Electron Drift Velocity Calculator

Drift velocity is the average velocity of free electrons inside a conductor when an electric field is present (e.g. when a wire is connected to a battery). Electrons actually move randomly very fast due to thermal energy, but the electric field gives them a slow, one-directional net motion — this net motion is called drift velocity, and this net motion is what forms the electric current.

v_d = I / (n × A × q). v_d is the drift velocity (m/s), I is the current (amperes), n is the free-electron number density per unit volume (m⁻³), A is the wire’s cross-sectional area (m²), and q is the charge of one electron, 1.602176634×10⁻¹⁹ coulombs (exact value per the 2019 SI definition). The inverse formula: I = n × A × q × v_d.

About 7.3430×10⁻⁵ m/s, or 0.07343 mm/s. The calculation: v_d = 1 / (8.5×10²⁸ × 1×10⁻⁶ × 1.602176634×10⁻¹⁹) = 1 / 13618.5 = 7.3430×10⁻⁵ m/s. Electrons crawl at less than a tenth of a millimeter per second — far slower than most people imagine.

In a 1 mm² copper wire carrying 1 A (v_d ≈ 7.3430×10⁻⁵ m/s), one electron needs about 3.78 hours to move 1 meter. In a 12 AWG wire carrying 10 A, electrons travel 100 meters in about 125.2 hours (more than 5 days). This is why this calculator has a transit-time mode: to show how slow drift is compared to the electrical signal.

What travels fast is not the electrons, but the electric field. When the switch is turned on, the electric field propagates along the wire near the speed of light (in typical copper cable about 2×10⁸ m/s), so all electrons throughout the circuit start shifting almost simultaneously. The electrons themselves crawl; the signal is what races.

This calculator uses typical literature values: copper 8.5×10²⁸ m⁻³, aluminum 1.81×10²⁹ m⁻³, silver 5.86×10²⁸ m⁻³, and gold 5.90×10²⁸ m⁻³. These are approximations (one free electron per atom, from density and molar mass); actual values may differ slightly with purity and temperature, but the order of magnitude is right for drift velocity calculations.

Yes, directly proportional — as long as the wire and material are the same. From v_d = I/(n×A×q), doubling the current doubles the drift velocity. Conversely, a wire with twice the cross-section at the same current has half the drift velocity, because the same current is spread over more electrons.

Current density J = I/A is directly proportional to drift velocity: J = n×q×v_d. So v_d = J/(n×q). This calculator shows current density (A/mm²) as extra information in every drift velocity calculation.

Current: amperes (A), milliamperes (mA), microamperes (µA). Cross-sectional area: mm², cm², or computed from wire diameter (mm) or AWG number (0–40). Drift velocity results are shown in m/s, mm/s, and µm/s together. Wire length for transit-time mode: mm, cm, m, or km.

Wire diameter follows the standard AWG formula: d (inches) = 0.005 × 92^((36−AWG)/39), then area = π/4 × d². Example: 12 AWG → 2.0525 mm diameter → 3.3088 mm² area; 24 AWG → 0.2047 mm²; 0 AWG → 53.4751 mm². This calculator uses that formula, not an approximation table.

No. Electrical signal speed (propagation of the electromagnetic field/wave in the cable) is on the order of 10⁸ m/s, while electron drift velocity is on the order of 10⁻⁴–10⁻⁵ m/s — about 12 orders of magnitude apart. They are different physical quantities and must not be conflated.

The formula has the same form, but in semiconductors there are two kinds of charge carriers: electrons and holes, each with different densities n and p and mobilities. This calculator models a single carrier type (ordinary metals/conductors). For semiconductors, compute the electron and hole contributions separately.

The formula v_d = I/(n×A×q) is exact classical physics for the free-electron model; the elementary charge q = 1.602176634×10⁻¹⁹ C is an exact SI value. The main uncertainty comes from n (free-electron density uses typical literature values, not measurements of your wire sample) and from the steady-DC, uniformly distributed current assumption. For educational and engineering-estimate purposes, the results are reliable.

This calculator computes charge-carrier velocity from current and wire geometry. For wire resistance (R = ρ×L/A) use wire-resistance; for choosing a wire size that safely carries current use 12v-wire-size; for AWG-to-mm² number conversion use awg-to-mm. All four answer different questions about the same wire.