Number Density Calculator
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 is the density of a material, its molar mass, and the number of free electrons per atom.
In the text below, we have explained what a charge carrier is 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.
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 structure of the material 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. Most of the well-known conductors are also metals.
How to calculate number density?
You can compute the charge carrier density with our number density calculator using the formula:
n = NA · Z · ρ / M
Where:
- n — Charge carrier number density;
- ρ — Density of a material;
- Z — Number of free electrons per atom;
- M — Molar mass; and
- NA — Avogadro constant, NA = 6.0221 × 10²³ mol⁻¹.
In our number density calculator, you can either choose a specific substance from our examples or enter your own parameters. Remember that the above equation can be applied only to conductors which have free electrons. If you want to calculate the carrier density in semiconductors, the intrinsic carrier concentration approach is more appropriate.
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 the material and the molar 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:
n = 8.491 × 10²⁸ carriers/m³
It's tough to imagine how many of them there are in one cubic meter. An astonishing number!
Unit Systems
Metric (SI) System
- Density (ρ): grams per cubic centimeter (g/cm³)
- Molar mass (M): grams per mole (g/mol)
- Free electrons per atom (Z): dimensionless
- Number density (n): carriers per cubic meter (m⁻³), also shown per cm³, mm³ and liter
American (Imperial) System
- Density (ρ): pounds per cubic foot (lb/ft³); 1 lb/ft³ = 0.01601846 g/cm³
- Molar mass (M): grams per mole (g/mol) — numerically equal to lb per lb-mol
- Free electrons per atom (Z): dimensionless
- Number density (n): also shown per cubic inch (in⁻³) and per cubic foot (ft⁻³)
Frequently Asked Questions
What is number density?
Number density is the number of particles (here, charge carriers such as free electrons) per unit volume. For metallic conductors it is typically on the order of 10²⁸ carriers per cubic meter.
How do I find the number density of a material?
Multiply the Avogadro constant by the number of free electrons per atom and the material's density, then divide by its molar mass: n = NA · Z · ρ / M. For copper this gives roughly 8.491 × 10²⁸ electrons per cubic meter.
Why is the charge carrier density of copper so high?
Copper has a high mass density (about 8.96 g/cm³), a relatively low molar mass (63.546 g/mol), and contributes one free electron per atom. Together these produce an enormous number of conduction electrons per cubic meter.
Can I use this calculator for semiconductors?
This formula assumes a conductor with a fixed number of free electrons per atom. Semiconductors have a temperature-dependent intrinsic carrier concentration and require a different model.