Avogadro's Number Calculator

What is Avogadro's Number?

Avogadro's number (Nₐ) is one of the most fundamental constants in chemistry. It represents the number of constituent particles (atoms, molecules, ions, or electrons) contained in one mole of a substance.

Avogadro's Number: Nₐ = 6.02214076 × 10²³ particles/mol

This constant was named after the Italian scientist Amedeo Avogadro, who first proposed in 1811 that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules.

How to Use This Calculator

1. Select conversion type: Choose whether to convert from moles to particles or particles to moles
2. Enter your value: Input the number of moles or particles
3. Get instant results: See the conversion with step-by-step explanation

Key Formulas

Moles to Particles

Number of Particles = Moles × Avogadro's Number

N = n × Nₐ

Where:

• N = number of particles
• n = number of moles
• Nₐ = 6.022 × 10²³

Particles to Moles

Moles = Number of Particles ÷ Avogadro's Number

n = N / Nₐ

Including Molar Mass

To convert from mass to number of particles:

Particles = (Mass / Molar Mass) × Avogadro's Number

N = (m / M) × Nₐ

Examples

Example 1: Moles to Atoms

How many atoms are in 2 moles of helium?

• Number of atoms = 2 mol × 6.022 × 10²³ atoms/mol
• Number of atoms = 1.2044 × 10²⁴ atoms

Example 2: Molecules to Moles

How many moles are in 3.011 × 10²³ water molecules?

• Moles = 3.011 × 10²³ / 6.022 × 10²³
• Moles = 0.5 mol

Understanding the Scale

Avogadro's number is extraordinarily large. To put it in perspective:

• If you counted one particle per second, it would take about 19 quadrillion years to count to Avogadro's number
• If you had Avogadro's number of pennies, they would cover the Earth to a depth of over 300 meters
• A mole of marbles would cover the entire United States to a height of about 7 km

Common Applications

• Stoichiometry: Calculating amounts of reactants and products in chemical reactions
• Molar mass calculations: Converting between mass and number of particles
• Gas law calculations: Ideal gas law applications
• Concentration calculations: Molarity and solution chemistry

Frequently Asked Questions

Why is Avogadro's number important?

It provides the connection between the microscopic world of atoms and molecules and the macroscopic world of grams and liters that we can measure.

Is Avogadro's number exact?

Yes, since 2019, Avogadro's number is defined exactly as 6.02214076 × 10²³ mol⁻¹ by the International Bureau of Weights and Measures.

What's the difference between atoms and molecules?

Atoms are single particles of an element. Molecules are groups of atoms bonded together. For example, O₂ is a molecule made of 2 oxygen atoms.

Tip: Remember that Avogadro's number applies to any type of particle - atoms, molecules, ions, electrons, or even photons!