Electron Drift Velocity Calculator

One of the most surprising results in introductory physics: the electrons in your household wiring are drifting 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

Copper: n ≈ 8.5 x 10^28 electrons/m^3 (one free electron per atom). Aluminum: n ≈ 6.0 x 10^28 electrons/m^3. Silver: n ≈ 5.9 x 10^28 electrons/m^3.

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 over an hour to reach an appliance 1 meter away. Yet the appliance responds in microseconds — the signal propagates as an electromagnetic wave, not as a particle journey.

Drift vs thermal velocity

Electrons in a metal are constantly in random thermal motion at roughly 10^5 to 10^6 m/s — the Fermi velocity. The drift velocity imposed by an applied current is a tiny directional bias on top of this random motion. The ratio v_drift / v_thermal is typically around 10^-9 for household currents. It is a whisper of order on top of enormous chaos.