Solenoid Magnetic Field Calculator
The magnetic field inside a solenoid from its turns, length, current and core material, and the inductance of the coil.
Inside a long coil the field is uniform and equal to μ₀ × μᵣ × n × I, where n is turns per metre.
How the solenoid magnetic field calculator works
Inside a long coil the field is uniform and equal to μ₀ × μᵣ × n × I, where n is turns per metre. An air core has μᵣ = 1; a soft-iron core multiplies the field hundreds or thousands of times, which is how an electromagnet lifts scrap. The inductance follows from the same geometry: L = μ₀ μᵣ N² A ÷ ℓ.
Formula: B = μ₀ μᵣ (N ÷ ℓ) I; L = μ₀ μᵣ N² A ÷ ℓ
Worked examples
| Inputs | Field inside the coil (T) | Note |
|---|---|---|
| 500 turns, 10 cm, 2 A, air core | 0.01257 | 12.57 mT |
| Same coil on a soft-iron core (μᵣ 1,000) | 12.56637 | 12.57 T — beyond saturation, in practice |
| 100 turns, 5 cm, 0.5 A | 0.00126 | 1.26 mT |
FAQFrequently asked questions
Where is the field uniform?
Well inside a coil that is much longer than its diameter. Near the ends it drops to about half the central value, and outside the coil it is weak — the formula is for the middle of a long solenoid.
What relative permeability should I use for an iron core?
Soft iron 200–5,000, mild steel about 100, ferrite 20–2,000, nickel–iron alloys up to 100,000. It varies with the field and saturates, so treat large values as upper estimates.
Does the wire gauge matter?
Not for the field — only turns per metre and current. It matters for how much current the wire can carry without overheating, and thinner wire lets you fit more turns per metre.
How strong is a tesla?
Very: Earth’s field is about 50 µT, a fridge magnet a few mT, an MRI scanner 1.5–3 T. Air-core coils reach a few mT; iron cores and superconductors are how larger fields are made.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G, g₀, R, c
- NIST Special Publication 811 — Guide for the use of the International System of Units — unit conversions
- The Engineering ToolBox — material properties — specific heats, expansion coefficients, densities
- National Physical Laboratory — the UK's national measurement institute
Last checked: September 2026. Constants are the CODATA 2018 values; formulas are the standard textbook forms.