Calculator inputs
Enter dimensions, current, and material data. The input area uses a three-column layout on large screens, two columns on smaller screens, and one column on mobile.
Example data table
| Case | Turns | Length (m) | Radius (m) | Current (A) | μr | z (m) | Ideal Field | Finite Field |
|---|---|---|---|---|---|---|---|---|
| Air-core teaching coil | 500 | 0.25 | 0.02 | 2.00 | 1 | 0.00 | 5.027 mT | 4.963 mT |
| High-permeability core | 800 | 0.30 | 0.03 | 1.50 | 200 | 0.05 | 1.005 T | 0.979 T |
| Long air-core coil | 1200 | 0.40 | 0.025 | 3.00 | 1 | -0.10 | 11.310 mT | 11.121 mT |
These examples illustrate how coil geometry, current, and core permeability influence the final magnetic field.
Formula used
n = N / l
H = nI
Bideal = μ0 μr nI
B(z) = (μ0 μr nI / 2) × [ (z + l/2) / √(R² + (z + l/2)²) - (z - l/2) / √(R² + (z - l/2)²) ]
A = πR²
L = μN²A / l
U = ½LI²
The finite-field equation is valid along the solenoid axis. The inductance expression is an engineering estimate that works best when fringing and leakage are limited.
How to use this calculator
- Enter the total number of turns in the winding.
- Provide the solenoid length and choose its unit.
- Enter the coil radius and choose its unit.
- Enter the current value and current unit.
- Set the relative permeability for the core material.
- Enter the axial position z measured from the coil center.
- Select the display unit for magnetic field output.
- Press Calculate Magnetic Field to see the result above the form.
- Review the summary cards, chart, and derived quantities.
- Download the results as CSV or PDF when needed.
Frequently asked questions
1) What does this calculator measure?
It estimates the magnetic flux density of a solenoid, especially along its centerline. It also reports field intensity, inductance, flux, stored energy, and the difference between ideal and finite-coil behavior.
2) What is the difference between ideal and finite field?
The ideal model assumes a very long solenoid with nearly uniform internal field. The finite model accounts for actual coil length and radius, so it better captures edge effects and off-center axial positions.
3) Why is axial position z important?
The magnetic field changes along the solenoid axis. At the center, the field is usually strongest and most uniform. Near the ends, fringing grows and the field begins to drop.
4) What value should I use for relative permeability?
Use μr = 1 for air or vacuum. Ferromagnetic cores can be far higher, but the actual value depends on material, operating point, and saturation. Use manufacturer data when accuracy matters.
5) Is the inductance result exact?
No. It is a standard engineering estimate based on uniform flux and limited fringing. Real inductance also depends on leakage, winding spacing, core geometry, and magnetic nonlinearity.
6) Can this be used for positions outside the coil?
Yes. The finite axial equation can evaluate points on the centerline both inside and outside the coil. The result usually decreases as the point moves farther from the winding.
7) Why does the chart matter?
The plot helps you see how the field changes from one end of the solenoid to the other. That makes it easier to judge uniformity, edge effects, and usable sensing or actuation regions.
8) Which units are supported?
You can enter lengths in meters, centimeters, or millimeters, current in amperes, milliamperes, or kiloamperes, and display the field in tesla, millitesla, microtesla, or gauss.