Drift velocity calculator
A current of 1.6 A through a 1 mm² wire holding 10²⁸ conduction electrons per cubic metre drifts at only 1 millimetre per second. Enter current, carrier density, cross-section and charge to get the drift speed in metres per second. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Current
- 1.6
- Density
- 10,000,000,000,000,000,000,000,000,000
- Area
- 0.000001
- Charge
- 0
- Drift velocity
- 0.001
Electron drift velocity is the average net speed of free charge carriers along a conductor when a steady current flows. Macroscopic current I is the flux of charge through a cross-section: I equals n times A times q times vd, so the working formula is vd equals I divided by the product of carrier density n, cross-sectional area A, and the elementary charge q. This calculator accepts those four SI quantities — amperes, carriers per cubic metre, square metres, and coulombs — validates that the cross-section is not zero, and returns the drift velocity in metres per second.
What vd = I/(n A q) means and which numbers to enter
In the microscopic picture of a conductor, a huge number of mobile charge carriers — typically electrons in a metal, or electrons and holes in a semiconductor — wander at thermal speeds of hundreds of kilometres per second while a much smaller average velocity builds along the applied electric field. That average net velocity is the electron drift velocity, usually written vd.
A steady current I through a uniform wire is the charge that crosses a given plane each second, which equals the product of carrier density n, cross-sectional area A, the charge q of each carrier, and the drift speed vd. Rearrangement produces the working identity vd equals I divided by n times A times q.
Typical copper densities sit near eight point five times ten to the twenty-eight carriers per cubic metre, so even a few amperes through a square millimetre of copper yield drift speeds of millimetres per second, far slower than the electromagnetic signal that travels near light speed along the same wire. This calculator exists so you can plug SI numbers once, see that order of magnitude, and pin a reproducible metres-per-second result without repeating the algebra.
The model assumes a single carrier type, uniform density, and a well-defined cross-section; it does not solve Boltzmann transport, temperature-dependent mobility, or mixed electron-hole currents. Enter current in amperes, density in inverse cubic metres, area in square metres, and charge in coulombs — for electrons the conventional magnitude is one point six times ten to the minus nineteen coulombs — and the engine returns vd in metres per second together with a formula tag you can quote in a lab notebook.
Where drift velocity is worth working out
Classrooms and tutoring platforms use an electron drift velocity calculator so learners can check millimetre-per-second results for arbitrary current, density, area, and charge without unit-conversion slips by hand. Exam-prep generators need a deterministic oracle that marks wrong the case of a zero cross-section instead of silently returning infinity that a buggy grader might treat as success. Failed validation does not consume balance.
Keep requests in SI units end to end, convert millimetre diameters into square metres with pi r squared before calling, and pin the metres-per-second value in tests so homework checks, LMS plugins, and edge workers stay reproducible without standing up a transport solver of your own. Mobility-based drift from an electric field, Ohm's-law current, and temperature-dependent conductivity remain outside this identity, so treat the number as the classic textbook baseline rather than a full semiconductor model.
What you can do with it
Wire and conductor order-of-magnitude estimates
Sanity-check how slowly electrons actually drift in a known gauge before lab write-ups or design notes that quote millimetres per second.
FAQ
How is electron drift velocity computed from I, n, A, and q?
Send finite numbers current (A), density (m^-3), area (m^2), and charge q (C).
Which value of q should I use for electrons?
Use the elementary charge magnitude about 1.6e-19 C. For holes or ions, pass the appropriate signed or multiple charge in coulombs; the calculator does not look it up for you.
Why is the drift so slow when a lamp lights up at once?
Because the carriers and the signal are different things. The electrons drift at millimetres per second, while the electromagnetic signal that sets them all moving travels along the wire near the speed of light.
How do I enter a wire cross-section given in square millimetres?
Convert it to square metres first: one square millimetre is one millionth of a square metre. The calculator expects SI units throughout and refuses a cross-section of zero or below.
Does it work for semiconductors with both electrons and holes?
Only for one type of carrier at a time. The model assumes a single carrier type with a uniform density, so mixed electron-hole currents and temperature-dependent mobility need a fuller transport model.
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/drift-velocity \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"current":1.6,"density":1e+28,"area":0.000001,"charge":1.6e-19}'const res = await fetch("https://api.kit.forhosting.com/phys/drift-velocity", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"current": 1.6,
"density": 1e+28,
"area": 0.000001,
"charge": 1.6e-19
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/phys/drift-velocity",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"current": 1.6,
"density": 1e+28,
"area": 0.000001,
"charge": 1.6e-19
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/phys/drift-velocity", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"current":1.6,"density":1e+28,"area":0.000001,"charge":1.6e-19}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"current":1.6,"density":1e+28,"area":0.000001,"charge":1.6e-19}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/phys/drift-velocity", 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": 1.6,
"density": 1e+28,
"area": 0.000001,
"charge": 1.6e-19
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "phys.drift_velocity",
"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_density | 1e+40 |
max_abs_area | 1000000 |
max_abs_charge | 0.000001 |
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
Cross-sectional area must be strictly greater than zero: a zero area is rejected with a message that cross-sectional area cannot be zero, because the physical current density would be undefined and the formula would divide by A. Negative area is likewise refused. Density and charge must be non-zero so the denominator n times A times q cannot vanish. Magnitude ceilings keep pathological inputs from overflowing isolate arithmetic while still covering classroom millimetre wires and ordinary laboratory currents. POST a JSON body with four required finite numbers: current, the electric current I in amperes; density, the charge carrier density n in carriers per cubic metre; area, the conductor cross-sectional area A in square metres; and charge, the carrier charge q in coulombs. Each field may arrive as a JSON number or as a numeric string; aliases I, n and carrier_density, A and cross_section, and q and elementary_charge are accepted so notebooks and CAD 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 four inputs, reports drift_velocity in metres per second rounded to twelve decimal places for stable goldens, and includes formula vd equals I over n times A times q, method microscopic_current, and a units object documenting metres per second, amperes, inverse cubic metres, square metres, and coulombs. Pair the response with your own mobility or resistivity identities if you next need electric field or conductivity; this endpoint computes scalar drift speed only and does not emit plots, material tables, or unit conversions from millimetres or AWG.
Where a drift-velocity API earns its keep
Process and curriculum scripts can call this endpoint with fixed n and q for a material table while varying I and A across problem sets.
Integration use cases
Homework and exam checks
Enter current, carrier density, cross-section, and elementary charge, compare metres-per-second results with hand work, and get a clear invalid_input when area is zero.
Curriculum fixtures and auto-graded drills
Produce SI-unit drift-velocity checks for demos, LMS items, and lab notebooks without embedding a charge-transport solver.
Technical questions
What happens if the cross-sectional area is zero?
The task fails with invalid_input. Zero area makes the ideal formula divide by A, so the engine rejects it and does not bill the call.
What does a successful drift-velocity response contain?
Echoed current, density, area, and charge, drift_velocity in m/s, formula vd = I / (n * A * q), method microscopic_current, and a units object for m/s, A, m^-3, m^2, and C.
What does the drift velocity calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.