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Electrical mobility

A carrier drifting at 5 centimetres per second in a field of 100 volts per metre has a mobility of 0.0005 square metres per volt-second. Enter the drift velocity and the field strength in SI units to get the mobility. Free in your browser.

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Worked example

If you enter

Drift velocity: 0.05
Electric field: 100

You get

Mobility: 0.0005

In metals, semiconductors, electrolytes, and ionized gases that ratio turns a measured or assigned drift velocity and a known field strength into a material figure of merit used in device design, Hall analysis, and classroom transport problems. This calculator accepts those two SI scalars, divides drift velocity in metres per second by electric field in volts per metre, and returns mobility together with the echoed inputs and the working formula.

Drift gained per unit of field

Electrical mobility tells you how readily a charge carrier picks up speed when an electric field pushes it. Carriers in a metal, a semiconductor, an electrolyte or an ionized gas move about at random, but the field adds a small average drift in one direction. Mobility is that drift velocity divided by the field strength, so it is measured in square metres per volt-second, the same figure semiconductor tables quote for electrons and holes. A carrier drifting at 5 centimetres per second in 100 volts per metre has a mobility of 0.0005 square metres per volt-second. The calculator does not look anything up in a material table: it works with the two numbers you already have.

Where the simple ratio fails, and common slips

The ratio holds in the low-field picture: one type of carrier, a uniform field and a drift that grows in step with that field. At high fields the drift speed saturates, and mixed electron and hole currents or Hall-factor corrections need a fuller model. The most frequent slip is units: centimetres per second or kilovolts per metre are not converted for you, so change them to metres per second and volts per metre first. A field of zero is refused, because the ratio is then undefined, while a drift of zero simply gives a mobility of zero.

What mobility means and when the simple ratio holds

Electrical mobility is the linear-response coefficient that links the average drift velocity of a charge carrier to the electric field that drives it. Typical classroom checks include a drift of five centimetres per second in a field of one hundred volts per metre, which is μ equal to 0.0005 square metres per volt-second, and a silicon-like pair of one hundred forty metres per second in one thousand volts per metre, which is μ equal to 0.14.

The formula assumes a single carrier type, a uniform field, and a drift that is proportional to that field; high-field velocity saturation, mixed electron-hole currents, and Hall-factor corrections need a different model. Because the arithmetic is a single division of finite floats, the result is deterministic: no network, no random draw, and no wall clock enter the solve path.

What you can do with it

Semiconductor low-field mobility from a time-of-flight trace

Divide a measured carrier drift speed by the applied field to report μ in m²/(V·s) for a process notebook or a device-model card.

Ionic and electrophoresis mobility checks

Convert an ion speed in a known electrophoresis field into electrical mobility for conductivity estimates and lab reports.

FAQ

Which units does the electrical mobility calculator expect?

SI only: drift velocity in metres per second and electric field in volts per metre.

Is this the same as the electron-mobility unit converter?

The converter sibling changes an already-known mobility between m²/(V·s) and cm²/(V·s) and does not divide velocity by field.

What does the electrical mobility calculator cost?

The browser tool is free and runs locally.

How do I find mobility from a time-of-flight measurement?

Divide the measured drift speed of the carriers by the applied field. Enter the speed in metres per second and the field in volts per metre, and the result comes out in square metres per volt-second for your notebook or device card.

When does this simple ratio stop being valid?

It assumes one type of carrier, a uniform field and a drift that grows in step with the field. At high fields the speed saturates, and mixed electron-hole currents or Hall corrections call for a different 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

POSThttps://api.kit.forhosting.com/phys/electrical-mobility

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/electrical-mobility \
  -H "Authorization: Bearer $KIT_KEY" \
  -H "Content-Type: application/json" \
  -d '{"drift_velocity":0.05,"electric_field":100}'

const res = await fetch("https://api.kit.forhosting.com/phys/electrical-mobility", {
  method: "POST",
  headers: {
    "Authorization": `Bearer ${process.env.KIT_KEY}`,
    "Content-Type": "application/json"
  },
  body: JSON.stringify({
    "drift_velocity": 0.05,
    "electric_field": 100
  })
});
const { task_id } = await res.json();

import os, requests

res = requests.post(
    "https://api.kit.forhosting.com/phys/electrical-mobility",
    headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
    json={
    "drift_velocity": 0.05,
    "electric_field": 100
},
)
task_id = res.json()["task_id"]

