Hall coefficient calculator
12 mV of Hall voltage across a strip half a millimetre thick, at 2 mA in a quarter-tesla field, gives a Hall coefficient of 0.012 m³/C. Enter volts, metres, tesla and amperes from a Hall-effect kit, an alloy check or a wafer test. Free in your browser.
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Run — free
Worked example
- Hall voltage
- 1
- Thickness
- 1
- Magnetic field
- 1
- Current
- 1
- Hall coefficient
- 1
- Hall coefficient unit
- m3/C
- Hall voltage unit
- V
- Thickness unit
- m
The Hall coefficient of a conductor is the signed material constant that turns a measured Hall voltage, sample thickness, current, and magnetic field into a volume per unit charge. This calculator accepts four SI numbers—Hall voltage in volts, conductor thickness in meters, magnetic field strength in tesla, and current in amperes—and returns R_H from the closed-form identity R_H equals V_H times t divided by I times B, reported in cubic meters per coulomb. Zero current is rejected for the same reason.
What the Hall coefficient means for a current-carrying conductor in a magnetic field
When a current-carrying conductor sits in a magnetic field that is not parallel to the current, charge carriers experience a Lorentz force that deflects them toward one face of the sample. Charge piles up until the electric field of that pile-up balances the magnetic force, and the voltage measured across the sample perpendicular to both current and field is the Hall voltage V_H.
The Hall coefficient R_H is defined so that this measured voltage, the conductor thickness t along the field, the current I, and the magnetic field strength B collapse to a single material property: R_H equals V_H times t divided by I times B, with SI unit cubic meters per coulomb. For a single carrier type the coefficient is also one over n q, so a negative R_H indicates electrons as the majority carriers (n-type) and a positive R_H indicates holes (p-type).
Metals typically show tiny coefficients near ten to the minus ten or ten to the minus eleven cubic meters per coulomb because carrier density is huge; doped semiconductors can be orders of magnitude larger, which is why Hall measurements remain a workhorse of wafer characterization, alloy checks, and student Hall-effect kits. The sign of R_H follows the signs you supply for V_H, I, and B, which is why reversing the magnet or the current should reverse the Hall voltage if the probes are wired consistently.
Units, laboratory numbers, and what this calculator is not
Keep units strictly SI: convert millivolts to volts, millimeters or micrometers to meters, gauss or millitesla to tesla (one tesla is ten thousand gauss), and milliamperes to amperes before you call, because this calculator does not expand prefixes or unit symbols. A typical copper-strip classroom kit might report a few microvolts of Hall voltage at several amperes in a fraction of a tesla, giving R_H on the order of ten to the minus ten cubic meters per coulomb with a negative sign for electrons.
A lightly doped semiconductor bar can produce millivolts of Hall voltage at milliamperes, so the same formula returns a much larger coefficient whose sign tells you n-type versus p-type without a separate carrier-density tool. The sign of R_H follows the signs of V_H, I, and B: reverse the field or the current and the Hall voltage should reverse; if it does not, check probe wiring before you trust the coefficient.
This landing is for people searching hall coefficient, Hall constant, or R_H equals V_H t over I B; it is not a Hall voltage solver for unknown V_H, not a carrier-density calculator (though n is one over the absolute value of R_H times e for a single carrier), not a Hall-mobility tool, and not a converter from gauss to tesla. Prefer this capability when you already have V_H, t, I, and B and only need the coefficient in cubic meters per coulomb.
What you can do with it
Semiconductor wafer Hall characterization
Convert a van der Pauw or bar Hall voltage, film thickness, bias current, and magnet tesla into R_H in m³/C and read n-type versus p-type from the sign.
Classroom Hall-effect labs
Let students enter measured V_H, t, I, and B and check the coefficient against the textbook identity without a spreadsheet rounding argument.
Metal and alloy carrier-type checks
Reduce microvolt Hall readings on copper, silver, or alloy strips to a signed Hall coefficient for comparison with published m³/C tables.
FAQ
What happens if the magnetic field is zero?
Hall coefficient R_H = V_H t / (I B) is undefined when B is zero, so the calculator rejects that input instead of returning Infinity.
What units does the Hall coefficient calculator use?
