About the Air Core Inductor Calculator
This air core inductor calculator uses Wheeler’s classic formula for single-layer solenoid coils. In the first mode you enter the coil diameter, winding length and number of turns to get the inductance in microhenries; in the second you enter a target inductance and it tells you how many turns to wind on the same former. It also gives the length of wire you need, the length-to-diameter ratio and the coil’s reactance at a frequency of your choice.
Air-cored coils are used wherever a magnetic core would saturate, add loss or drift with temperature: RF tank circuits, antenna loading coils, crystal radio tuners, passive crossover networks and impedance-matching networks. Because there is no core, inductance depends only on geometry, which makes a good formula very accurate.
Measure the diameter to the centre of the wire (former diameter plus one wire diameter) and the length from the first to the last turn. Wheeler’s formula is accurate to about 1% when the coil is longer than 0.4 times its diameter; for short, pancake-like coils the error grows, and self-capacitance limits the useful frequency of any real coil.
How to use the air core inductor calculator
- 1Choose whether to find inductance or the turns for a target inductance.
- 2Enter the coil diameter measured to the centre of the wire.
- 3Enter the winding length from the first turn to the last.
- 4Enter the turns (or the target inductance in µH).
- 5Read the result, wire length and pitch, and the reactance at your operating frequency.
Formula and method
Harold Wheeler’s 1928 approximation for a single-layer air-core solenoid gives inductance in microhenries from the coil diameter d and length ℓ in inches and the number of turns N. The calculator converts millimetres to inches (÷ 25.4) before applying it. Inductance grows with the square of the turns, so doubling the turns on the same length quadruples L.
Solving the same formula for N gives the turns needed for a target inductance. The formula assumes evenly spaced turns and a diameter measured to the centre of the wire; it is within about 1% for ℓ > 0.4d. Wire length is N × π × d, and the reactance at frequency f is 2πfL.
- L
- Inductance in microhenries
- d
- Coil diameter to the wire centre (inches in the formula)
- ℓ
- Winding length (inches in the formula)
- N
- Number of turns
- XL
- Inductive reactance at frequency f
Worked examples
20 turns on a 10 mm former, 20 mm long
d = 0.3937 in and ℓ = 0.7874 in, so L = 0.155 × 400 ÷ (7.087 + 31.496) ≈ 1.607 µH. The coil uses 20 × π × 10 mm ≈ 0.63 m of wire and has a reactance of about 101 Ω at 10 MHz.
1-inch diameter, 1-inch long, 10 turns
In inches the formula is simply 1² × 10² ÷ (18 + 40) = 100 ÷ 58 = 1.724 µH. At 7 MHz the reactance is 2π × 7 × 10⁶ × 1.724 × 10⁻⁶ ≈ 75.8 Ω.
Turns for a 10 µH coil, 25 mm diameter, 40 mm long
With d = 0.9843 in and ℓ = 1.5748 in, N = √(10 × (17.717 + 62.992)) ÷ 0.9843 ≈ 28.9 turns, so wind 29. That is a 1.39 mm pitch, so 1.2 mm enamelled wire fits, and about 2.27 m of wire is needed.
Frequently asked questions
How do you calculate the inductance of an air core coil?+
For a single-layer coil use Wheeler’s formula L(µH) = d²N² / (18d + 40ℓ), with diameter d and length ℓ in inches. For example a 1 in × 1 in coil of 10 turns is 100 / 58 ≈ 1.72 µH.
How many turns do I need for a given inductance?+
Rearrange Wheeler’s formula: N = √(L × (18d + 40ℓ)) / d, with L in µH and dimensions in inches. Fix the former diameter and the winding length first, then check that the resulting pitch is larger than your wire diameter.
Which diameter should I use — the former or the wire?+
Use the mean diameter to the centre of the wire, which is the former diameter plus one wire diameter. On small coils with thick wire this makes a noticeable difference to the result.
How accurate is Wheeler’s formula?+
Wheeler stated about 1% accuracy for coils longer than 0.4 times their diameter. Very short coils need Nagaoka’s correction or a numerical method, and real coils also have lead inductance and self-capacitance.
Does spacing the turns change the inductance?+
Yes. Stretching a coil to the same turns over a longer length reduces inductance, which is why RF builders tune air coils by squeezing or spreading the turns. Enter the new length to see the effect.