Calculator
Air-core coil inductance
Calculate the inductance of a single-layer, multilayer, flat spiral or toroidal air-core coil, or the turns you need for a given inductance. It also gives the wire length, resistance and copper weight.
Coil
- Inductance
- 13.5 µH
- Check (Wheeler)
- 13.9 µH (+3.4 %)
- Turns
- 20
- Winding length
- 30 mm
- Outer diameter
- 43 mm
Wire
- Wire length
- 2.61 m
- DC resistance (20 °C)
- 25.4 mΩ
- Copper mass
- 41.3 g
To use it in a flashlamp network, enter the coil resistance as the series resistance in Simulate mode of the PFN calculator.
How to use it
- Pick the shape: single layer (solenoid), multilayer, flat spiral or toroid.
- Enter the copper wire diameter and the geometry. The pitch is the center-to-center distance between turns: leave it empty for close-wound turns (with enameled wire the real pitch is slightly larger than the copper).
- Choose whether you want the inductance for a number of turns or the turns for your target inductance.
The method
- Single layer, multilayer and spiral: each turn is treated as a circular loop and the mutual inductance of every pair is summed with Maxwell’s formula, using elliptic integrals, plus each loop’s self-inductance. It is the most accurate method for round-wire coils.
- Checked against Nagaoka’s formula with Rosa’s round-wire correction: they agree within 0.01 %. Next to it you see Wheeler’s result, the classic radio formula, which is usually within 1 to 3 %.
- Toroid: closed formulas. Circular section: L = µ0·N²·(R − √(R² − a²)). Rectangular section: L = µ0·N²·h/(2π)·ln(r2/r1).
- Resistance is the DC resistance of copper at 20 °C (1.724·10⁻⁸ Ω·m).
Model limits
It holds at low frequency: it ignores skin and proximity effects, which at high frequency slightly lower the inductance and raise the resistance. It also ignores the helical pitch, which matters little for close-wound coils, and the inter-turn capacitance. For flashlamp network pulses (hundreds of µs to ms) the error is small.
Sources
- J. C. Maxwell, A Treatise on Electricity and Magnetism, 1873: mutual inductance of two circular loops.
- H. Nagaoka, "The inductance coefficients of solenoids", 1909, and E. B. Rosa, round-wire correction (Bulletin of the Bureau of Standards, 1906).
- F. W. Grover, Inductance Calculations, 1946.
- H. A. Wheeler, "Simple inductance formulas for radio coils", Proc. IRE, 1928.