Drift Velocity Calculator

Background.

Switch on a lamp and it lights at once, which makes it natural to picture electrons racing through the wire. They do not. In a copper wire carrying a few amps, the electrons' net progress along the wire is a fraction of a millimetre per second — about the speed of the tip of a 12 cm minute hand on a wall clock. What travels quickly is the electric field that pushes them, which sets the free electrons all around the circuit moving almost together, the way water already filling a hose comes out the far end as soon as the tap opens.

The slow pace follows from how much mobile charge a metal holds. Copper supplies roughly one free electron per atom, about 8.5 × 10²⁸ in every cubic metre. With that much charge packed into the wire, only a tiny collective shuffle is needed to carry 3 coulombs past any point each second. Divide the current by the mobile charge in each metre of conductor — carrier density times carrier charge times cross-sectional area — and you have the drift velocity: v_d = I / (nqA).

Underneath that average the electrons are anything but still. They move randomly at speeds of order 10⁶ m/s, scattering constantly off vibrating ions and impurities; the drift is a faint bias on top of that motion. With alternating current the bias flips every half-cycle, so at 50 Hz an electron in a 1 mm² wire carrying 3 A shuttles back and forth by about a micrometre rather than going anywhere.

The page returns the drift speed as a magnitude. Electrons move opposite to the conventional current direction, and the calculation assumes a steady current spread evenly across the section; it does not work out mobility, heating or how the field is distributed.

What is drift velocity calculator?

Drift velocity is the average velocity that mobile charge carriers — electrons in a metal, electrons and holes in a semiconductor, ions in an electrolyte — acquire along a conductor when a current flows. It is a small net drift superimposed on much faster random motion. It links the current I to the material through I = nqv_dA: carriers per cubic metre, charge per carrier, drift speed and cross-sectional area. Rearranged, v_d = I / (nqA), in metres per second.

How to use this calculator.

1. 01Enter the current in amperes. For alternating current, entering the RMS current gives the RMS drift speed; the instantaneous speed swings between zero and a peak in each direction every cycle.
2. 02Enter the number density of mobile carriers per cubic metre. For copper the textbook value is about 8.5 × 10²⁸ m⁻³; other metals and doped semiconductors need their own figure from a data table.
3. 03Enter the magnitude of each carrier's charge in coulombs. Electrons and holes carry the elementary charge, 1.602176634 × 10⁻¹⁹ C; a doubly charged ion such as Cu²⁺ carries twice that.
4. 04Enter the cross-sectional area in square metres, not mm². A 1 mm² cable is 1 × 10⁻⁶ m²; for a round wire of diameter d, the area is πd²/4.
5. 05Read the drift speed in metres per second. Multiply by 1,000 for millimetres per second, which is usually the more readable scale for metal wires.

The formula.

v_d = I / (nqA). The denominator is the mobile charge contained in one metre of conductor: n carriers per cubic metre, each with charge q, across an area A. Dividing the current — coulombs per second — by that charge per metre leaves metres per second. Three of the four inputs sit in the denominator, so the drift speed falls in proportion to each of them: double the cross-section and the carriers move half as fast for the same current, while halving the area doubles it. The carrier density dominates comparisons between materials, because it ranges over many orders of magnitude between metals and semiconductors. The charge is fixed by nature for electrons at exactly 1.602176634 × 10⁻¹⁹ C, the value used to define the SI ampere since 2019. All four inputs must be positive.

A worked example.

Frequently asked questions.

References& sources.

1. [1]OpenStax, University Physics Volume 2, section 9.1, Electrical Current.
2. [2]Halliday, Resnick and Walker, Fundamentals of Physics, 12th ed. (PRINT), chapter 26, drift speed.
3. [3]BIPM, The International System of Units (SI Brochure), 9th ed., version 3.01, coherent derived units and quantity equations.