Coil Inductance Calculator

This calculator uses Wheeler's formula for a single-layer solenoid: L (µH) = (r² × N²) / (9r + 10l), where r is the coil radius in inches, N is the number of turns, and l is the coil length in inches. For SI units, the formula is converted using µ₀ = 4π × 10⁻⁷ H/m. Wheeler's formula is widely accepted for RF coil design and is accurate to within 1% when the coil length is greater than 0.4× the diameter.

Toroid inductance is calculated using L = (µ₀ × µr × N² × h × ln(OD/ID)) / (2π), where µ₀ is the permeability of free space, µr is the core's relative permeability, N is the number of turns, h is the core height, OD is the outer diameter, and ID is the inner diameter. Toroids are preferred in RF applications because their closed magnetic path minimises flux leakage.

Inductance is measured in Henrys (H). Because one Henry is quite large for most practical coils, sub-units are commonly used: milli-henry (mH = 10⁻³ H), micro-henry (µH = 10⁻⁶ H), and nano-henry (nH = 10⁻⁹ H). RF inductors for amateur radio or matching circuits typically fall in the µH to mH range.

Relative permeability (µr) describes how much more magnetically permeable a core material is compared to free space (air, µr = 1). A ferrite toroid core might have µr values from 10 to several thousand. Higher µr dramatically increases inductance — multiplying the air-core value by µr — which is why ferrite cores allow more compact coil designs.

Yes, coil length has a significant effect. A shorter coil (more tightly wound turns) produces higher inductance for the same number of turns and diameter, while a longer coil results in lower inductance. This is because a tighter winding increases the magnetic flux linkage between adjacent turns.

Wire diameter itself has a minor direct effect on inductance for a fixed coil geometry, but it determines the maximum number of turns that can fit in a given coil length. Thinner wire allows more turns per unit length, increasing inductance. Wire diameter also affects the coil's DC resistance and Q-factor, which are important for efficiency.

A single-layer coil has all turns in one continuous helical layer, making it simpler to wind and analyse. Multi-layer coils stack turns in multiple concentric layers, achieving higher inductance in a shorter length — useful when space is constrained. Single-layer coils generally have lower self-capacitance and higher Q, making them preferred for RF applications.

Yes — this calculator is well suited for designing RF chokes, tank circuit inductors, and matching network components. Enter your target frequency and desired inductance, then adjust the number of turns and coil dimensions until you reach the required value. For air-core coils at RF frequencies, keep the coil length-to-diameter ratio close to 1:1 for maximum Q.