# Drift Velocity Calculator

Created by Dominik Czernia, PhD
Reviewed by Bogna Szyk and Steven Wooding
Last updated: Jun 05, 2023

With this drift velocity calculator, you can compute the velocity of any charged particle in a specific material.

Have you ever wondered what the electrical current speed is in a cable? How fast does electricity travel? Read on if you want to find the answers to these questions.

The drift velocity is the average velocity that a particle (e.g., electron, electron-hole, ion) attains in a material due to an applied voltage. To determine the drift velocity, we need to know the number density, which tells us how many carriers are in a unit volume of material (usually expressed in carriers per cubic meter). In the text below, we present the drift velocity equation and some simple calculations of the velocity of an electron.

You may also be interested in how a charged particle behaves in the magnetic field (check out the Lorentz force calculator) and calculating the force acting on a wire with an electric current in a magnetic field (see our electromagnetic force on a current-carrying wire calculator).

Wonder what this all means? Check out our exploration into why electrons are so slow here:

## How fast does electricity travel?

An electric current is a movement of electric charges (usually electrons) in a wire. It may be a surprise, but these particles have a limited velocity. When you connect the electrical device to the socket, it immediately reacts. So how fast does electricity travel?

We have conducted some basic calculations of drift velocity for an electron in the text below if you want to learn more about it. We can already say that the current speed is relatively small, but there are a massive number of electrons that simultaneously feel an applied voltage. That's why our electrical device reacts so fast after connecting to a socket.

## Drift velocity equation

Our drift velocity calculator can be used for any charged particle and uses the below drift velocity formula:

$u = \frac{I}{nAq},$

where:

• $u$ – Drift velocity (average velocity of a particle);
• $I$ – Current (you can compute it using our Ohm's law calculator);
• $n$ – Charge carrier number density;
• $A$ – Cross-sectional area of a wire; and
• $q$ – Charge on the charge carrier.

The simple mode of our drift velocity calculator assumes that a current appears as a result of the flow of electrons with the elementary charge $\small q = e = 1.6 \times 10^{-19}\ \rm C$. If you want to change the type of charge carrier, go to the advanced mode.

## Velocity of electron

Let's, for example, calculate the velocity of an electron in a thin copper wire $\small (A = 1\ \rm mm^2)$ with an electrical current $\small I = 10\ \rm A$. Copper is a conductor with a density of $\small 8.94\ \rm g/cm^3$, an atomic weight of $\small 63.546\ \rm g/mol$, and one free electron per atom.

Using that data and our number density calculator you can estimate the charge carrier number density $\small n = 8.5 \times 10^{28}\ \rm electrons/m^3$.

Finally, with our drift velocity calculator, we can compute that $\small u = 7.343 \times 10^{-4}\ \rm m/s$, which is surprisingly slow!

Dominik Czernia, PhD
Current
A
Area
in²
Number density
×10²⁸ carriers/
cu ft
Drift velocity
ft/s
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