Air Core Inductor Calculator
Estimate inductance for a single-layer air-core solenoid using Wheeler’s formula.
Formula: L(µH) = (r²N²) / (9r + 10l), where r and l are in inches.
What this calculator does
This tool helps you quickly estimate the inductance of an air core inductor, which is a coil that uses air (instead of ferrite or iron) as the magnetic core. Air-core inductors are common in RF circuits, filters, oscillators, matching networks, and antenna designs because they avoid core saturation and often have better high-frequency behavior.
Enter the number of turns, the coil diameter, and the winding length. The calculator then applies a standard Wheeler approximation to compute inductance in microhenries (µH) and millihenries (mH).
How the calculation works
Wheeler single-layer formula
For a single-layer solenoid coil, Wheeler’s equation is:
L(µH) = (r²N²) / (9r + 10l)
- L = inductance in microhenries
- r = coil radius in inches
- l = coil length in inches
- N = number of turns
The formula is fast and useful for design iteration. For final precision, always validate with measurement (LCR meter, VNA, or impedance analyzer), because real coils are affected by spacing, wire insulation, nearby metal, and lead geometry.
Input tips for better results
1) Use mean diameter, not former outer diameter
The most accurate diameter is the approximate centerline diameter of the wire path. If your wire is thick, adjust diameter accordingly instead of using only the mandrel size.
2) Measure wound length carefully
Coil length should cover only the section occupied by turns. Loose winding or intentional spacing increases length and changes inductance.
3) Keep units consistent
You can enter mm, cm, or inches. The calculator converts dimensions internally to inches before applying Wheeler’s equation.
Optional outputs included
- Inductive reactance (XL) if you enter a frequency in kHz.
- Estimated turns for a target inductance if coil geometry is fixed.
These extras are convenient for RF prototyping when you know operating frequency or need to hit a target inductance quickly.
Worked example
Suppose you wind a coil with:
- 20 turns
- 25 mm mean diameter
- 20 mm coil length
With those values, the calculator returns an inductance in the low tens of microhenries range. If your circuit runs at 1 MHz, entering 1000 kHz also shows the reactance, which helps decide if the inductor is suitable for tuning or filtering.
Design guidance for air-core inductors
When air core is a strong choice
- High-frequency circuits where core losses matter.
- Applications requiring linear inductance over current.
- Situations where avoiding magnetic saturation is important.
Tradeoffs to keep in mind
- Air-core inductors usually need more turns for the same L compared with ferrite cores.
- Physical size can become large at higher inductances.
- Parasitic capacitance can create a self-resonant frequency limit.
Common mistakes
- Using outside form diameter instead of mean turn diameter.
- Ignoring turn spacing changes after soldering or handling.
- Placing the coil near metal surfaces that reduce effective inductance.
- Expecting one formula to cover multi-layer coils accurately.
Frequently asked questions
Is this calculator valid for multilayer inductors?
Not directly. This page uses a single-layer Wheeler approximation. Multilayer coils require different models.
Why does measured inductance differ from calculated inductance?
Small geometric differences, wire insulation thickness, test frequency, fixture parasitics, and nearby objects all affect measured values. Treat the result as a design estimate, then trim in hardware.
Can I use this for RF work?
Yes. It is useful for initial RF design and coil prototyping, especially when paired with measurement tools for final tuning.
Final note
Use this air core inductor calculator to get fast first-pass values, then build, measure, and iterate. That workflow gives the best real-world performance in analog and RF circuits.