Magnetic moment calculator
A 10-turn coil carrying 2 A around 0.05 m² has a magnetic moment of 1 A·m². Enter current, number of turns and loop area to get the moment of a whole coil, not just a single loop. Free in your browser.
- Free
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- No sign-up
- Your data stays on your device
Run — free
Worked example
- Current
- 2
- Turns
- 10
- Area
- 0.05
- Magnetic moment
- 1
This magnetic moment calculator returns the magnetic moment of a planar current loop from three SI quantities: the electric current I in amperes, the number of turns N in the winding, and the enclosed loop area A in square metres. The closed-form relation is μ equals N times I times A, so the moment grows with current, with extra turns, and with a larger loop. The result is reported in ampere-square metres, which is identical to joules per tesla.
What a current-loop magnetic moment is and which SI quantities to enter
The magnetic moment of a planar current loop is the dipole descriptor of how that loop couples to an external magnetic field. In SI units a single-turn planar loop that carries current I and encloses area A has magnetic-moment magnitude μ equals I times A, with the direction given by the right-hand rule along the loop normal.
A tightly wound coil of N turns that share the same area behaves, to this dipole order, as N copies of that loop, so the moment becomes μ equals N times I times A. Current is in amperes, area is in square metres, N is dimensionless, and the product is in ampere-square metres, which is identical to joules per tesla. The formula is the textbook current-loop dipole used in electromagnetism courses, coil-design notes, and the derivation of torque τ equals μ cross B.
It is not a unit conversion: if you already have a moment in Bohr magnetons or erg per gauss, a converter is the right tool; this calculator builds the moment from circuit quantities. It is also not a field solver: it does not return B at a point, mutual inductance, or stored magnetic energy. A zero or negative loop area is not a physical enclosed area for this model, so the engine refuses that domain instead of returning a silent zero that a grader might treat as success.
Convert centimetres squared to square metres and milliamperes to amperes before calling, then pin the ampere-square-metre result in tests. A negative current or a negative turn count reverses the signed moment along the chosen normal, which is the linear dipole response of this model, while zero current or zero turns yields a zero moment without error.
Where a magnetic moment calculator earns its keep
Classrooms and tutoring platforms use a magnetic moment calculator so learners can check μ equals N I A for arbitrary current, turns, and area without unit-conversion slips by hand. Exam-prep generators need a deterministic oracle that marks wrong the case of a zero or negative loop area instead of silently returning zero that a buggy grader might treat as success.
Coil and electromagnet notes convert a winding current, a turn count, and a former area into a dipole moment before estimating torque in a known field or comparing two coil geometries. Failed validation does not consume balance. Keep requests in SI units end to end, convert square centimetres and milliamperes before calling, and pin the ampere-square-metre value in tests so homework checks, LMS plugins, and edge workers stay reproducible without standing up a magnetostatics solver of your own.
Finite-length coils, non-planar windings, and distributed current density remain outside the ideal planar-loop formula, so treat the number as the classic textbook baseline rather than a full field solution. High-turn multilayer coils still use the same product when every turn encloses the same area; if the turns have different areas, sum the individual N I A contributions yourself before comparing to this single-area result.
What you can do with it
Coil and electromagnet notes
Turn a winding current, a turn count, and a former area into a dipole moment in A·m² before estimating torque in a known field.
FAQ
How is the magnetic moment of a current loop computed?
Send finite numbers current I in amperes, turns N, and area A in square metres with A > 0.
What units does the magnetic moment calculator use?
Current is in amperes, area is in square metres, turns are dimensionless, and magnetic moment is in ampere-square metres (A·m²), which is identical to joules per tesla. Convert centimetres squared and milliamperes before calling.
Does this convert Bohr magnetons or erg per gauss?
No. This calculator builds μ from current, turns, and loop area. If you already have a moment and need another unit, use a magnetic-moment unit converter instead.
How do extra turns change the magnetic moment?
A tightly wound coil whose turns share the same area acts like that many copies of one loop, so the moment grows in direct proportion to the number of turns. Ten turns give ten times the moment of a single loop.
Why is a zero or negative loop area rejected?
Because a collapsed or inverted area is not a physical current loop. Instead of returning a silent zero, the calculator refuses it, so a typing slip never passes as a valid moment.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/phys/magnetic-moment \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"current":2,"turns":10,"area":0.05}'const res = await fetch("https://api.kit.forhosting.com/phys/magnetic-moment", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"current": 2,
"turns": 10,
"area": 0.05
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/phys/magnetic-moment",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"current": 2,
"turns": 10,
"area": 0.05
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/phys/magnetic-moment", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"current":2,"turns":10,"area":0.05}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"current":2,"turns":10,"area":0.05}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/phys/magnetic-moment", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"current": 2,
"turns": 10,
"area": 0.05
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "phys.magnetic_moment",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Limits
max_abs_current | 1000000000000 |
max_abs_turns | 1000000000000 |
max_abs_area | 1000000000000 |
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
Input contract, response shape, and error behaviour
Area must be strictly greater than zero: both a zero square-metre input and a negative area fail with a message that a zero or negative loop is not a physical current loop, matching the product promise that a collapsed or inverted area never masquerades as a finite dipole. Current and turns may be zero or negative: zero I or zero N yields zero moment, and a reversed current or turn sense reverses μ. Magnitude ceilings keep pathological inputs from overflowing isolate arithmetic while still covering classroom ampere currents and ordinary laboratory loop areas. POST a JSON body with three required finite numbers: current, the winding current I in amperes; turns, the number of turns N; and area, the enclosed loop area A in square metres. Each field may arrive as a JSON number or as a numeric string; aliases I, i, amperes and amps, N, n, number_of_turns and turns_count, and A, loop_area and area_m2 are accepted so notebooks and lab exports map without renaming columns. Missing fields, empty strings, and non-finite values fail with invalid_input naming the field. On success the body echoes the three inputs, reports magnetic_moment in ampere-square metres, and includes formula μ equals N times I times A, method current_loop, and a units object documenting A·m², A, 1, and m². Pair the response with your own Biot–Savart or torque code if you next need the field at a point or τ equals μ cross B; this endpoint computes the current-loop moment only and does not emit plots, vector maps, or inductance matrices. Round-trip checks are easy: multiply N by I by A and confirm it equals the published magnetic_moment within the same twelve-decimal rounding used for goldens.
Integration use cases
Homework and exam checks
Enter current, turns, and loop area, compare μ = N I A with hand work, and get a clear invalid_input when the enclosed area is zero or negative.
Curriculum fixtures and lab notebooks
Produce SI-unit magnetic-moment checks for demos, auto-graded drills, and write-ups without embedding a magnetostatics solver.
Technical questions
What happens if the loop area is zero or negative?
The task fails with invalid_input. Enclosed area must be positive; a zero or negative loop is not a physical current loop for μ = N I A, so the engine rejects the request and does not bill the call.
What does the magnetic moment calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.