Drift velocity calculator
See how slowly electrons really move in a wire: 2 A through 1 square millimetre of typical copper, with 8.5 × 10²⁸ carriers per cubic metre, drift at well under a millimetre per second. Enter current, density, area and charge in SI units. Free in your browser.
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Worked example
- Current
- 2
- Density
- 85,000,000,000,000,000,000,000,000,000
- Area
- 0.000001
- Charge
- 0
- Drift velocity
- 0.0001470588 m/s
Drift velocity is the average net speed of charge carriers along a conductor when a steady current flows. In the standard microscopic model of current, the electric current I equals the product of carrier density n, cross-sectional area A, carrier charge q, and drift velocity vd, which rearranges to the working formula vd equals I divided by n times A times q. This capability takes those four scalars in SI units — amperes, carriers per cubic metre, square metres, and coulombs — and returns the drift velocity in metres per second together with the inputs and the formula label so you can audit the result in lab reports, homework checks, or automation pipelines without re-deriving the algebra every time.
What drift velocity means and when this formula applies
In metals and many semiconductors, free charge carriers move randomly at high thermal speeds but acquire a small average velocity opposite or along the applied field, depending on the sign of the charge. That average net velocity is the drift velocity. Macroscopic current is the flux of charge through a cross-section: I equals n A q vd when n is uniform and the current is steady.
Solving for vd gives a direct estimate of how slowly carriers actually drift compared with the nearly instantaneous propagation of the electromagnetic signal along the wire. Typical copper wire numbers produce drift speeds on the order of millimetres per second or less at ordinary currents, which surprises many students the first time they plug in realistic n, A, and q.
Use this calculator when you already know I, n, A, and q in SI units and need a reproducible vd for a lab notebook, a teaching demo, or a script that grades numerical answers. The model assumes uniform density and cross-section and a single carrier type; multi-carrier systems or position-dependent density need a more detailed transport model than this scalar formula provides.
How to read your drift velocity result
For electrons, q is commonly 1.6e-19 C; for holes or ions use the appropriate elementary multiple. Density and charge must also be non-zero so the denominator does not vanish. Invalid combinations are not charged: missing fields, non-finite values, zero area, zero density, or zero charge.
Keep units consistent: convert millimetres squared to square metres and millimetres of diameter into area with pi r squared before calling, because the capability does not perform unit conversion.
Classroom labs, wire design checks, and automation tips
In introductory electricity labs, students often measure current through a known wire gauge, look up approximate free-electron density for the metal, take q as the elementary charge, and compute vd to compare with textbook orders of magnitude. Prefer SI throughout your pipeline: store AWG or mm diameter only at the edge, convert once to m^2, then call this capability. Never pass area equal to zero or leave density unset when generating synthetic datasets.
When you need resistivity, Ohm's law, or mobility-based drift from electric field, use a dedicated calculator rather than stretching this formula.
What you can do with it
Estimate carrier drift in a copper wire
Given measured current, published free-electron density, wire cross-section, and elementary charge, compute vd in m/s for a lab report or demo.
Batch-check design scenarios
Sweep current or cross-section for a fixed material density and charge to see how drift velocity scales before choosing a conductor size.
FAQ
What formula does the drift velocity calculator use?
vd = I / (n · A · q), where I is current in amperes, n is carrier density in m^-3, A is cross-section in m^2, and q is carrier charge in coulombs. The result is in metres per second.
Why is zero cross-section area rejected?
Area appears in the denominator of the drift-velocity formula.
What value should I use for electron charge q?
Use approximately 1.6×10^-19 C (1.6e-19) for the elementary charge magnitude of a single electron. For ions or multi-electron carriers, scale by the charge number.
Must density and charge be positive?
They must be non-zero finite numbers. Sign conventions for current and charge affect the sign of vd; physically, density is positive and |q| is the charge magnitude, but the solver applies the arithmetic as given.
Why do electrons drift so slowly if a lamp lights up at once?
Because the carriers themselves only creep along, often at millimetres per second or less, while the electromagnetic signal travels along the wire almost instantly. The current starts everywhere in the circuit together even though each electron moves very little.
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/elec/drift-velocity \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"current":2,"density":8.5e+28,"area":0.000001,"charge":1.6e-19}'const res = await fetch("https://api.kit.forhosting.com/elec/drift-velocity", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"current": 2,
"density": 8.5e+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/elec/drift-velocity",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"current": 2,
"density": 8.5e+28,
"area": 0.000001,
"charge": 1.6e-19
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/elec/drift-velocity", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"current":2,"density":8.5e+28,"area":0.000001,"charge":1.6e-19}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"current":2,"density":8.5e+28,"area":0.000001,"charge":1.6e-19}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/elec/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": 2,
"density": 8.5e+28,
"area": 0.000001,
"charge": 1.6e-19
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "elec.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.
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
How to call the calculator and interpret the JSON result
POST an object with four required numbers: current (I in amperes), density (n in m^-3), area (A in m^2), and charge (q in coulombs). Cross-section area must be strictly greater than zero — a zero area is rejected with invalid_input because the physical current density would be undefined. The response echoes the four inputs, returns drift_velocity as a finite number, sets unit to m/s, and includes the formula string vd = I / (n · A · q) for documentation.
Classroom labs, wire design checks, and automation tips
Process and curriculum scripts can call this endpoint with fixed n and q for a material table while varying I and A across problems. Document examples with round scientific notation such as I equals 2 A, n equals 8.5e28 m^-3, A equals 1e-6 m^2, and q equals 1.6e-19 C so reviewers can recompute vd by hand and match the API within floating-point tolerance.
Integration use cases
Grade homework answers automatically
Call the API from a grading script with I, n, A, and q and compare the returned drift_velocity to student submissions without maintaining a separate formula sheet.
Technical questions
How much does the API cost?
Successful calls are billed at $0.002 per item from your prepaid KIT balance. Failed invalid_input requests are not charged. The browser widget runs the same solver free for interactive use.