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Air-Core Coil Inductance Calculator

Enter coil diameter, length and turns to estimate the inductance of an air-core coil.

Result

5.965 µH
0.00597 mH

How it is calculated

The tool applies Wheeler's approximation for a single-layer coil: L = d² × N² / (18d + 40l). Here L is the inductance in microhenries, d the coil diameter in inches, l the winding length in inches and N the number of turns. You type diameter and length in millimetres; the engine divides each by 25.4 before using the formula. The answer is shown in µH to three decimals and in mH to five decimals. Diameter and turns must be above zero, and a length of zero is accepted, but a negative length that makes the denominator zero or less returns no result. The formula assumes a single layer of closely wound wire, so use it as an estimate.

Worked example

Take a coil 25 mm across, 30 mm long, with 20 turns. Converted to inches, the diameter is 0.9843 and the length is 1.1811. The denominator is 18 × 0.9843 + 40 × 1.1811 = 17.717 + 47.244 = 64.961. The numerator is 0.9843² × 20² = 387.5. Dividing gives 5.965 µH, which is 0.00597 mH.

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Common mistakes

  • Entering the diameter in inches or the length in centimetres. Both fields expect millimetres; the conversion to inches happens inside the tool.
  • Typing the coil radius instead of the diameter. This halves the diameter and gives an inductance that is far too small.
  • Entering the length of the wire instead of the length of the winding. Only the axial length of the finished coil goes in the length field.
  • Expecting the inductance to scale linearly with turns. It scales with the square: 10 turns on this coil give 1.491 µH, 20 turns give 5.965 µH, four times as much.
  • Using the estimate for multi-layer coils or coils with a core. The formula describes one layer of wire with no core, so such coils will measure differently.

About this calculator

An air-core coil is a wound wire helix with no magnetic core material, used where core saturation, hysteresis losses, or nonlinearity would be a problem — mainly in radio-frequency circuits. Its inductance is commonly estimated with Wheeler's formula, L (µH) = (r² × N²) / (9r + 10l), where r is the coil radius in inches, N is the number of turns, and l is the coil length in inches; the formula is accurate to within about 1% for coils where length is at least 0.4 times the diameter.

RF and radio amateurs, antenna builders, and electronics hobbyists use this kind of calculation when winding tank circuit coils, RF chokes, Tesla coil secondaries, or loading coils for antennas, since air-core inductors are far more predictable and lower-loss at high frequencies than iron- or ferrite-core designs.

Wheeler's formula turns the coil diameter, winding length and turn count you enter into an inductance estimate, so you can size a coil on paper instead of winding and rewinding wire until it hits the target value.

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Comments (1)

  • Editorial team

    The tool does not check whether your turns physically fit in the winding length. A coil 30 mm long with 20 turns needs a pitch of 1.5 mm, so the wire plus its insulation must be thinner than that. To hit a target, use the square law: for 10 µH on the 25 mm by 30 mm example, 26 turns gives 10.081 µH. What band or circuit are you winding for?

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