Hong Life CalculatorsUnderstanding the Avogadro's number calculator — concept and principle
The Avogadro constant links the amount of substance in moles with the number of particles. This calculator converts between moles, particles and grams, counts atoms in molecules and gives the mass of a single particle.
How it is calculated
- NA = 6.02214076 × 10²³ per mole, exact since the 2019 redefinition of the SI.
- Particles = moles × NA; moles = particles ÷ NA.
- Moles = mass (g) ÷ molar mass (g/mol); mass = moles × molar mass.
- Atoms = particles × atoms per particle.
- Mass of one particle = molar mass ÷ NA.
The principle
Atoms are far too small to count one by one, so chemists count them in moles, like counting eggs by the dozen. One mole is defined as exactly 6.02214076 × 10²³ particles. The molar mass in grams per mole is numerically equal to the particle's mass in atomic mass units, so weighing a sample tells you how many moles, and therefore how many particles, it contains.
Worked example
Default inputs: 2.5 mol of water, molar mass 18.015 g/mol, 3 atoms per molecule.
- Particles = 2.5 × 6.02214076 × 10²³ ≈ 1.50554 × 10²⁴ molecules.
- Atoms = 1.50554 × 10²⁴ × 3 ≈ 4.51661 × 10²⁴.
- Mass = 2.5 × 18.015 = 45.0375 g.
- Mass of one molecule = 18.015 ÷ 6.02214076 × 10²³ ≈ 2.991 × 10⁻²³ g.
- Amount = 2.5 mol.
| Amount to convert | Number of particles |
|---|---|
| 0.625 | 3.76384e+23 |
| 1.25 | 7.52768e+23 |
| 1.88 | 1.12915e+24 |
| 2.5 | 1.50554e+24 |
| 3.12 | 1.88192e+24 |
| 3.75 | 2.2583e+24 |
| 5 | 3.01107e+24 |
How to read the result
Numbers of particles are enormous even for small samples: 45 g of water, less than a quarter of a cup, holds about 1.5 × 10²⁴ molecules. Use moles in chemical equations, because coefficients refer to particle ratios.
Common mistakes
- Forgetting to multiply by atoms per molecule when atoms are asked for.
- Using a rounded NA (6.02 × 10²³) where more precision is needed.
- Confusing molar mass (g/mol) with the mass of one molecule.
- Mixing grams and kilograms.
Frequently asked questions
What is Avogadro's number?
Exactly 6.02214076 × 10²³, the number of particles in one mole.
How many molecules are in a mole of water?
The same as in a mole of anything: 6.02214076 × 10²³.
How do I convert grams to molecules?
Divide grams by molar mass to get moles, then multiply by NA.
Sources: BIPM, The International System of Units (SI Brochure), 9th edition (2019) · CODATA 2018/2022 recommended values of the fundamental physical constants (NIST)