Air-Core Coil Calculator (Single-Layer)
Use this tool to estimate inductance using the Wheeler equation for a single-layer air-core solenoid.
L(µH) = (r² × N²) / (9r + 10l), where r and l are in inches.
What is an air inductor?
An air inductor (more precisely, an air-core inductor) is a coil of wire that stores energy in a magnetic field, but uses air as the magnetic core instead of ferrite or iron. Because air has very low magnetic losses, air-core inductors are popular in RF circuits, antenna matching networks, filters, and oscillators.
How this calculator works
This calculator estimates inductance for a single-layer cylindrical coil. It applies a common engineering approximation known as the Wheeler formula. For practical hobby and prototype work, this is often accurate enough to get very close before final tuning.
Equation used
L(µH) = (r² × N²) / (9r + 10l)
- L = inductance in microhenries (µH)
- r = coil radius in inches
- l = coil length in inches
- N = number of turns
Inputs are in millimeters for convenience, and converted internally to inches before computing the result.
How to use the air inductor calculator
- Enter the number of turns.
- Enter the outside coil diameter in millimeters.
- Enter the wound length of the coil in millimeters.
- Optionally enter frequency to compute inductive reactance.
- Optionally enter a target µH value to estimate needed turns.
- Click Calculate.
Design tips for better real-world results
- Keep turn spacing uniform. Uneven spacing changes inductance.
- Use thicker wire when you need lower resistance and higher Q.
- Leave room for tuning; practical coils often need slight compression or stretching.
- Avoid nearby metal objects during measurement or operation.
- At RF, lead length and layout parasitics can matter as much as the coil itself.
Worked example
Suppose you wind a coil with 12 turns, 25 mm diameter, and 18 mm length:
- Radius = 12.5 mm = 0.492 in
- Length = 18 mm = 0.709 in
- Estimated L ≈ a few µH range (calculator gives the exact result)
If the coil is used at 7.1 MHz, the reactance is:
XL = 2πfL.
This helps determine impedance in matching and filter designs.
Limitations and assumptions
This tool is intended for single-layer, air-core, round coils. It does not model:
- Multi-layer winding effects
- Skin effect and proximity effect losses in depth
- Self-capacitance and self-resonant frequency directly
- Nearby dielectric or conductive material loading
For precision RF work, verify with an LCR meter or vector network analyzer after construction.
Quick FAQ
Can I use this for ferrite-core inductors?
No. Ferrite or powdered-iron cores need core permeability (AL value) based calculations.
What if I need an exact value?
Use this estimate for design start, then tune experimentally by adjusting turns or coil spacing.
Why does diameter affect inductance so strongly?
Larger diameter increases loop area, which increases magnetic flux linkage per turn, raising inductance.