Number density counts particles per cubic metre. For metals, the free-electron density sets electrical conductivity and the Fermi energy: copper has about 8.5 × 10²⁸ conduction electrons per m³.
How to use the Number Density Calculator
- Substance
- Density ρ
- Molar mass M (g/mol)
- Free electrons per atom
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Choose a substance or enter its density, molar mass and free electrons per atom.
Inputs explained
| Field | What to enter |
|---|---|
| Substance | Choose one: Aluminium, Copper, Gold, Silver … |
| Density ρ | Units: g/cm³, kg/m³ |
| Molar mass M (g/mol) | A number |
| Free electrons per atom | A number |
What each result means
- Number density of atoms = [rho]×1e6×6.02214076e23÷[M]
- Free-electron density = [Number density of atoms]×[fe]
- Atoms per cm³ = [Number density of atoms]÷1e6
Example values
How the main result changes when Density ρ changes and everything else stays at the example values above:
| Density ρ (g/cm³) | Number density of atoms (m⁻³) |
|---|---|
| 4.48 | 8.4912e28 |
| 6.72 | 8.4912e28 |
| 8.96 | 8.4912e28 |
| 11.2 | 8.4912e28 |
| 13.44 | 8.4912e28 |
| 17.92 | 8.4912e28 |
Formula
n = ρ·N_A / M, n_e = n × (free electrons per atom)
Worked example
Inputs — Substance: Copper.
Results — Number density of atoms = 8.4912e28 m⁻³; Free-electron density = 8.4912e28 m⁻³; Atoms per cm³ = 8.4912e22 cm⁻³.
Key terms
- Number density
- Particles per unit volume.
Frequently asked questions
What is the free-electron density of copper?
About 8.5 × 10²⁸ m⁻³.
Why multiply by free electrons?
Each atom contributes its valence electrons to the conduction band.
What is Avogadro's number?
6.02214076 × 10²³ per mole, exact by definition.
Where is number density used?
Drift velocity, plasma physics, gas kinetics.