What formula does this tool use?

B = μ₀ · μᵣ · n · I, where μ₀ = 4π × 10⁻⁷ T·m/A is the permeability of free space, μᵣ is the relative permeability of the core material (1 for air), n is the number of turns per meter, and I is the current in amperes.

What is the difference between N and n?

N is the total number of wire turns wound on the solenoid. n (lowercase) is the turn density: n = N / L, where L is the solenoid length in meters. The field depends on turn density, not total turns alone.

Why does the formula assume an ideal solenoid?

An ideal solenoid is infinitely long and tightly wound. In this model, the field inside is perfectly uniform and parallel to the axis, and the field outside is zero. For real solenoids, fringing fields appear at the ends, but the formula is accurate in the center region.

How does a ferromagnetic core change the field?

A ferromagnetic core (iron, silicon steel, ferrite) has a relative permeability μᵣ much greater than 1 — often hundreds to thousands. The field is multiplied by μᵣ, which is why transformer and relay cores dramatically amplify the flux compared to an air-core coil.

What units does this calculator use?

Input: amperes (A) for current, meters (m) or centimeters (cm) for length. Output: Tesla (T), millitesla (mT), microtesla (μT), and Gauss (G). 1 T = 1000 mT = 10,000 G.

Magnetic Field Solenoid

Enter turns per meter and current to compute the uniform magnetic field inside an ideal solenoid via B = μ₀nI.

Solenoid Parameters

Number of Turns (N)

Total wire turns wound on the solenoid.

Solenoid Length (L)

Physical length of the winding.

Current (I)

Current through the solenoid wire in amperes.

Relative Permeability (μᵣ)

1 = air/vacuum; iron ~200–5000; ferrite ~100–10000.

Formula

B = μ₀ · μᵣ · n · I

μ₀ = 4π × 10⁻⁷ T·m/A | n = N / L

Results

Enter solenoid parameters and click Calculate.

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Summary

This tool calculates the uniform magnetic field (B) inside an ideal, infinite solenoid using B = μ₀nI, where μ₀ is the permeability of free space (4π × 10⁻⁷ T·m/A), n is the number of turns per meter of length, and I is the current in amperes. You can enter turns and length separately, or supply n directly. Results are shown in Tesla, millitesla, microtesla, and Gauss.

How it works

Enter the number of turns (N) and the solenoid length, or enter turns per meter (n) directly.
Enter the current (I) flowing through the solenoid wire in amperes.
Optionally enter a relative permeability (μᵣ) for a ferromagnetic core; default is 1 (air/vacuum).
The tool computes n = N / L if N and L are given, then evaluates B = μ₀ · μᵣ · n · I.
Results are displayed in Tesla, millitesla, microtesla, and Gauss.

Use cases

Physics homework and exam preparation involving solenoid problems.
Designing electromagnets for lab experiments or classroom demos.
Estimating the field strength inside a relay or contactor coil.
Comparing air-core vs. ferromagnetic-core solenoid fields.
Verifying hand calculations with a quick sanity check.
Teaching the proportional relationship between turns, current, and field.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu