Solenoid Calculator (Magnetic Field and Inductance)

What this tool does

Inside a long coil the field is almost perfectly uniform and depends only on turns per metre and current — not on the diameter. The textbook inductance formula assumes the coil is much longer than it is wide; real coils leak field at the ends and come out lower. Wheeler's 1928 formula allows for that and is accurate to about 1 % for air-cored coils longer than 0.4 times their diameter, which is why both are shown. An iron core multiplies the field by its relative permeability only until it saturates, somewhere around 1.5 to 2 T for iron and much earlier for ferrite.

Formula

B = μ₀ μᵣ N I ÷ l · L = μ₀ μᵣ N² A ÷ l · Wheeler (air): L[µH] = r² N² ÷ (2.54 × (9r + 10l)), r and l in cm

Variables

Worked example

Limitations

• The formula assumes ideal geometry — an infinitely long wire or coil, a perfectly uniform sphere — in empty space or a uniform material. Real parts come close, but ends, nearby metal and magnetic materials change the field.
• The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.