309.3 Ω |
| Resistance DC / RF | 48.28 mΩ / 466.8 mΩ |
| Q factor at 7 MHz | 663 |
| Wire length | 1.948 m · Turn pitch 2 mm |
Formula
Single-layer: L = µ0 N² A K ÷ l (K after Lundin), compared with Wheeler L = r² N² ÷ (9 r + 10 l) (inches, µH). Multilayer after Wheeler: L = 0.8 r² N² ÷ (6 r + 9 l + 10 b) (inches, µH, r mean radius, b winding depth). Self-capacitance after Medhurst, SRF = 1 ÷ (2π √(L C)). Q factor Q = 2π f L ÷ R with skin effect.
Example
20 turns of 1 mm wire on a 30 mm diameter, 40 mm long: about 7.0 µH (Wheeler 7.0 µH), self-capacitance 1.44 pF, self-resonance around 50 MHz. At 7 MHz theoretical Q factor around 660.
Notes
- Diameter = coil former; the calculation uses the wire centre (former + wire).
- For single-layer coils Wheeler is accurate to about 1 % as long as the length is at least 0.8 × radius; Lundin applies to any length.
- The Q factor is theoretical (copper and skin effect only); in practice it is lower because of the former, enamel and surroundings.
- Near self-resonance the coil no longer acts as an inductance; stay well below it.
- Measure with an LCR meter or via a resonant circuit with a known capacitor.