How this instrument works
Push 10 amps through copper and its electrons do not race — they crawl. Every cubic metre of that metal offers about 8.5 × 10²⁸ mobile electrons, so an enormous crowd carries a modest current, and each member need shuffle only fractions of a millimetre per second. Drift velocity names that shuffle: net displacement per second of one charge carrier, averaged over its chaotic thermal motion.
Paul Drude assembled this picture in 1900, treating conduction electrons as a gas rattling between fixed ions. Quantum mechanics later rewrote almost everything underneath his model, yet v_d = I ⁄ (nAq) survived intact. Individual electrons inside copper already move near 1.6 × 10⁶ m/s — Fermi velocity, not thermal jostling — in every direction at once. An applied field biases that storm by a whisper, and a whisper is all any current amounts to.
Three assumptions hold this formula together. Charge spreads evenly across a section, which breaks above a few kilohertz once skin effect crowds carriers toward outer surfaces. One carrier species does all conducting, which breaks in semiconductors where electrons and holes share duty. And carriers answer field strength linearly, which breaks in silicon past roughly 10⁴ V/m, where drift saturates near 10⁵ m/s however hard you push.
- Set Current to whatever your circuit actually draws — amps, milliamps or kiloamps, whichever your meter reads.
- Enter Charge carrier density (per m³): 8.5e28 for copper, 5.9e28 for silver, orders of magnitude lower for doped silicon.
- Give Conductor cross-section in mm², cm² or m² — 2.5 mm² is a common household ring-main conductor.
- Read Drift velocity below, and switch its unit to km/h if you want a number that really makes this point land.
Worked example — 10 amps in 2.5 mm² copper
A kitchen ring main draws 10 A through a 2.5 mm² copper conductor. Copper contributes one free electron per atom, giving n = 8.5 × 10²⁸ m⁻³. Convert that section first: 2.5 mm² = 2.5 × 10⁻⁶ m². Multiply out below the line — 8.5 × 10²⁸ × 2.5 × 10⁻⁶ × 1.602176634 × 10⁻¹⁹ = 34 046.25 — then divide: v_d = 10 ⁄ 34 046.25 = 2.93718 × 10⁻⁴ m/s.
Call it 0.294 millimetres per second, or about 1.06 metres across one full hour: comfortably slower than a garden snail. One electron leaving your fuse box would need most of one working day to reach your bedside lamp ten metres away, yet that lamp lights instantly, because what travels at nearly light speed is an electromagnetic field guided along and around your cable — never its cargo.
Questions
Why is drift velocity so much slower than a signal in a wire?
Because they describe different things. Drift velocity tracks charge carriers themselves, millimetres per second in copper at ordinary currents. Signal travel is a field disturbance propagating along and around a conductor at 50–99% of light speed, set by cable geometry and insulation rather than by carrier motion. Household plumbing offers one fair picture: open your tap and flow begins at the far end at once, though any given molecule takes ages to make that journey.
What sign should drift velocity carry?
This instrument reports magnitude only. Inside metals, carriers are negative, so their real displacement points against conventional current — a fact that surfaces as sign of Hall voltage, and one that puzzled physicists until band theory explained positive Hall coefficients in metals like beryllium. Negate this answer whenever you need a signed vector and your carriers are electrons.
Where does a carrier density figure come from?
For metals, from atomic density times free electrons per atom: copper at 8960 kg/m³ and 63.55 g/mol yields 8.49 × 10²⁸ atoms per cubic metre, each donating one electron, hence 8.5 × 10²⁸ m⁻³. Doping sets it in semiconductors instead, typically 10²⁰ to 10²⁴ m⁻³. Hall-effect measurement supplies n experimentally and remains a standard laboratory route.
Does drift velocity keep climbing with current?
In a metal at everyday currents, yes, proportionally, since n, A and q all stay fixed. Two limits spoil that. Heating raises resistivity and eventually melts a conductor; and in semiconductors carriers stop accelerating once optical phonon emission takes over, pinning drift near 10⁵ m/s in silicon however strong its field. Copper wiring fails thermally long before reaching any such ceiling.
How does drift velocity relate to mobility?
Mobility μ is drift velocity per unit electric field: v_d = μE. Copper sits near 4.4 × 10⁻³ m²/V·s, while electrons in silicon reach about 0.14 and in gallium arsenide 0.85 — one reason compound semiconductors dominate high-frequency parts. Reach for this calculator when current and geometry are known; reach for mobility when field strength is what you have instead.
What mistake do people actually make here?
Feeding cross-section figures in mm² into arithmetic expecting m². A 2.5 mm² wire measures 2.5 × 10⁻⁶ m², so that slip inflates drift velocity one-million-fold and yields answers faster than light. Pick your unit from the Conductor cross-section menu rather than converting by hand, then sanity-check any metal result against millimetre-per-second reality.