Curie's law calculator
A sample with a Curie constant of 2.4 K in a 500 A/m field at 300 K magnetizes to 4 A/m. Enter the Curie constant, the applied field and the absolute temperature to get the magnetization and the susceptibility. Free in your browser.
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- Your data stays on your device
Run — free
Worked example
- Curie constant
- 2.4
- Magnetic field
- 500
- Creativity
- 300
- Magnetization
- 4
- Susceptibility
- 0.008
This Curie's law calculator returns the magnetization of an ideal paramagnetic material from three SI quantities: the Curie constant C of the sample, the applied magnetic field strength H in amperes per metre, and the absolute temperature T in kelvin. The closed-form relation is M equals C times H divided by T, so magnetization grows with the Curie constant and the field and falls as the sample warms.
What Curie's law computes and which SI quantities to enter
Curie's law, established by Pierre Curie in 1895, states that the magnetization of a paramagnetic sample is proportional to the applied magnetic field and inversely proportional to absolute temperature. In SI form the volume magnetic susceptibility is chi equals C over T, and magnetization is M equals chi times H, which collapses to the single quotient M equals C times H divided by T.
The Curie constant C is a material property that collects the density of magnetic moments and their individual strength; for a simple Langevin paramagnet it is proportional to the number of moments per unit volume times the square of the moment over three Boltzmann constants, and in the dimensionless-chi convention it carries the unit kelvin. Magnetic field strength H is the applied field in amperes per metre, not the flux density B in tesla, unless the caller has already absorbed vacuum permeability into a differently defined C.
The inverse-T factor is why paramagnetic response is strong at low temperature and weak when the sample is hot, because thermal agitation randomizes the moments against the aligning field. This calculator evaluates the linear Curie regime only: it does not saturate at high field the way a Brillouin or Langevin function would, and it does not include a Weiss molecular field. Ferromagnets below the Curie point and antiferromagnets near the Néel temperature need Curie–Weiss or other models.
Where a Curie's law calculator earns its keep
Classrooms and tutoring platforms use a Curie's law calculator so learners can check magnetization for arbitrary C, H, and T without unit-conversion slips by hand. Exam-prep generators need a deterministic oracle that marks wrong the case of a zero or negative temperature instead of silently returning infinity that a buggy grader might treat as success. Materials and cryogenics labs compare measured low-field slopes against C over T before fitting a Curie–Weiss theta or a saturation moment.
Failed validation does not consume balance. Keep requests in SI units end to end, convert gauss or oersted fields and Celsius readings to amperes per metre and kelvin before calling, and pin the magnetization value in tests so homework checks, LMS plugins, and edge workers stay reproducible without standing up a magnetostatics solver of your own. High-field saturation, shape demagnetization, and ferromagnetic order remain outside the ideal formula, so treat the number as the classic textbook baseline rather than a full mean-field magnet.
Round-trip checks are easy: divide C by T to recover susceptibility, multiply by H, and confirm it equals the published magnetization within the same twelve-decimal rounding used for goldens.
What you can do with it
Low-field materials screening
Convert a measured Curie constant and a lab field into M = C H / T before fitting Curie–Weiss theta or a saturation curve.
FAQ
Does this implement Curie–Weiss law or high-field saturation?
No. It evaluates the linear Curie form M = C H / T only. Weiss molecular-field shifts (T − θ) and Langevin or Brillouin saturation are out of scope.
What happens if the temperature is zero or negative?
The calculation is refused, because the temperature must be an absolute value in kelvin above zero and the law divides by it. Convert Celsius readings to kelvin first; room temperature is about 300 K.
Why does magnetization fall as the sample warms?
Because thermal agitation randomizes the magnetic moments against the aligning field. The response follows one over the temperature, so it is strong at low temperature and weak when the sample is hot.
Should I enter the field strength H or the flux density B?
The field strength H in amperes per metre, not the flux density B in tesla. Convert gauss or oersted readings first; a zero field gives zero magnetization and a reversed field reverses it.
What is the susceptibility shown with the result?
It is the Curie constant divided by the temperature, the dimensionless factor that multiplies the applied field to give the magnetization. It shrinks as the sample warms and, in this linear model, does not change with the field.
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/curies-law \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"curie_constant":2.4,"magnetic_field":500,"temperature":300}'const res = await fetch("https://api.kit.forhosting.com/phys/curies-law", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"curie_constant": 2.4,
"magnetic_field": 500,
"temperature": 300
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/phys/curies-law",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"curie_constant": 2.4,
"magnetic_field": 500,
"temperature": 300
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/phys/curies-law", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"curie_constant":2.4,"magnetic_field":500,"temperature":300}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"curie_constant":2.4,"magnetic_field":500,"temperature":300}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/phys/curies-law", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"curie_constant": 2.4,
"magnetic_field": 500,
"temperature": 300
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "phys.curies_law",
"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_curie_constant | 1000000000000 |
max_abs_magnetic_field | 1000000000000 |
max_abs_temperature | 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
What Curie's law computes and which SI quantities to enter
Absolute temperature T must be in kelvin: room temperature is about three hundred kelvin, liquid nitrogen about seventy-seven kelvin, and a value at or below zero kelvin is not a thermodynamic temperature.
Input contract, response shape, and error behaviour
Temperature must be strictly greater than zero: both a zero kelvin input and a negative temperature fail with a message that temperature must be a positive absolute temperature, matching the product promise that the one-over-T singularity never masquerades as a finite answer. Curie constant and field strength may be zero or negative: zero C or zero H yields zero magnetization, and a reversed field reverses M, which is the linear response of this model. Magnitude ceilings keep pathological inputs from overflowing isolate arithmetic while still covering classroom ampere-metre fields and ordinary laboratory kelvin ranges. POST a JSON body with three required finite numbers: curie_constant, the material Curie constant C; magnetic_field, the applied field strength H in amperes per metre; and temperature, the absolute temperature T in kelvin. Each field may arrive as a JSON number or as a numeric string; aliases C, curie and curie_const, H, field, field_strength, magnetic_field_strength and h, and T, t, absolute_temperature and kelvin 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 magnetization in amperes per metre, reports susceptibility chi equals C over T as a dimensionless number, and includes formula M equals C times H over T, method curies_law, and a units object documenting A/m, K, A/m, K, and 1. Pair the response with your own saturation or Curie–Weiss code if you next need high-field or ordered-phase behaviour; this endpoint computes the linear Curie magnetization only and does not emit plots, hysteresis loops, or Brillouin curves.
Integration use cases
Homework and exam checks
Enter Curie constant, field strength, and kelvin temperature, compare magnetization with hand work, and get a clear invalid_input when T is zero or negative.
Curriculum fixtures and lab notebooks
Produce SI-unit magnetization checks for demos, auto-graded drills, and write-ups without embedding a magnetic mean-field solver.
Technical questions
How is magnetization computed from Curie's law?
Send finite numbers curie_constant (C), magnetic_field H in A/m, and temperature T in kelvin with T > 0. The API returns M = C · H / T in A/m, plus susceptibility χ = C / T, the echoed inputs, formula, and SI units.
What happens if temperature is zero or negative?
The task fails with invalid_input. Absolute temperature must be positive; at or below zero kelvin Curie's law divides by T, so the engine rejects the request and does not bill the call.
Is magnetic_field the flux density B in tesla or the field strength H?
This calculator wants magnetic field strength H in amperes per metre. If your problem states B in tesla, convert with the SI relation appropriate to your Curie-constant convention before calling; do not paste tesla as H.
What does the Curie's law calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.