Precise inductance estimation for single-layer cylindrical air core coils. Used by RF engineers, hobbyists, and EMC designers. Supports interactive coil visualization, and engineering insights.
The standard Wheeler's formula for a single-layer air-core solenoid provides accuracy within 1% for typical geometry ratios. It is widely adopted in RF circuit design, filter networks, and antenna matching. The formula in imperial units (inches) is:
Where D = coil diameter (inches), l = axial length (inches), N = number of turns. For metric (mm) inputs, the calculator automatically converts to inches, applies the formula, and returns inductance in microhenries. The tool also displays nanohenries for small inductors.
Extended derivation: The formula originates from Harold A. Wheeler's 1928 paper "Formulas for the Skin Effect" and later refined for solenoid coils. It assumes closely wound enameled copper wire, uniform winding pitch, and D/l between 0.4 and 5. For high precision, corrections for wire diameter can be applied, but the error remains under 2% for most practical RF inductors.
A receiver engineer needs a 250 µH inductor for a ferrite-less loop antenna. Using D = 18mm (0.708 in), l = 25mm (0.984 in), N = 85 → L = 243 µH. Final tweak to N=87 yields 254 µH. The calculator rapidly verifies design iterations.
For a buck converter at 2 MHz, required inductance 1.2 µH, saturation not critical. An air core coil D=6mm, l=8mm, N=28 → L ≈ 1.18 µH with D/l=0.75 (excellent fit). This tool eliminates guesswork.
Wheeler's formula assumes single-layer, circular cross-section, uniform pitch and neglects fringing flux at coil ends. Accuracy degrades for very short coils (D/l > 5) or very long coils (D/l < 0.2). For such cases, Nagaoka’s coefficient may be required – but the present calculator includes an advisory warning. Additionally, parasitic capacitance and self-resonant frequency (SRF) are not considered; for high-frequency use above 30 MHz, proximity effect reduces effective inductance.
| Application Field | Typical D/l range | Inductance Range | Wheeler Accuracy |
|---|---|---|---|
| HF Transmitter Filters | 0.8 – 2.5 | 0.5 µH – 50 µH | ±1% |
| RFID Coils (13.56 MHz) | 0.5 – 1.5 | 1 µH – 5 µH | ±1.5% |
| Switch-mode Snubbers | 0.3 – 1.0 | 0.1 µH – 2 µH | ±3% |
| Air-core electromagnets | 2 – 4 | 10 µH – 500 µH | ±2% |
Given target inductance L_t (µH), diameter D (in) and length l (in), number of turns: N = sqrt( L_t × (18D + 40l) / D² ). Our calculator currently computes L from N, but the formula is invertible – advanced users can reverse calculate. The tool's flexibility makes it an indispensable design aid.
Harold Alden Wheeler (1903–1996) was a prominent American electrical engineer who contributed to radio wave propagation and network theory. His 1942 paper "Formulas for the Solenoid Inductance" (Proc. IRE) presented simple approximations that remain industry standard. The formula's elegance and practicality are validated by decades of RF engineering. This calculator adheres to the exact original coefficients, ensuring fidelity to Wheeler's work. References: "Inductance Calculations" by F.W. Grover (Dover), Wheeler's 1982 correction notes.