Inductance of a solenoid coil

◇Regarding the “Calculation Method” input field
When calculating air-core coils, we recommend selecting “Specify Nagaoka Coefficient”; for core-type coils, select “Permeance Method.”
(For details on the permeance method, see the related link “Apparent… of Solenoid Coil Cores.”)

◇Calculation Formula (m = meters):
Inductance (when “Specify Nagaoka Coefficient” is selected)
= (Nagaoka Coefficient) × (Permeability in Vacuum) × (Relative Permeability) × (Coil Cross-sectional Area: m²) × (Square of the Number of Turns) ÷ (Coil Length: m)
= K * (4 * π * 10^(-7)) * μr * (π * ((D / 2)^2)) * (N^2) / l

*When “Permiance Method” is selected, replace “(Nagaoka Coefficient) × (Relative Permeability)” with “(Apparent Relative Permeability of the Core).”

Magnetic Flux Density [T: Tesla]
= (Applied Voltage [V]) × (Application Time [seconds]) ÷ (Magnetic Circuit Cross-sectional Area [m²]) ÷ (Number of Turns)

◇ Examples of Relative Permeability (from Wikipedia)
Permalloy: 8000
Iron (99.8% pure iron): 5000
Ferrite (manganese-zinc-based): 640 (or higher)
Ferrite (nickel-zinc-based): 16 – 640
Wood: 1.00000043
Air: 1.00000037
Water: 0.999992