Avogadro’s number, Nᴀ = 6.02214076 × 10²³ per mole, is the bridge between the invisible world of atoms and the grams on a laboratory balance. Since the 2019 redefinition of the SI it is exact: one mole is defined as exactly that many elementary entities. It was chosen so that the molar mass of a substance in grams per mole equals the mass of one of its particles in daltons – 12 g of carbon-12 contains Nᴀ atoms.
Every mole calculation uses two links: the molar mass M connects mass and moles (n = m/M), and Avogadro’s number connects moles and particles (N = n × Nᴀ). With these, 6 mol of methane (CH₄, 16.043 g/mol) is 96.26 g and 3.61 × 10²⁴ molecules; because each methane molecule has five atoms, it holds 1.81 × 10²⁵ atoms in total.
Choose which two quantities you know. The calculator fills in the rest, gives the mass of a single particle and – if you enter how many atoms one particle contains – the total number of atoms, so you can answer textbook questions such as “how many hydrogen atoms are in 10 g of water?” in one go.
How to use the Avogadro’s Number Calculator
- I know
- Mass
- Amount of substance
- Molar mass (molecular weight)
- Number of particles — Scientific notation works, e.g. 3.613e24
- Atoms per particle (optional) — CH₄ = 5, H₂O = 3, NaCl = 2, a single atom = 1
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
The two known values fix the third of mass, moles and molar mass (m = n·M); the particle count follows from N = n × Nᴀ, and the atom count multiplies N by the atoms per particle. The mass of one particle is M/Nᴀ.
Worked example
How many molecules and atoms are in 6 mol of methane, CH₄ (16.043 g/mol)? N = 6 × 6.02214076 × 10²³ = 3.613 × 10²⁴ molecules. Each molecule has 1 C + 4 H = 5 atoms, so there are 1.807 × 10²⁵ atoms. The sample weighs 6 × 16.043 = 96.26 g, and one methane molecule weighs 16.043 ÷ 6.022 × 10²³ = 2.664 × 10⁻²³ g.
How big is a mole?
A mole of grains of sand would cover a large country in a thick layer, yet a mole of water is just 18 mL – a little more than a tablespoon. That contrast is why chemists count particles by weighing: the numbers are far too large to count any other way, and Avogadro’s number converts a convenient mass into an exact particle count.
Tips
- Always start from a balanced equation – coefficients give the mole ratio.
- Convert everything to moles first, then use the ratio, then convert back.
- Every field has its own unit menu – g, mg, mol, mmol, L and mL all work.
- Everything is calculated in your browser.
Common mistakes to avoid
- Using mass ratios instead of mole ratios.
- Forgetting water of crystallisation in the molar mass of hydrates.
- Confusing molarity (per litre of solution) with molality (per kilogram of solvent).
Inputs explained
| Field | What to enter |
|---|---|
| I know | Choose one: Mass and molar mass, Moles and molar mass, Number of particles and molar mass, Mass and moles … |
| Mass | Units: g, mg, µg, kg, oz, lb |
| Amount of substance | Units: mol, mmol, µmol, nmol, kmol |
| Molar mass (molecular weight) | Units: g/mol, kg/mol, Da (u), kDa |
| Number of particles | A number. Scientific notation works, e.g. 3.613e24 |
| Atoms per particle (optional) | A number. CH₄ = 5, H₂O = 3, NaCl = 2, a single atom = 1 |
What each result means
- Number of particles = [Amount of substance (moles)]×6.02214076e+23
- Total number of atoms = [Number of particles]×[Atoms per particle (optional)]
- Mass of one particle = [Molar mass]÷6.02214076e+23
- Avogadro’s number = 6.02214076e+23
Example values
How the main result changes when Mass changes and everything else stays at the example values above:
| Mass (g) | Number of particles |
|---|---|
| 48.13 | 3.6133e24 |
| 72.2 | 3.6133e24 |
| 96.26 | 3.6133e24 |
| 120.33 | 3.6133e24 |
| 144.39 | 3.6133e24 |
| 192.52 | 3.6133e24 |
Formula
N = n × Nᴀ · n = m ÷ M · m = n × M · Nᴀ = 6.02214076 × 10²³ mol⁻¹ (exact) · mass of one particle = M ÷ NᴀWorked example
Inputs — I know: Moles and molar mass; Amount of substance: 6 mol; Molar mass (molecular weight): 16.043 g/mol; Atoms per particle (optional): 5.
Results — Amount of substance (moles) = 6 mol; Number of particles = 3.6133e24; Mass = 96.258 g; Molar mass = 16.043 g/mol; Total number of atoms = 1.8066e25; Mass of one particle = 2.6640e-23 g; Avogadro's number = 6.0221e23 mol⁻¹.
Key terms
- Avogadro constant (Nᴀ)
- 6.02214076 × 10²³ mol⁻¹, the number of entities in one mole (exact).
- Mole
- SI unit of amount of substance, containing exactly Nᴀ elementary entities.
- Elementary entity
- The particle being counted: an atom, molecule, ion, electron or formula unit.
- Molar mass
- Mass per mole of a substance, numerically equal to the particle mass in daltons.
Frequently asked questions
What is Avogadro's number?
Exactly 6.02214076 × 10²³ particles per mole – the number of atoms in 12 g of carbon-12. It is an exact defined constant since 20 May 2019.
How many molecules are in 6 moles of methane?
6 × 6.02214076 × 10²³ = 3.613 × 10²⁴ molecules, containing 5 × 3.613 × 10²⁴ = 1.807 × 10²⁵ atoms.
How many molecules are in 1 g of water?
1 ÷ 18.015 = 0.05551 mol, × Nᴀ = 3.343 × 10²² molecules.
How do I convert particles to grams?
Divide by Nᴀ to get moles, then multiply by the molar mass: 1.0 × 10²⁴ atoms of iron = 1.661 mol × 55.845 g/mol = 92.7 g.
What is the mass of one atom of carbon?
12.011 ÷ 6.02214076 × 10²³ = 1.994 × 10⁻²³ g.
Is Avogadro's number the same as the Avogadro constant?
The Avogadro constant Nᴀ carries the unit mol⁻¹; Avogadro's number is the same value as a pure number. They are used interchangeably in practice.
Who determined Avogadro's number?
Amedeo Avogadro proposed in 1811 that equal gas volumes hold equal numbers of molecules; Jean Perrin named the constant after him and measured it around 1909. Today it is fixed by definition.
What formula does the Avogadro's Number Calculator use?
N = n × Nᴀ · n = m ÷ M · m = n × M · Nᴀ = 6.02214076 × 10²³ mol⁻¹ (exact) · mass of one particle = M ÷ Nᴀ.