Solenoid Field Calculator

Estimate the magnetic field of a long cylindrical coil

Calculation
Quick Guide

For an ideal long solenoid, the inner field is approximately homogeneous. Field strength depends on turn density and current.

The model is a practical first estimate for air-core and core-loaded coils with assumed constant μr.

Schema:
1) Set geometry and material
2) Enter N/I or set target B
3) Evaluate B, H and inverse requirements
Formulas (MathJax)
\[H\approx\frac{N\,I}{l}\]
\[B\approx\mu_0\mu_r\frac{N\,I}{l}\]
\[I=\frac{B\,l}{\mu_0\mu_rN}\]
\[N=\frac{B\,l}{\mu_0\mu_rI}\]
Legend
  • \(B\): Flux density [T]
  • \(H\): Field strength [A/m]
  • \(N\): Turns [-]
  • \(I\): Current [A]
  • \(l\): Magnetic length [m]
  • \(\mu_r\): Relative permeability [-]
  • \(\mu_0\): vacuum permeability \(4\pi\cdot10^{-7}\,\mathrm{H/m}\)


Examples
With N=500, I=1.2A and l=200mm at μr=1, the resulting B is in the mT range with clearly defined H.
For target B=4mT, required current or required turn count can be solved directly in inverse mode.
Detailed Documentation & Summary

The solenoid-field calculator is based on the standard long-coil approximation. Inside the coil, the magnetic field is approximately uniform, while edge effects occur near coil ends. This makes the model suitable for first-pass sizing, educational use, and plausibility checks.

With ferromagnetic cores, μr is not truly constant and depends on B, temperature, and bias. For precise design, include saturation, air-gap effects, leakage, frequency, and losses. Still, the linear model is very useful in early design phases.

Summary
  • Calculates B and H for a solenoid setup
  • Supports inverse solutions for I and N
  • Well suited for quick preliminary magnetic design

Is this page helpful?            
Thank you for your feedback!

Sorry about that

How can we improve it?