Air Core Inductor Calculator
This Air Core Inductor Calculator estimates single-layer coil inductance from finished diameter, winding length, and turn count using Wheeler's approximation.
Reverse mode estimates the turns required for a target inductance. It is useful for RF filters, oscillators, antenna matching, resonant tanks, prototypes, and hand-wound coil design.
The result is an initial engineering estimate. Verify the finished coil with an LCR meter because winding pitch, leads, nearby metal, fixtures, and operating frequency affect real inductance.
Engineering tool
Air Core Inductor Calculator
Estimate a single-layer air-core coil inductance or reverse-calculate the turns required for a target value using Wheeler's formula.
Outside diameter of the finished winding.
Axial length occupied by the complete winding.
Total turns in the single-layer winding.
Estimated inductance
401.735497 nH
L(µH) = r²N² / (9r + 10l)
Result console
- Estimated inductance
- 401.735497nH
- Calculated turns
- 10turns
- Practical whole turns
- 10turns
- Coil radius
- 0.1969inch
- Coil length
- 0.7874inch
Wheeler's equation estimates a single-layer air-core coil. Verify the finished winding with an LCR meter and adjust turns or spacing as needed.
Air-Core Coil Dimensions
Diameter is measured across the winding, while length is the axial span occupied by all turns. Wheeler's equation uses radius, not diameter.
Formula reference
Wheeler Air-Core Coil Formula
Wheeler's single-layer approximation requires radius and length in inches. The calculator accepts metric or inch dimensions and performs conversion before applying the equation.
Inductance: L(µH) = r² × N² / (9r + 10l)Required turns: N = √(L × (9r + 10l) / r²)Radius: r = coil diameter / 2Variable definitions
- L
- Estimated inductance in microhenries (µH)
- r
- Coil radius in inches (half the finished diameter)
- l
- Axial winding length in inches
- N
- Number of turns
How to Use This Calculator
- Select whether to estimate inductance or required turns.
- Enter finished coil diameter and axial winding length.
- Enter turn count or target inductance and choose the appropriate units.
- Build and measure the coil, then trim turns or adjust spacing to reach the final value.
Worked Example
10 mm Diameter, 20 mm Length, 10 Turns
r = 5 mm = 0.19685 inch
l = 20 mm = 0.78740 inch
L = (0.19685² × 10²) / (9 × 0.19685 + 10 × 0.78740)
L ≈ 0.401735 µH = 401.735 nH
Engineering Notes
Single-layer approximation
Wheeler's formula is an approximation intended for single-layer cylindrical air-core coils.
Winding geometry matters
Coil spacing, wire diameter, winding pitch, lead length, and nearby metal affect real inductance.
Useful at radio frequencies
Air-core inductors are widely used in RF circuits, filters, antennas, oscillators, and resonant networks.
Measurement is the final check
Measured inductance can differ from the calculated value, so prototypes should be characterized at the intended frequency.
Parasitic capacitance limits frequency
Inter-turn capacitance combines with inductance to create a self-resonant frequency above which the coil no longer behaves as an ideal inductor.
Common Mistakes
- Entering diameter where Wheeler's equation expects radius.
- Mixing millimeters and inches without conversion.
- Using former dimensions instead of the finished winding diameter.
- Ignoring lead inductance, nearby shields, and conductive mounting hardware.
- Assuming the low-frequency inductance remains valid near self-resonance.
Support reference
FAQ
How do you calculate an air-core inductor?
For a single-layer coil, measure winding radius and axial length, count the turns, and apply Wheeler's approximation. This calculator handles the required unit conversion and returns estimated inductance.
What is Wheeler’s formula?
Wheeler's single-layer air-core formula is L(µH) = r²N² / (9r + 10l), where radius and coil length are in inches and N is the number of turns.
Does wire diameter affect inductance?
Yes. Wire diameter affects winding pitch, coil length, spacing, proximity effect, and parasitic capacitance. The basic Wheeler formula represents these effects only indirectly through finished coil dimensions.
Why is measured inductance different from calculated inductance?
Dimension tolerances, winding pitch, lead length, nearby conductors, measurement frequency, fixture parasitics, and the limits of the approximation can shift measured inductance.
Where are air-core inductors used?
Air-core inductors are common in RF filters, oscillators, antenna matching networks, resonant circuits, high-frequency chokes, and applications that must avoid magnetic-core saturation.
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Browse the Inductors calculator category or review component information in the Engineering Reference Center.
This calculator provides a Wheeler-formula estimate for a single-layer air-core coil. Verify geometry, wire properties, Q factor, parasitic capacitance, self-resonance, and measured inductance before production use.