Last updated: 2026-07-01

Drift Velocity

Drift velocity is the net average speed at which charge carriers — usually free electrons — travel along a conductor when a current flows through it. The carriers themselves move rapidly and chaotically, colliding constantly with the atoms of the metal, but a small steady drift superimposed on that random motion is what carries the current. This calculator finds the drift velocity from the current, the density of charge carriers, the conductor's cross-sectional area, and the charge on each carrier, using $v_d = I / (n A q)$.

Where the formula comes from

In a time $t$, the carriers drift a distance $v_d\, t$ along the wire. All the carriers within that length pass through a given cross-section, so the volume they sweep out is $A\, v_d\, t$. Multiplying by the carrier density $n$ gives the number of carriers, and multiplying by the charge $q$ on each gives the total charge that crosses the section:

Current is charge per unit time, $I = Q/t$, so the time cancels:

Solving for the drift velocity gives $v_d = I / (n A q)$.

Formula

For a metal, $n$ is the number of free electrons per cubic metre — about $8.5\times10^{28}\ \text{m}^{-3}$ for copper — and $q$ is the elementary charge $e = 1.602\times10^{-19}\ \text{C}$.

Worked example

Consider a current of $I = 1\ \text{A}$ in a copper wire with a cross-sectional area of $A = 1\ \text{mm}^2 = 1\times10^{-6}\ \text{m}^2$. Copper has $n = 8.5\times10^{28}$ free electrons per cubic metre, and each electron carries $q = 1.602\times10^{-19}\ \text{C}$:

That is about 0.073 mm/s, or roughly 7 centimetres per hour — a strikingly slow crawl for something that lights a bulb the moment the switch is flipped.

Why drift velocity is so small

The drift velocity is tiny not because the electrons are sluggish but because there are so many of them. A single cubic millimetre of copper contains around $8.5\times10^{19}$ free electrons. With such an enormous reservoir of carriers, each one only has to inch forward to deliver a substantial current. The random thermal speed of those same electrons is on the order of $10^6\ \text{m/s}$ — more than ten billion times faster than the drift — but that motion averages to zero and contributes no net current.

Drift velocity versus signal speed

The slowness of the drift raises an obvious puzzle: if electrons creep along at fractions of a millimetre per second, why does a lamp light up the instant the switch closes? The answer is that the electric signal is not the same as the electrons. When the circuit is completed, an electric field spreads through the conductor at a large fraction of the speed of light, and every carrier along the wire begins to drift almost simultaneously. The current is established across the whole circuit in a tiny fraction of a second, even though any individual electron has barely moved.

Limitations

The formula assumes a single type of carrier with a uniform density moving through a conductor of constant cross-section. In semiconductors both electrons and holes contribute, each with its own density and mobility, so the current is the sum of two drift terms. The carrier density $n$ also varies between materials by many orders of magnitude, which is why the same current produces a far higher drift velocity in a lightly doped semiconductor than in a metal. For everyday metallic wiring, though, the single-carrier result above is an excellent estimate.