Wheeler's Approximation
Single-layer air-core coil. Inductance, wire length, and DC resistance.
N Turns
d Coil Diameter
l Coil Length
w Wire Diameter (optional — for DCR)
Results
Inductance (Wheeler)
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Long Solenoid Formula
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Turns
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Wire Length
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Length/Diameter
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DC Resistance
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Helical Coil Calculator
Coil — Single-layer helical winding. Wheeler formula is accurate for l/d > 0.4.
d — Mean coil diameter (centre of wire to centre of wire).
l — Winding length (end to end of the coil, not wire length).
Wire — Conductor diameter. Used to calculate DC resistance (copper assumed).
d — Mean coil diameter (centre of wire to centre of wire).
l — Winding length (end to end of the coil, not wire length).
Wire — Conductor diameter. Used to calculate DC resistance (copper assumed).
Helical Coil Calculator
Wheeler's approximation gives the inductance of a single-layer air-core coil from its physical dimensions. It is more accurate than the long-solenoid formula for practical coils where the length-to-diameter ratio is moderate (0.4 to 10). This calculator also computes wire length and DC resistance.
Wheeler's Formula
L(µH) = d²N² / (18d + 40l) — d, l in inches
More accurate than L = μ₀N²A/l for short coils.
Valid for single-layer, air-core, circular cross-section.
More accurate than L = μ₀N²A/l for short coils.
Valid for single-layer, air-core, circular cross-section.
{body_sibs['solenoid-inductance']} {all_sibs['solenoid-inductance'][1]}.
RF Coil (10 turns / 8mm / 15mm)
d = 0.315 in, l = 0.591 in
L = 0.315² × 100 / (18×0.315 + 40×0.591)
L = 9.92 / 29.31 = 0.34 µH = 338 nH
Wire: 10 × π × 8mm = 251 mm
L = 0.315² × 100 / (18×0.315 + 40×0.591)
L = 9.92 / 29.31 = 0.34 µH = 338 nH
Wire: 10 × π × 8mm = 251 mm
338 nH — typical for VHF/UHF tank circuits. {body_sibs['inductance-calculator']} {all_sibs['inductance-calculator'][1]}.
RF Choke (50 turns / 20mm / 40mm)
L = 12.4 µH. Wire length: 3.14 m.
DCR (0.8mm copper): ~0.11 Ω
DCR (0.8mm copper): ~0.11 Ω
{body_sibs['inductor-energy']} {all_sibs['inductor-energy'][1]}.
Frequently Asked Questions
How does this fit in the inductor calculator family?
Each inductor calculator covers a different aspect: energy storage, current rise, time constant, mutual coupling, load analysis, physical design (solenoid, helical, toroid), and measurement (inductance calculator). Use them together for complete inductor design.
Last updated: March 2026