Coil Inductance Calculator
Single-Layer Coil (Solenoid)
Wheeler's formula for single-layer air-core solenoid
Multi-Layer Coil
Wheeler's formula for multi-layer air-core coil
Formula
Single-layer: L(µH) = (r² × N²) / (9r + 10l) | Multi-layer: L(µH) = 0.8 × (r² × N²) / (6r + 9l + 10d) | (r, l, d in inches)
Frequently Asked Questions
What is Wheeler's formula?
Wheeler's formula is an empirical approximation for calculating the inductance of air-core coils. For single-layer solenoids: L(µH) = (r² × N²) / (9r + 10l), where r is the radius and l is the length in inches. It is accurate to within 1% when the coil length is greater than 0.4 times the diameter.
How does coil geometry affect inductance?
Inductance increases with the square of the number of turns, and with larger coil diameter. Longer coils (more spread out turns) have lower inductance. A compact coil with many turns on a small form will have higher inductance per unit length.
What about coils with magnetic cores?
This calculator is for air-core coils. For coils with ferrite or iron cores, multiply the air-core inductance by the relative permeability (µr) of the core material. Ferrite cores typically have µr from 100 to 10,000.
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