What this air-core inductance calculator does
This tool estimates the inductance of a single-layer air-core solenoid. Air-core coils are popular in RF circuits, filters, oscillators, antenna matching networks, and precision sensing because they avoid magnetic-core saturation and hysteresis. You get quick results in microhenries (µH), plus an optional reactance value if you enter frequency.
Formula used in the calculator
The calculator uses the classic Wheeler approximation for a single-layer coil:
L(µH) = (d² × N²) / (18d + 40l)
where d is mean coil diameter in inches, l is coil length in inches, and N is number of turns. This equation is fast, reliable for practical coil geometry, and widely used by hobbyists and engineers.
Secondary check shown
The result panel also shows an ideal-solenoid estimate using:
L = μ0N²A / l
This gives a useful reference point, although real-world coils can differ due to spacing, wire thickness, lead length, nearby metal, and non-ideal winding shape.
How to use the calculator correctly
- Enter the total number of turns.
- Choose a dimension unit (mm, cm, or inches).
- Enter mean coil diameter, not necessarily former outside diameter.
- Enter coil length measured along the coil axis (winding span).
- Optionally enter frequency to calculate inductive reactance, XL = 2πfL.
Practical design tips
How to increase inductance
- Increase turns (strongest effect because inductance scales with N²).
- Increase coil diameter.
- Reduce coil length for the same number of turns (tighter winding).
How to decrease inductance
- Use fewer turns.
- Use a smaller diameter.
- Spread turns to increase winding length.
Example
Suppose you build a 20-turn air-core coil with 50 mm mean diameter and 30 mm winding length. The calculator gives an inductance close to the low tens of microhenries. At 1 MHz, you can then estimate inductive reactance to understand how strongly the coil opposes AC current in RF applications.
Limitations and accuracy notes
- This model is for single-layer, air-core, approximately cylindrical coils.
- Multi-layer coils need different equations.
- At high frequencies, parasitic capacitance and skin effect become important.
- Nearby conductive objects can lower Q and shift effective inductance.
Final takeaway
For quick coil prototyping, this inductance calculator is a strong starting point. Use it to size your coil, then validate with measurement (LCR meter or VNA) before finalizing a high-performance design.