Magnetic dipole moment calculator
A loop carrying 2 A around an area of 0.5 m² has a magnetic dipole moment of 1 A·m². Enter the current and the enclosed area of a single flat loop to get its moment, signed by the right-hand rule. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Current
- 2
- Area
- 0.5
- Magnetic dipole moment
- 1 A·m²
The magnetic dipole moment of a planar current loop is the product of the electric current in the wire and the geometric area that loop encloses: m equals I times A, reported in ampere-square-metres. That closed form is the working definition used in first-year electromagnetism, magnetic-torque problems, and the far-field of a small loop, and it is exactly what this calculator returns from two SI numbers. Send a finite current in amperes and a non-negative finite loop area in square metres; the engine multiplies them with deterministic floating-point arithmetic and echoes the inputs, the moment, the formula string, and the unit.
What the loop formula means and what you get
A planar current loop that carries a steady current I and encloses a geometric area A behaves, at distances large compared with the loop size, as a magnetic dipole whose moment magnitude is the product m equals I times A. In SI units I is in amperes, A is in square metres, and m is in ampere-square-metres, a unit identical to joules per tesla.
The direction of the vector moment is the right-hand-rule normal to the plane of the loop; this calculator returns the signed scalar along that convention, so a positive current with a positive area yields a positive moment and a reversed current yields a negative moment of the same magnitude. The identity is the same one that appears in the torque formula tau equals m cross B, in the potential energy minus m dot B, and in the far-field of a small loop antenna.
It is not a unit conversion: converting an already-known moment among ampere-square-metres, Bohr magnetons, and erg per gauss is a different search intent served by a dedicated converter. This page only multiplies current and area. Zero area is valid and yields a zero moment.
If you have an N-turn coil rather than a single loop, form an effective current N times I first, because the enclosed area is counted once per turn.
Where current-loop magnetic moment calculations fit in study, lab, and product work
Students meet the current-loop formula when a textbook moves from Biot-Savart to the magnetic dipole, when a lab asks for the expected moment of a wire square or circular coil before measuring torque in a known field, or when a contest problem gives I and A and demands m in ampere-square-metres without calculus. Teachers can pre-generate answer keys for modest currents and areas without trusting opaque calculator apps that silently switch units from A·m² to erg per gauss.
Developers call the same contract from scripts to seed deterministic test vectors for magnetostatics demos, to normalize user-entered loop specs before UI plots of torque or far-field, or to satisfy programming-challenge statements that demand m rather than a hand-waved sketch. Contest practice often needs a fast, offline source of ideal-loop values so solutions can be checked without graphing calculators under time pressure. Product and education tools use the product when a learner types amperes and square metres and the UI must show the moment and a clean formula reminder.
Pair it with a magnetic-moment unit converter when you already have m and only need another unit, and with solenoid-field or Lorentz-force helpers when you are building a small lab of free, deterministic electromagnetism tools.
What you can do with it
Homework and lab checks
Compute m = I·A for textbook current loops and verify expected torque or far-field scaling before or after lab measurements.
Coil design and tutoring software
Normalize user-entered loop current and area into the signed scalar moment for design sketches, lessons, and interactive demos.
FAQ
What does the magnetic dipole moment calculator cost?
It is free in your browser on this page.
How is the magnetic dipole moment of a current loop defined?
For a planar current loop, m = I · A, where I is the current in amperes and A is the enclosed area in square metres. The result is in ampere-square-metres (A·m²), equivalent to joules per tesla.
What happens if the area is negative?
If you meant the opposite normal, send a negative current instead of a negative area.
How do I handle an N-turn coil?
The page implements the single-loop product m = I·A. For N turns send an effective current N·I (ampere-turns), or multiply the returned moment by N yourself. Do not send a negative area.
Is this the same as converting magnetic-moment units?
No. This calculator computes m from current and loop area. Converting an already-known moment among A·m², Bohr magnetons, erg/G, and J/T is a different search and belongs on a unit-converter page.
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-dipole-moment \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"current":2,"area":0.5}'const res = await fetch("https://api.kit.forhosting.com/phys/magnetic-dipole-moment", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"current": 2,
"area": 0.5
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/phys/magnetic-dipole-moment",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"current": 2,
"area": 0.5
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/phys/magnetic-dipole-moment", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"current":2,"area":0.5}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"current":2,"area":0.5}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/phys/magnetic-dipole-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,
"area": 0.5
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "phys.magnetic_dipole_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 | 1000000000000000 |
max_abs_area | 1000000000000000 |
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
A negative area, or an area that is not a finite number, is rejected with invalid_input so a signed or corrupted surface cannot silently become a wrong moment. Successful API calls are billed at $0.002; invalid inputs are not charged.
What m = I · A means and what the response contains
The response echoes the normalized current and area, the magnetic_dipole_moment, a method tag current_loop, the formula string m = I · A, and the unit A·m². There is no Biot-Savart integration, no finite-element path, and no random sampling of geometry: the engine either multiplies two finite numbers inside the supported magnitude range or rejects the input with invalid_input. Rejected cases include a missing current or area, a non-finite value, a magnitude above the documented ceiling, and a negative area.
How current and area are read and why negative area fails
Optional leading plus signs and scientific notation on numeric strings are allowed when they parse as finite decimals; embedded spaces, hex prefixes, and non-numeric tokens are rejected with a clear message so a bad cell does not become a wrong ampere-square-metre value. Zero for either input is valid and simply yields a zero magnetic dipole moment. Negative current is allowed: it encodes the opposite right-hand-rule sense without forcing you to flip the geometric area. An area that is missing, infinite, or otherwise not a finite number is likewise rejected, naming the field so the form can mark the control. The preferred fields are current for the loop current in amperes and area for the enclosed surface in square metres, but aliases I, i, amperes, and amps for the current, and A, loop_area, and surface for the area, are accepted so spreadsheets, query strings, and typed forms can reuse the same contract. Negative area is always rejected with invalid_input, because a signed surface does not belong in this scalar current-loop model; if you meant a reversed normal, send a negative current instead of a negative area. Pair the free browser run on this page with the priced API when you need the identical mathematical result inside an automated pipeline without re-implementing the product yourself.
Where current-loop magnetic moment calculations fit in study, lab, and product work
On this page the work runs entirely in your browser; through the API each successful lookup costs $0.002, failed validation is not charged, and nothing is stored after the response returns. That split — free interactive exploration and a priced, identical API — matches the rest of the KIT tier-A catalog and lets you move from a classroom demo to an automated pipeline without changing the mathematical result.
Integration use cases
Deterministic test fixtures
Generate reproducible magnetic_dipole_moment values for unit tests, property checks, and CI assertions on magnetostatics code.