Magnetic Field Calculator
The electromagnet's reach: B = μ₀NI/l for your own solenoid, priced against Earth's field and a fridge magnet, with the push on a wire computed live.
Magnetic Field Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- Long air-core solenoid interior
- No ferromagnetic core — vacuum μ₀ only
In short: The 500-turn coil, 20 cm long, carrying 2 A: B = μ₀NI/l = 6.283185 mT — 125.663706 times Earth's field (≈ 50 µT, approximate) and fridge-magnet class (≈ 5 mT). An MRI torpedoes 1.5–3 T: hundreds of these coils end to end. The force card prices what the field does to a visitor: a 0.1 m wire carrying the same 2 A across the bore feels F = B·I·L = 1.256637 mN — small, but motors are this card multiplied by cleverness. Current off, field off: B = 0 is the electromagnet's honest rest state.
Formula
B = μ₀·N·I / l · F = B·I·L (wire broadside) · Earth ≈ 50 µT, MRI 1.5–3 T
A solenoid's interior field is current times turns per metre, scaled by the vacuum permeability — the field lives in the bore and dies at the ends. It is an ELECTROMAGNET's field: off with the current, on with it, no permanent magnet in sight. The force card is F = BIL, the same law that turns motors, wearing the numbers of your own coil.
Worked Example
- Enter turns, current and coil length.
- Read B in tesla and millitesla.
- Price it against Earth and the fridge magnet before believing it is 'strong'.
- Use the force card to see what the field does to a current-carrying visitor.
Defaults: 6.283185 mT; 125.663706× Earth, fridge-magnet class; wire push 1.256637 mN.
Strengths & Limits Of This Model
Where this engine is strong
- Field priced against Earth and MRI, not in a vacuum
- Wire-push card makes the field tangible
Where it stops
- No core saturation or μᵣ factors
- No exterior field map
Practical Use Cases
Electromagnets
size the winding before spooling
Sensors
know the test field you are making
Teaching
current makes field, quantitatively
Methodology & Editorial Standards
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Magnetic Field Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
Why is the field uniform inside and weak outside?
Inside a long solenoid every turn's field adds straight down the bore; outside, the contributions curl and largely cancel — the field lines that leave must return. The formula prices the interior, where the cancellation is cleanest and the assumption holds best.
How strong is 6.3 millitesla, really?
About 125 times Earth's ~50 microtesla and fridge-magnet class near 5 mT. Clinical MRI runs 1.5–3 T — a few hundred times stronger. The compare card exists because teslas are unfamiliar units and 'milli' hides quickly.
Why does the field vanish with the current?
Because an electromagnet's field IS the current's: B = μ₀NI/l has no other source term. Cut the current and the field collapses — inducing, as it goes, the flyback kick the inductance page prices. Zero field here is the honest off state, not a failure.
Where does the force card's law come from?
F = B·I·L: a wire of length L carrying I across a field B feels a push broadside to both. It is the same interaction that turns motors — there the 'wire' is a loop, the push is a torque, and the current commutates so the push never stops pushing.
Why does more length mean LESS field?
The same turns spread over more length means fewer turns per metre, and the bore field follows turns-per-metre: B = μ₀(N/l)I. Short and dense beats long and sparse — the same lesson the inductance formula teaches from the other side.
What is mu-naught, again?
The vacuum's exchange rate between current and field: 4π×10⁻⁷ T·m/A, traditionally exact, measured to the same eight digits ever since the SI redefined the ampere. Iron cores multiply it by hundreds — the formula's μ₀ becomes μ₀·μᵣ and the same coil bites far harder.
Does the field penetrate the coil's wire?
Copper is effectively transparent to static magnetic fields — the field threads metal unless it is ferromagnetic or moving. Shielding needs iron or active cancellation, which is why magnetically quiet rooms are built, not bought.
How does this pair with the inductance page?
Same coil, two questions: that page prices how hard the coil fights CHANGE (its inertia, L), this page prices how hard it PUSHES (its field, B). The geometry matches across both pages, so the chain — turns, length, current — carries.