Solenoid Magnetic Field Calculator

Formula

How this is calculated

A solenoid is a tightly wound coil of wire. When current flows through it, the field inside an ideal (infinitely long) solenoid is nearly uniform and parallel to its axis. This calculator takes three inputs: the number of turns N (dimensionless count of wire loops), the coil length L in meters, and the current I in amperes. The turn density is computed as n = N / L, the number of turns per meter.

The axial field is then B = μ0 · n · I, where μ0 = 4π×10⁻⁷ T·m/A is the permeability of free space. The result B is reported in tesla, along with handy conversions to millitesla and gauss (1 T = 10⁴ G). Increasing the turns, increasing the current, or shortening the coil all raise the field.

The model assumes an air (or vacuum) core, a long coil where edge effects are negligible, and a single layer of evenly spaced turns. For a ferromagnetic core, multiply by the relative permeability μr. Near the ends of a real solenoid the field is roughly half the interior value, and outside an ideal solenoid the field is approximately zero. Length must be greater than zero to define a finite turn density.