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Avogadro's Number Calculator

Calculate atoms, molecules, or particles from mass and molar mass using Avogadro's number (6.022×10²³). Supports reverse calculations and 20+ substance presets.

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About

Avogadro's constant NA = 6.02214076 × 1023 mol−1 defines the number of constituent particles in one mole of substance. Since the 2019 SI redefinition it is an exact, fixed value rather than an experimentally measured one. Errors in stoichiometric calculations propagate multiplicatively: a 1% mistake in molar mass M produces a 1% error in the computed particle count, which at the scale of 1023 means billions of trillions of phantom atoms. This calculator applies the relation N = mM × NA with IUPAC 2021 standard atomic weights and handles reverse lookups (particles to mass, moles to particles). It assumes standard laboratory conditions and pure substances. For mixtures or isotopically enriched samples you must supply the effective molar mass manually.

avogadro moles particles atoms molecules molar mass chemistry stoichiometry mol

Formulas

The fundamental mole-particle relationship derives from the definition of the mole as exactly NA entities:

N = mM × NA

where N = number of particles (atoms, molecules, or formula units), m = sample mass in g, M = molar mass in g/mol, and NA = 6.02214076 × 1023 mol−1.

The number of moles n is:

n = mM

To find total atoms in a compound with k atoms per formula unit:

Natoms = k × mM × NA

where k = sum of all subscripts in the molecular formula (e.g., for H2O, k = 3). Reverse: given N particles, mass is m = N × MNA.

Reference Data

SubstanceFormulaMolar Mass g/molParticles in 1 gState (25°C)
Hydrogen gasH22.0162.987 × 1023(g)
HeliumHe4.0031.504 × 1023(g)
CarbonC12.0115.014 × 1022(s)
Nitrogen gasN228.0142.149 × 1022(g)
Oxygen gasO231.9981.882 × 1022(g)
WaterH2O18.0153.343 × 1022(l)
Sodium chlorideNaCl58.4401.030 × 1022(s)
Calcium carbonateCaCO3100.0866.017 × 1021(s)
IronFe55.8451.078 × 1022(s)
CopperCu63.5469.474 × 1021(s)
GoldAu196.9673.057 × 1021(s)
SilverAg107.8685.583 × 1021(s)
GlucoseC6H12O6180.1563.343 × 1021(s)
EthanolC2H5OH46.0681.307 × 1022(l)
Sulfuric acidH2SO498.0796.140 × 1021(l)
AmmoniaNH317.0313.536 × 1022(g)
Carbon dioxideCO244.0091.369 × 1022(g)
MethaneCH416.0433.754 × 1022(g)
Acetic acidCH3COOH60.0521.003 × 1022(l)
AluminumAl26.9822.232 × 1022(s)
MagnesiumMg24.3052.477 × 1022(s)
Potassium hydroxideKOH56.1061.073 × 1022(s)

Frequently Asked Questions

The 26th General Conference on Weights and Measures (CGPM) redefined the mole by fixing NA to an exact integer-free value, decoupling it from the kilogram prototype. Before 2019, the constant was defined relative to 12 grams of carbon-12, introducing measurement uncertainty (~0.0000044 × 1023). The new definition eliminates that uncertainty entirely.
Molar mass M is expressed in g/mol and is numerically equal to the relative molecular mass (molecular weight) or relative formula mass (for ionic compounds), which are dimensionless. In practice all three give the same number. Use molecular weight for covalent molecules (H2O) and formula weight for ionic lattices (NaCl) where discrete molecules do not exist.
Hydrated salts include water of crystallisation. For example, CuSO4·5H2O has M = 249.685 g/mol, not 159.609 g/mol (anhydrous). Using the anhydrous value overstates formula-unit count by 56%. Always verify hydration state before calculation.
No. The formula N = (m ÷ M) × NA depends only on mass and molar mass, both of which are independent of T and P. Temperature and pressure affect volume and density, not particle count per gram. If you measured volume instead of mass (e.g., for a gas), you must first convert to mass via the ideal gas law or known density at those conditions.
Multiply the molecule count by the atomicity k (sum of all atomic subscripts in the formula). For glucose C6H12O6, k = 6 + 12 + 6 = 24. This calculator provides an Atoms per Formula Unit field for this purpose.
JavaScript uses IEEE 754 double-precision floats, giving approximately 15 - 17 significant decimal digits. Since NA has 9 significant figures in its exact definition, and typical molar masses are known to 3 - 6 significant figures, the bottleneck is always your input precision, not the calculator. Results are displayed to 6 significant figures by default.