Coil Inductance Design Calculator
Estimate inductance using a long-solenoid or single-layer air-core Wheeler model, then solve dimensions or turns from a target inductance.
Inputs and reverse calculation
Calculated results
| Inductance | 493.48 nH |
|---|---|
| Diameter | 10 mm |
| Length | 20 mm |
| Turns | 10 |
| Cross-sectional area | 78.54 mm² |
| Relative permeability | 1 |
How to interpret the result
Coil inductance depends on geometry, turns and the magnetic path. The long-solenoid model assumes a nearly uniform internal field. The Wheeler model estimates a single-layer air-core cylindrical winding. Editing geometry calculates L; editing L changes only the selected inverse quantity.
Formulas and units
A=πd²/4. Solenoid: L=μ₀μrN²A/l, with μ₀=4π×10⁻⁷ H/m. Wheeler: L[µH]=d[in]²N²/(18d[in]+40l[in]); dimensions are converted from metres to inches before calculation.
Worked example
An air coil 10 mm in diameter, 20 mm long and 10 turns gives about 0.49348 µH with the long-solenoid model. For a Wheeler example with diameter=length=25.4 mm and 10 turns, L=100/(18+40)=1.72414 µH. Different model assumptions need not give identical values.
Scope and limitations
These estimates omit leads, winding capacitance, skin effect, losses, core saturation and operating frequency. This Wheeler formula is a single-layer air-core approximation, rather than a toroidal, planar or multilayer-core model. Inverse turns may be fractional; round to a buildable value and calculate forward again. Invalid geometry and numeric overflow are rejected.
Common questions
Is diameter the wire diameter or coil diameter?
Enter the mean winding diameter, rather than the wire diameter. Length is the winding’s axial length.
Why is permeability hidden in Wheeler mode?
This formula is restricted to a single-layer air-core coil. Multiplying by a permeability value does not model a core and air gap accurately.
Why can solving for length fail?
The chosen diameter and turns may not reach the target at any positive length. A nonpositive inverse length is rejected while the previous result is retained. Try solving turns or diameter.
Related tools
Formula and data sources
- H. A. Wheeler: Simple Inductance Formulas for Radio Coils (1928)
- MIT electromagnetic field text: solenoid inductance
- Coilcraft: Current and temperature ratings
Rebuilt from the extracted Electrodoc Pro 5.2 specification. Added, inferred and corrected behavior is identified in the limitations. Updated 2026-11-13.