SI only: Hall voltage in volts, thickness in meters, magnetic field in tesla, current in amperes. The coefficient is returned in m³/C (cubic meters per coulomb). Convert millivolts, millimeters, and gauss before you call.
What does a negative Hall coefficient mean?
A negative R_H indicates electrons as the majority carriers (n-type). A positive R_H indicates holes (p-type). The sign follows the signs you supply for V_H, I, and B.
What Hall coefficient should I expect for a metal?
A tiny one, typically around 10^-10 or 10^-11 cubic metres per coulomb, because metals have an enormous carrier density. Doped semiconductors can be orders of magnitude larger, which is why Hall measurements are used to characterise them.
What happens if the current or the thickness is zero?
The calculation is refused. A zero current puts a zero in the denominator, and a real conductor must have a positive thickness. Check the values and enter them again in amperes and metres.
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/hall-coefficient \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"hall_voltage":1,"thickness":1,"magnetic_field":1,"current":1}'const res = await fetch("https://api.kit.forhosting.com/phys/hall-coefficient", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"hall_voltage": 1,
"thickness": 1,
"magnetic_field": 1,
"current": 1
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/phys/hall-coefficient",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"hall_voltage": 1,
"thickness": 1,
"magnetic_field": 1,
"current": 1
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/phys/hall-coefficient", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"hall_voltage":1,"thickness":1,"magnetic_field":1,"current":1}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"hall_voltage":1,"thickness":1,"magnetic_field":1,"current":1}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/phys/hall-coefficient", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"hall_voltage": 1,
"thickness": 1,
"magnetic_field": 1,
"current": 1
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "phys.hall_coefficient",
"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.
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 zero magnetic field makes the formula undefined, so the task fails with invalid_input instead of Infinity.
What the Hall coefficient means for a current-carrying conductor in a magnetic field
This endpoint uses the four-number laboratory form, not a microscopic one-over-n-q identity, and does not convert gauss, millimeters, or millivolts for you. Zero magnetic field would send the formula through a zero denominator, so it is rejected with invalid_input rather than a non-finite coefficient that a grader might treat as success.
Input contract, response shape, and error behaviour
If current is zero the task fails similarly. If thickness is not positive the task fails because a physical conductor must have a positive thickness. A pedagogical check: one volt, one meter, one tesla, and one ampere yields a Hall coefficient of one cubic meter per coulomb. A laboratory-scale check with twelve millivolts, half a millimeter, two milliamperes, and a quarter tesla yields 0.012 cubic meters per coulomb. Failed validation is not billed. Send a JSON body with four required finite numbers. hall_voltage, aliases vh, Vh, V_h, and voltage, is the Hall voltage in volts and may be signed so the polarity of the probe pair is preserved. thickness, aliases t and d, is the conductor thickness in meters along the magnetic field and must be strictly positive. magnetic_field, aliases B, b, field, field_strength, and magnetic_field_strength, is the magnetic field strength in tesla; it may be signed for field direction, but it must not be zero. current, aliases I, i, and amperage, is the sample current in amperes and may be signed, but it must not be zero because R_H would then be undefined. Missing fields, empty strings, non-numeric values, and non-finite numbers fail with invalid_input naming the field. If magnetic_field is zero the task fails with a message that magnetic field must be non-zero. On success the body echoes the cleaned hall_voltage, thickness, magnetic_field, and current, sets hall_coefficient to V_H t divided by I B as the primary result in cubic meters per coulomb, hall_coefficient_unit to m3/C, formula to the string R_H = V_H t / (I B), and SI unit labels for every input. Successful API calls cost $0.002 per request.
Units, laboratory numbers, and what this calculator is not
Round-trip checks are easy: hall_coefficient times I times B should recover V_H times t. Invalid_input tasks do not consume prepaid balance, which keeps exploratory scripts cheap when learners deliberately set the magnetic field to zero to confirm the documented error.
Technical questions
How is the Hall coefficient calculated from Hall voltage, thickness, field, and current?
Send finite SI numbers hall_voltage (V), thickness (m, strictly positive), magnetic_field (T, non-zero), and current (A, non-zero). The API returns R_H = V_H t / (I B) in cubic meters per coulomb.
What does the Hall coefficient calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.