How strong is the Earth magnetic field for comparison?

About 25 to 65 microtesla depending on location. A typical air core solenoid produces millitesla range. An iron core electromagnet produces 0.1 to 2 Tesla. MRI machines use 1.5 to 7 Tesla.

What limits the maximum field strength?

Core saturation. Ferrite saturates at about 0.3 to 0.5 Tesla. Iron saturates at about 1.5 to 2 Tesla. Beyond saturation increasing current gives diminishing returns as mu r drops toward 1.

Solenoid Magnetic Field Calculator – Flux Density & Field Strength

B = μ₀μ_r × N × I / l

Magnetic flux density (Tesla) and field strength (A/m) inside a solenoid.

N Number of Turns

I Current

l Solenoid Length

μ_r Relative Permeability (1 = air)

Analysis Results

Flux Density B
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Field Strength H
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B (Gauss)

Turns Density

Ampere-Turns

μ_r

Magnetic Field Inside a Solenoid

Inside a long solenoid, the magnetic field is uniform and parallel to the axis. The field strength depends on turns per unit length, current, and core permeability. Outside the solenoid, the field is approximately zero.

B — Magnetic flux density in Tesla. The "strength" of the field that determines force on a current-carrying conductor.
N × I — Ampere-turns. The magnetomotive force (MMF) driving the field.
l — Solenoid length. Field strength H = NI/l. Shorter solenoid = stronger field.
μ_r — Core permeability. Multiplies B by this factor. Iron cores can amplify the field 1000–10000×.

Solenoid Magnetic Field Calculator

This calculator finds the magnetic flux density (B) and field strength (H) inside a solenoid. The field depends on the number of turns, the current, the solenoid length, and the core material. It is uniform and parallel to the axis inside a long solenoid, and approximately zero outside.

B and H Formulas

H = N × I / l — field strength (A/m)
B = μ&sub0;μ_r × H — flux density (Tesla)

μ&sub0; = 4π × 10&supmin;&sup7; T·m/A
NI = ampere-turns (magnetomotive force)

H depends only on geometry and current. B depends on H multiplied by the core permeability. A high-permeability core dramatically increases B without changing H. For the inductance of this same solenoid, see the Solenoid Inductance Calculator.

Units: Tesla, Gauss, A/m

1 Tesla = 10000 Gauss. Tesla is SI. Gauss is CGS (still widely used in magnetics industry).

Earth's field: ~50 µT = 0.5 Gauss.
Fridge magnet: ~5 mT = 50 Gauss.
Strong electromagnet: 0.1–2 T = 1000–20000 Gauss.
MRI machine: 1.5–7 T.
Strongest lab magnet: ~45 T.

Air-Core Coil (100 turns / 1A / 50mm)

H = 100 × 1 / 0.05 = 2000 A/m
B = 4π×10&supmin;&sup7; × 1 × 2000 = 2.51 mT
= 25.1 Gauss

2.5 mT — about 50 times the Earth's field. Enough for basic experiments and sensor testing, but too weak for actuators. For the current rise time when energising this coil, see the Inductor Current Calculator.

Electromagnet (500 turns / 2A / μ_r = 5000)

H = 500 × 2 / 0.1 = 10000 A/m
B = 4π×10&supmin;&sup7; × 5000 × 10000 = 62.8 T

62.8 T is above saturation for any real iron core (~2 T max). In practice, the core saturates and the actual field is limited to ~1.5–2 T. The calculator gives the theoretical value assuming constant permeability — always check against the core's saturation limit.

Relay Coil (1000 turns / 100mA / μ_r = 2000)

H = 1000 × 0.1 / 0.02 = 5000 A/m
B = 4π×10&supmin;&sup7; × 2000 × 5000 = 12.6 T

Again above saturation. Real relay cores operate at 0.5–1.0 T. The formula shows the mmf (5000 A/m) and the theoretical B — the actual B is limited by the core material. For the coupling between this coil and a nearby coil, see the Mutual Inductance Calculator.

Core Saturation

Ferrite: saturates at 0.3–0.5 T. Good for high-frequency, low-power applications.

Silicon steel: saturates at 1.5–2.0 T. Used in power transformers and motors.

Soft iron: saturates at 1.5–2.0 T. Used in relays and electromagnets.

Beyond saturation: μ_r drops toward 1, and the inductor/electromagnet loses its effectiveness. Increasing current gives diminishing returns.

Frequently Asked Questions

What is the difference between B and H?

H is the applied field (depends on current and geometry only). B is the resulting flux density (depends on H and the core material). In vacuum B = μ&sub0;H. In a core B = μ&sub0;μ_rH. Think of H as the cause and B as the effect.

Is the field really uniform inside the solenoid?

For a long solenoid (length >> diameter), yes, in the central region. Near the ends the field drops to about half. For short coils the approximation is less accurate and numerical methods are needed for precise field mapping.

How do I increase the magnetic field?

Increase NI (more turns or more current), decrease length (concentrate the turns), or add a high-permeability core. The core is the most effective approach — iron can multiply the field by 1000–5000 times.

Can this calculator be used for permanent magnets?

No. This calculator is for electromagnets (field generated by current). Permanent magnets have a fixed magnetisation that does not depend on external current. The remanent flux density B_r is a material property listed on the magnet datasheet.

Last updated: March 2026