# Avogadro’s Number Calculator

URL: https://speedycalculator.com/calculators/chemistry/avogadro/
Last updated: 2026-10-30

> Use Avogadro's number to convert between the number of particles (atoms, molecules, ions), the amount in moles, the mass and the molar mass of a substance – enter any two and get the rest, plus the total number of atoms and the mass of a single particle.

## Inputs

- I know
- Mass (g, mg, µg, kg, oz, lb)
- Amount of substance (mol, mmol, µmol, nmol, kmol)
- Molar mass (molecular weight) (g/mol, kg/mol, Da (u), kDa)
- 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

- Amount of substance (moles)
- Number of particles
- Mass
- Molar mass
- Total number of atoms
- Mass of one particle
- Avogadro's number

## Formula

```
N = n × Nᴀ · n = m ÷ M · m = n × M · Nᴀ = 6.02214076 × 10²³ mol⁻¹ (exact) · mass of one particle = M ÷ Nᴀ
```

## Explanation

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

FieldWhat to enterI knowChoose one: Mass and molar mass, Moles and molar mass, Number of particles and molar mass, Mass and moles …MassUnits: g, mg, µg, kg, oz, lbAmount of substanceUnits: mol, mmol, µmol, nmol, kmolMolar mass (molecular weight)Units: g/mol, kg/mol, Da (u), kDaNumber of particlesA number. Scientific notation works, e.g. 3.613e24Atoms 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 particles48.133.6133e2472.23.6133e2496.263.6133e24120.333.6133e24144.393.6133e24192.523.6133e24

## Worked 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.

## FAQ

**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.


## Sources

- [BIPM – The International System of Units (SI Brochure, 9th edition)](https://www.bipm.org/en/publications/si-brochure)
- [NIST – Fundamental physical constants (CODATA)](https://physics.nist.gov/cuu/Constants/)
- [OpenStax – Chemistry 2e](https://openstax.org/details/books/chemistry-2e)