Number Density Calculator

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


With our number density calculator, you can estimate the charge carrier number density of specific metals. It is a physical quantity that describes how many charge carriers are in a volume unit. All you need to know are the density of a material, its molar mass, and the number of free electrons.

In the text below, we have explained what is a charge carrier and how to calculate the number density of charge carriers. Copper remains the preferred electrical conductor in almost every branch of electrical wiring. We can find it nearly everywhere. That's why we have also performed example calculations for the charge carrier density of copper.

Most of the well-known conductors are also metals. Do you know what happens when light falls on a metal surface? Check our photoelectric effect calculator to learn more about it!

What is a charge carrier?

A charge carrier is an object which carries electric charge during current flow. The charge carrier type depends on the material's structure in which the charge is transported. For example, there are free electrons in metals, and in semiconductors, there could be both electrons and electron holes.

Every electrical circuit has a resistance (except superconductors) which can be described by Ohm's law. This resistance slows down charge carriers, and therefore they can't reach high speeds. You can check our drift velocity calculator to see how fast charge carriers are.

How to calculate number density?

You can compute charge carrier density with our number density calculator:

n=NAZρmM,n = \frac{N_{\rm A}Z\rho_{\rm m}}{M},

where:

  • nn – Charge carrier number density;
  • ρ\rho – Density of a material;
  • ZZ – Number of free electrons per atom;
  • MM – Molar mass (see molarity calculator); and
  • NAN_{\rm A} – Avogadro constant NA=6.0221×1023 mol1\small N_{\rm A} = 6.0221 \times 10^{23}\ \rm mol^{-1}.

In our number density calculator, you can either choose a specific substance from our examples or enter your parameters.

Remember that the above equation can be applied only to the conductors which have free electrons. If you want to calculate the carrier density in semiconductors, we recommend checking our intrinsic carrier concentration calculator.

Charge carrier density of copper

Copper is a metal that has high electrical conductivity, and for that reason, many electrical devices rely on copper wiring.

Let's compute the charge carrier density of copper with our number density calculator. We can easily find both the density of a material and the molecular mass of copper (we have provided them as an example substance). Because copper has only one free electron per atom, its charge carrier density is 8.491 ⁣× ⁣1028 carriers/m3\small 8.491\! \times\! 10^{28}\ \rm carriers/m^3. It's tough to imagine how many of them are in one cubic meter. Astonishing number!

Dominik Czernia, PhD
Substance (optional)
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Density
lb/cu yd
Molar mass
g/mol
Number of free electrons
Number density
×10²⁸ carriers/
cu yd
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