# Inductance of a single-layer close-wound air-cored coil.

Calculations to give the inductance of a single-layer close-wound air-cored coil are extremely complex, but a good approximation is given by the following formula provided that these assumptions are adhered to:

• Wire diameter is less than 10% of the coil diameter.
• Wire is close wound in a single layer.
• The coil's length is 0.4 to 3 times the diameter.

The formula is often called Wheeler's Formula

MathML formulaFormula ImageStraight text formula
$L = N 2 d2 18d+40b$ L = N^2[d^2 / (18d + 40b)]
$N = L18d+40b d$ N = [(L*(18d + 40b))^0.5] / d

Where

L is inductance in µH,

d is coil diameter in inches,

b is coil length in inches,

N = number of turns

Coil Diameter: inches mm cm inches mm cm

Inductance: