Electron Drift Velocity Calculator

One of the most surprising results in introductory physics: the electrons in your household wiring drift at roughly the speed of a slow-walking snail, about 0.1 mm/s. The light turns on instantly not because the electrons travel fast, but because the electric field propagates through the wire at close to the speed of light.

The formula

v_d = I / (n x q x A)

Where: I = current in amperes. n = number of free electrons per cubic meter (charge carrier density). q = electron charge = 1.602 x 10^-19 C. A = cross-sectional area of the wire in m^2.

Charge carrier density

All three figures below count one free electron per atom, which is the standard textbook simplification:

Copper: n ≈ 8.5 x 10^28 electrons/m^3. Aluminum: n ≈ 6.0 x 10^28 electrons/m^3. Silver: n ≈ 5.9 x 10^28 electrons/m^3.

Copper and silver genuinely do contribute about one electron each. Aluminium is the odd one out: it has three valence electrons, so a full band-structure treatment puts n nearer 1.8 x 10^29, and the drift velocity you get from the 6.0 x 10^28 figure is roughly three times too high. Most introductory texts still use 6.0 x 10^28, which is why it is the number offered here, but be aware of what it assumes.

Wire diameters

The AWG diameters in the dropdown are the bare conductor, not the insulated cable. AWG numbers run backwards, so a bigger number is a thinner wire, and every step of 6 gauges roughly halves the cross-sectional area. That is why moving from 14 AWG to 10 AWG cuts the drift velocity by a factor of about 2.5 at the same current.

Working through an example

A 10 A current in 12 AWG copper wire (diameter = 2.053 mm, A = 3.31 mm^2):

v_d = 10 / (8.5e28 x 1.602e-19 x 3.31e-6) ≈ 2.2 x 10^-4 m/s = 0.22 mm/s

At this drift speed, an electron starting at the power outlet would take about 75 minutes to reach an appliance 1 meter away. Yet the appliance responds in nanoseconds, because the signal propagates as an electromagnetic wave rather than as a particle journey.

Drift vs thermal velocity

Electrons in a metal are in constant random motion at around 10^6 m/s, the Fermi velocity (1.57 x 10^6 m/s in copper). The drift velocity imposed by an applied current is a tiny directional bias on top of that. For the example above the ratio v_drift / v_thermal is about 1.4 x 10^-10, a whisper of order on top of enormous chaos.

Note that this random motion is not thermal in the everyday sense. At room temperature the electrons near the Fermi level are moving at that speed because of the Pauli exclusion principle, not because the metal is warm. Cool the wire to near absolute zero and the Fermi velocity barely changes.