Magnetic Field of a Wire Calculator
The magnetic field around a long straight wire carrying a current — and, for comparison, the field inside a solenoid of the same current — from the Biot–Savart result.
Around a long straight wire the field is μ₀I / 2πr: it falls off with the first power of distance, not the square.
How the magnetic field of a wire calculator works
Around a long straight wire the field is μ₀I / 2πr: it falls off with the first power of distance, not the square. A 10-ampere wire produces 40 microtesla at 5 centimeters — about the strength of the Earth's field.
A solenoid concentrates the same current: μ₀ n I inside, where n is turns per meter. A thousand turns per meter at 10 A gives 12.6 millitesla, three hundred times the wire.
Formula: B = μ₀ I / (2π r); B_solenoid = μ₀ n I
Worked examples
| Inputs | Field around the wire (µT) | Note |
|---|---|---|
| 10 A at 5 cm | 40 | 40 µT — about the Earth's field |
| A household cable | 8.667 | well below the Earth's field |
| An iron-cored solenoid | 40 | a field in tesla |
FAQFrequently asked questions
How strong is the field around a wire?
Weak — 10 A at 5 cm gives about 40 µT, roughly the Earth's field. Household cables produce far less at normal distances.
Why does it fall with distance, not distance squared?
Because the field lines are circles around the wire, and the field spreads over a circumference proportional to r, not an area proportional to r².
What is a solenoid?
A coil of wire. The turns add their fields inside, giving a uniform field of μ₀nI that is far stronger than a single wire's.
What does an iron core do?
Multiplies the field by the core's relative permeability — hundreds to thousands for soft iron — which is how electromagnets reach tesla fields.
Is this the Biot–Savart law?
It is the result of applying it to a straight wire. The general law integrates along any current path; the straight wire and the solenoid are the two closed forms everyone uses.
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 Institute of Standards and Technology — the US measurement authority
Last checked: September 2026. Constants are the CODATA 2018 values; formulas are the standard textbook forms.