Electron Speed (Drift Velocity) Calculator

Formula

How this is calculated

When a voltage is applied across a conductor, each free electron experiences a net electric force directed opposite to the field. Between collisions with lattice atoms the electrons accelerate, then scatter and lose their gained momentum. The net result is a slow, steady average displacement called drift velocity. It is given by v_d = I / (n × A × e), where I is the current in amperes, n is the free-electron density of the material (electrons per m³), A is the cross-sectional area of the wire (m²), and e = 1.602 × 10⁻¹⁹ C is the elementary charge.

For copper carrying 10 A in a 2 mm-diameter wire, the drift velocity is only about 0.24 mm/s — far slower than a snail. Yet the electric field that exerts the force on all electrons propagates at a large fraction of the speed of light (~2 × 10⁸ m/s in a typical cable). The signal travels fast because the field nudges every electron in the wire simultaneously; the individual electrons themselves hardly move. Think of a long row of marbles: push one end and the far end responds almost instantly, even though each marble barely shifts.

Free-electron density values used here are standard textbook figures: copper ≈ 8.5 × 10²⁸ /m³ (one valence electron per atom; density 8,960 kg/m³; molar mass 63.55 g/mol). The formula assumes uniform current density across the cross-section, which holds well at DC and at low frequencies; at high AC frequencies skin effect concentrates current toward the surface, reducing the effective area and increasing the true drift velocity there.