Avogadro constant, N_A

The number of entities in one mole: 6.02214076 × 10²³ of them, exactly. The pure number is Avogadro’s number; the Avogadro constant is the same number with the unit mol⁻¹.

N_A = 6.02214076 × 10²³ mol⁻¹

Exact by definition, so it has no uncertainty at all.

In other units

Measured values are in CODATA’s concise form: the digits in brackets are the standard uncertainty in the last two places, so 6.67430(15) means 6.67430 ± 0.00015.

Avogadro constant in SI units and in other units
Quantity	Value
N_A	6.02214076 × 10²³ mol⁻¹
N_A	6.02214076 × 10²⁰ mmol⁻¹
N_A	6.02214076 × 10¹⁷ µmol⁻¹
N_A	6.02214076 × 10¹⁴ nmol⁻¹

Avogadro constant in mmol⁻¹

6.02214076 × 10²³ mol⁻¹ × 10⁻³ mol/mmol
= 6.02214076 × 10²⁰ mmol⁻¹

Avogadro constant in µmol⁻¹

6.02214076 × 10²³ mol⁻¹ × 10⁻⁶ mol/µmol
= 6.02214076 × 10¹⁷ µmol⁻¹

Avogadro constant in nmol⁻¹

6.02214076 × 10²³ mol⁻¹ × 10⁻⁹ mol/nmol
= 6.02214076 × 10¹⁴ nmol⁻¹

Where the value comes from

Until 2019 the mole was defined as the amount of substance in exactly 12 g of carbon-12, so the Avogadro constant was however many atoms that turned out to be, and measuring it meant counting atoms. The most precise count came from spheres of almost pure silicon-28, whose volume and crystal spacing gave the number of atoms they held.

The revision fixed the constant at exactly 6.02214076 × 10²³ mol⁻¹, chosen to agree with those counts, and the mole became a number of entities rather than a mass. One consequence is that 12 g of carbon-12 is no longer exactly a mole: CODATA 2022 gives carbon-12’s molar mass as 12.0000000126(37) g/mol, which differs from 12 by about 1 part in a billion.

Which form to use

To go from a molar mass to a single atom, divide by the Avogadro constant: iron’s 55.845 g/mol gives 9.2733 × 10⁻²³ g per atom. To count the particles in a sample, multiply its amount in moles by it.

In biochemistry the per-micromole form is the useful one: a micromole of a protein is 6.022 × 10¹⁷ molecules, and a nanomole is 6.022 × 10¹⁴.

Common mistakes

Dropping the unit. The Avogadro constant is 6.02214076 × 10²³ per mole; the bare number is Avogadro’s number, and using one where the other belongs leaves a mol⁻¹ unaccounted for.
Multiplying when you should divide. The mass of one atom is the molar mass divided by the Avogadro constant, a very small number; the product of the two has no physical meaning.
Assuming 12 g of carbon-12 is exactly one mole. It was until 2019; now carbon-12’s molar mass is measured, and on CODATA 2022’s figure 12 g falls short of a mole by about 1 part in a billion, which matters only in metrology.

Tools that use it

Molar Mass Calculator counts the formula units in a sample with it.
Ideal Gas Law Calculator counts the molecules in the gas with it.
Photon Energy Calculator gives the energy of a mole of photons.
Crystal Lattice Explorer turns a unit cell into a density with it.
Electromagnetic Spectrum Explorer gives the energy of a mole of photons at every point of the spectrum, to set against bond energies.
States of Matter Simulator gives the energy stored between the atoms per mole with it.

Related constants

Molar gas constant, R = 8.31446261815324 J/(mol·K)
Faraday constant, F = 96,485.33212… C/mol
Boltzmann constant, k = 1.380649 × 10⁻²³ J/K
Elementary charge, e = 1.602176634 × 10⁻¹⁹ C