Number Density Calculator
Use this number density calculator to compute the charge carrier number density of specific conductors.
Number density8.4644e+28 per m³ρN_A/M for Mild steel — 8.4644e+22 per cm³
Mean atomic spacing227.7548 pmn^(−1/3), the cube root of the volume per atom. Solids land within a factor of two of 0.25 nm almost regardless of what they are made of
Molar volume7.11465 cm³/molagainst 22,414 cm³/mol for an ideal gas at standard conditions — a solid is about a thousand times denser in atoms
Volume per atom1.1814e-29 m³11.81415 cubic ångströms
Mass of one atom9.2741e-26 kg55.85 g/mol divided by Avogadro's number
Atoms in that volume8.4644e+22in 1 cm³
Mass of that volume7.85 g
Moles in it0.140555 mol
Why solids are all much the same density in atomsatoms are all much the same sizeatomic radii vary by only about a factor of three across the whole periodic table, so differences in mass density come mostly from differences in atomic MASS rather than from how tightly atoms pack
The formula
n = ρN_A/M; spacing ≈ n^(−1/3)
Counting atoms from bulk properties
Number density is density times Avogadro's number over molar mass — the only three things needed to count atoms in a lump of material you cannot see inside. From it, the cube root of the volume per atom gives a mean spacing.
That spacing is remarkably consistent: almost every solid lands within a factor of two of a quarter of a nanometre, because atomic radii vary by only about threefold across the entire periodic table. Differences in mass density therefore come mostly from differences in atomic mass, not from how tightly things pack. Lead is dense because lead atoms are heavy, not because they are close together.