Air-Core Coil Inductance Calculator
A single-layer air-core coil is the simplest inductor: a length of wire wound in a helix with nothing but air inside. Its inductance depends on how many turns it has, how wide it is, and how long the winding is. This calculator uses Wheeler's well-known approximation, which is accurate to roughly 1 percent for coils that are not too short, to return the inductance in microhenries from the coil diameter, the winding length, and the number of turns. Use it to design RF and audio inductors, antenna loading coils, and tank circuits.
Wheeler inductance formula
L (microhenries) = (d^2 * N^2) / (18*d + 40*l)
d = coil diameter (inches)
l = winding length (inches)
N = number of turns
millihenries = microhenries / 1000
Valid for a single-layer air-core solenoid with l at least about 0.4 times d. Inductance scales with the square of turns and with diameter.
Coil design context
- Doubling the turns roughly quadruples inductance because of the N-squared term.
- A wider coil has more inductance than a narrow one with the same turns.
- Stretching the winding longer reduces inductance for a fixed turn count.
- The formula assumes an air core; a ferrite core multiplies the result by its effective permeability.
- Best accuracy is for closely spaced single-layer windings that are not extremely short.
Coil inductance: frequently asked questions
What formula does this air-core coil calculator use?
It uses Wheeler's classic approximation for a single-layer air-core solenoid: L (microhenries) = (d squared times N squared) divided by (18 times d plus 40 times l), where d is the coil diameter and l is the coil length in inches and N is the number of turns. It is accurate to about 1 percent when the coil length is at least 0.4 times the diameter.
Does this work for coils with a magnetic core?
No. Wheeler's formula assumes an air core (relative permeability of 1). A ferrite or iron core multiplies inductance by the effective permeability of the core, which depends on the material and geometry, so a cored coil needs the core's AL value instead.
What units does the calculator expect?
Enter coil diameter and length in inches and the number of turns as a count. The result is in microhenries. Wheeler's original formula is defined in inches, so keep both length inputs in inches for the stated accuracy.
How do I increase the inductance of a coil?
Inductance rises with the square of the number of turns and with the coil diameter, and falls as the coil is made longer for a fixed turn count. Adding more turns is the most effective single change because of the squared dependence.
Why is my measured inductance slightly different?
Wheeler's formula is an approximation valid for closely wound single-layer solenoids that are not too short. Wire thickness, spacing between turns, nearby metal, and frequency all shift the real value. Treat the result as a starting point for a design you then measure.
Official sources
- NIST: fundamental constants and electromagnetic units.
- IEEE Standards Association: electrical and inductance standards.
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.