Avogadro's Number Calculator: Moles, Particles and Mass
Enter any two of moles, particles, or mass (plus molar mass) and this calculator solves the rest using Avogadro's constant. It shows the full step-by-step working, a visual comparison of your values, and a reference table of common substances so you can check your chemistry homework in seconds.
Formula
Worked example
For 18.015 g of water (molar mass 18.015 g/mol): n = 18.015 / 18.015 = 1.000 mol. Then N = 1.000 x 6.02214076 x 10^23 = 6.022 x 10^23 molecules. That is roughly 602 sextillion individual water molecules in a single teaspoon.
What is Avogadro's number?
Avogadro's number (N_A = 6.02214076 x 10^23 mol^-1) is the number of elementary entities - atoms, molecules, ions, or formula units - in exactly one mole of any substance. It was named after the Italian scientist Amedeo Avogadro, whose 1811 hypothesis about equal gas volumes containing equal numbers of particles laid the groundwork for modern stoichiometry. Since the 2019 redefinition of the SI system, Avogadro's constant is exact by definition, not a measured approximation. This precision matters in analytical chemistry, pharmaceutical dosing, and materials science where tiny mole-fraction differences can have large physical consequences. One mole of water (18 g) contains exactly the same number of molecules as one mole of gold (197 g). The mole is simply a counting unit, like a dozen - it scales the atomic world up to amounts we can weigh and pour.
How the moles-particles-mass triangle works
Three quantities define how much of a substance you have: the number of moles (n), the number of particles (N), and the mass (m). They connect through two equations:
- N = n x N_A - multiply moles by Avogadro's constant to get particle count.
- n = m / M - divide mass by molar mass (g/mol) to get moles.
- N = (m / M) x N_A - combine both to go from mass directly to particle count.
How to find the molar mass of any substance
The molar mass of a compound is the sum of the atomic masses (from the periodic table) of all atoms in one formula unit, expressed in g/mol. For water (H2O): 2 x 1.008 (H) + 1 x 15.999 (O) = 18.015 g/mol. For sodium chloride (NaCl): 22.990 (Na) + 35.45 (Cl) = 58.44 g/mol. For glucose (C6H12O6): 6 x 12.011 + 12 x 1.008 + 6 x 15.999 = 180.156 g/mol. The reference table on this page lists molar masses for eight common substances. For any other compound, add up the atomic masses from the periodic table and enter the result into the molar mass field.
Worked example: molecules in a cup of water
A standard 250 mL cup of water has a mass of about 250 g (density approximately 1 g/mL at room temperature). Molar mass of H2O = 18.015 g/mol.
- Moles: n = 250 g / 18.015 g/mol = 13.878 mol
- Molecules: N = 13.878 mol x 6.02214076 x 10^23 = 8.355 x 10^24 molecules
Significant figures and precision in Avogadro's constant
Since the 2019 SI redefinition, Avogadro's constant is fixed at exactly 6.02214076 x 10^23 mol^-1 with no uncertainty. Before 2019, it was a measured quantity with an experimental uncertainty of about +/-0.00000014 x 10^23 (CODATA 2014). For most classroom and lab work, rounding to 6.022 x 10^23 introduces negligible error (less than 0.001%). For high-accuracy metrology, spectroscopy, or pharmaceutical calculations, use the full 9-significant-figure value. When reporting your results, limit your significant figures to those in your least precise input. If your mass is measured to 3 significant figures (for example, 18.0 g), reporting the particle count to 10 significant figures is false precision.
Molar masses and particle counts for common substances
| Substance | Formula | Molar mass (g/mol) | Particles in 1 mol |
|---|---|---|---|
| Water | H2O | 18.015 | 6.022 x 10^23 molecules |
| Sodium chloride | NaCl | 58.443 | 6.022 x 10^23 formula units |
| Carbon dioxide | CO2 | 44.009 | 6.022 x 10^23 molecules |
| Oxygen gas | O2 | 31.998 | 6.022 x 10^23 molecules |
| Glucose | C6H12O6 | 180.156 | 6.022 x 10^23 molecules |
| Ethanol | C2H5OH | 46.068 | 6.022 x 10^23 molecules |
| Hydrogen gas | H2 | 2.016 | 6.022 x 10^23 molecules |
| Calcium carbonate | CaCO3 | 100.086 | 6.022 x 10^23 formula units |
Calculated for exactly 1 mole of each substance using N_A = 6.02214076 x 10^23 mol^-1.
Frequently asked questions
What is Avogadro's number and why is it 6.022 x 10^23?
Avogadro's number (6.02214076 x 10^23) is the number of atoms or molecules in one mole of a substance. It was chosen so that one mole of carbon-12 atoms has a mass of exactly 12 grams, aligning the atomic mass unit with the gram. The value was determined experimentally over more than a century and has been exact by SI definition since 2019.
How do I calculate the number of molecules from moles?
Multiply the number of moles by Avogadro's constant: N = n x 6.02214076 x 10^23. For example, 0.5 mol of CO2 contains 0.5 x 6.022 x 10^23 = 3.011 x 10^23 molecules.
How do I convert grams to moles?
Divide the mass in grams by the molar mass of the substance (in g/mol): n = m / M. For example, 36 g of water (molar mass 18.015 g/mol) is 36 / 18.015 = 1.999 mol, essentially 2 moles.
What is the difference between Avogadro's number and Avogadro's constant?
Avogadro's number is the dimensionless value 6.02214076 x 10^23. Avogadro's constant (N_A) carries the unit mol^-1, making it a physical constant: 6.02214076 x 10^23 mol^-1. In practice, both terms are used interchangeably in stoichiometry problems because the mole appears as a unit in the input.
How many atoms are in 1 gram of hydrogen?
Hydrogen atoms have a molar mass of approximately 1.008 g/mol. So 1 g of hydrogen atoms is 1 / 1.008 = 0.9921 mol. Multiplying by Avogadro's constant: 0.9921 x 6.022 x 10^23 = 5.975 x 10^23 atoms. Note that hydrogen gas (H2) has a molar mass of 2.016 g/mol, giving half as many molecules.
How do I find the number of formula units in an ionic compound?
Use the same moles-to-particles formula. For NaCl (molar mass 58.44 g/mol): if you have 5.844 g, that is 5.844 / 58.44 = 0.0999 mol, which contains 0.0999 x 6.022 x 10^23 = 6.016 x 10^22 formula units. Each formula unit is one Na+ ion paired with one Cl- ion.
Can Avogadro's number be used for elements and compounds?
Yes. Avogadro's constant applies to any type of elementary entity: atoms (monatomic elements like iron or argon), molecules (covalent compounds like water or CO2), ions, or formula units (ionic compounds like NaCl). The key is to be clear about what you are counting and use the corresponding molar mass.