<?php
$res = file_get_contents("https://api.kit.forhosting.com/phys/electrical-mobility", false, stream_context_create([
  "http" => [
    "method"  => "POST",
    "header"  => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
    "content" => '{"drift_velocity":0.05,"electric_field":100}',
  ],
]));
$task = json_decode($res, true);

body := bytes.NewBufferString(`{"drift_velocity":0.05,"electric_field":100}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/phys/electrical-mobility", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)

Example request

{
  "drift_velocity": 0.05,
  "electric_field": 100
}

Example response

{
  "task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
  "type": "phys.electrical_mobility",
  "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

Per request$0.002

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

Electrical mobility is the drift speed a charge carrier gains per unit electric field: μ equals v_d divided by E, reported in square metres per volt-second. A vanishing field is rejected with invalid_input because the ratio is undefined.

What electrical mobility is and when μ = v_d / E applies

In the simplest isothermal, uniform, low-field model the vector relation is v_d equals μ times E for positively charged carriers, and v_d equals minus μ times E when the signed charge is negative and mobility is kept as a positive scalar. Rearranging the scalar magnitudes gives the working identity μ equals v_d divided by E, with SI unit square metres per volt-second, which is identical to square metres per newton-second times coulomb because a volt is a newton-metre per coulomb. That unit is the same figure of merit semiconductor tables quote for electrons and holes in silicon, gallium arsenide, or organic films, and it is also the mobility that appears in the Einstein relation connecting diffusion to drift. This calculator does not look up a material table: it evaluates the ratio from the two numbers you already have.

Input contract, response shape, and why a zero field fails

Numeric values and numeric strings are both accepted; SI prefix strings such as centimetres per second or kilovolts per metre are not expanded, so convert to SI before calling. Each magnitude must stay at most one times ten to the fifteen. Zero drift velocity is legal and yields zero mobility, which is the honest result when carriers are not moving in a finite field. Sign is preserved, so opposite signs of velocity and field produce a negative mobility rather than taking an absolute value that would hide a convention mismatch. POST a JSON body with two required finite numbers: drift_velocity in metres per second and electric_field in volts per metre. Missing fields, empty strings, NaN, Infinity, and non-numeric text fail with invalid_input and name the offending field. On success the body echoes the cleaned inputs, returns mobility as the primary value, sets unit to m^2/(V·s), restates the formula μ = v_d / E, and labels the method drift_over_field.

Where electrical mobility shows up in real work

Semiconductor labs extract a low-field mobility from a measured drift or from a time-of-flight trace and a known applied field, then compare that number with a process table for silicon, germanium, or an organic semiconductor. Introductory electricity courses ask students to combine a drift-velocity homework item with an electric-field homework item so they see that mobility, not current, is the material property. The sibling that converts already-known mobility between m²/(V·s) and cm²/(V·s) answers a different query, as does the calculator that finds drift velocity from current, carrier density, area, and charge. Electrochemistry and electrophoresis quote ionic mobility the same way: a measured ion speed in a known field is μ equals v_d over E, which then feeds conductivity estimates through the product of density, charge, and mobility. Device-model scripts that already store a drift speed and a bias field can call this endpoint instead of re-deriving the algebra in every notebook. Because the implementation is a pure parse engine there is no model, no outbound network, and no clock; every successful API call costs the published base of $0.002 per item and failed validation does not consume prepaid balance. Keep this landing for the search “electrical mobility calculator” (compute μ from v_d and E).

Integration use cases

Classroom transport drills

Students combine a drift-velocity result with a known electric field and check that μ = v_d / E matches the answer key without a unit-conversion side quest.

Technical questions

How do I calculate electrical mobility from drift velocity?

Send finite drift_velocity in m/s and electric_field in V/m. The API returns μ = v_d / E in m²/(V·s), plus the echoed inputs and the formula string.

What happens if the electric field is zero?

The task fails with invalid_input. Electrical mobility μ = v_d / E is undefined when the field vanishes, so that request is not billed.

Read the full KIT documentation →

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