Number Density Calculator

Calculate the number density of particles in a substance from its mass density, molar mass, or from ideal gas law parameters. Used in plasma physics, astrophysics, and material science.

NUMBER DENSITY
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Number Density (m⁻³)
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Particles per cm³
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Mean Spacing
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Moles per m³
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What Is Number Density?

Number density is the number of particles (atoms, molecules, ions, or other entities) per unit volume. It is a fundamental quantity in physics and chemistry, commonly denoted by n and measured in particles per cubic meter (m⁻³) or particles per cubic centimeter (cm⁻³). Number density connects macroscopic properties like mass density to the microscopic particle count.

Number density is essential in kinetic theory of gases, plasma physics, semiconductor physics, astrophysics, and chemical kinetics. It determines collision rates, mean free paths, reaction rates, and optical properties of materials. The Loschmidt constant (2.687×10²⁵ m⁻³) is the number density of an ideal gas at STP.

Formula

n = ρ × NA / M
n = P / (kB × T)   (ideal gas)

Where ρ is mass density, NA is Avogadro's number, M is molar mass, P is pressure, kB is Boltzmann constant, and T is temperature.

Typical Number Densities

MaterialNumber Density (cm⁻³)
Air at STP2.7 × 10¹⁹
Water3.3 × 10²²
Copper (solid)8.5 × 10²²
Interstellar medium1

Frequently Asked Questions

What is the difference between number density and concentration?

Number density counts individual particles per volume (m⁻³), while molar concentration counts moles per volume (mol/L or M). They are related by Avogadro's number: n = NA × c, where c is molar concentration.

How is number density used in semiconductors?

In semiconductors, number density of electrons (n) and holes (p) determines electrical conductivity. Intrinsic silicon has n = p ≈ 1.5×10¹⁰ cm⁻³ at room temperature. Doping changes these densities by orders of magnitude to create n-type or p-type material.