Avogadro's Number Calculator

Frequently Asked Questions

What is Avogadro's number and why is it 6.022 x 10^23?

Avogadro's number (NA = 6.02214076 x 10^23 mol^-1) is defined so that 1 mole of carbon-12 atoms has a mass of exactly 12 grams. The 2019 SI redefinition fixed NA to an exact value. It is large because atoms are extremely small - a single carbon atom weighs about 2 x 10^-23 g.

How do I calculate the number of atoms in a sample?

First convert mass to moles: moles = mass / molar mass. Then multiply by Avogadro's number: N = moles x 6.022 x 10^23. For example, 12 g of carbon = 1 mol, so it contains 6.022 x 10^23 carbon atoms. For compounds, this gives molecules; for ionic compounds, formula units.

What is the mass of a single atom or molecule?

Divide the molar mass by Avogadro's number. A single water molecule: 18.015 g/mol / (6.022 x 10^23) = 2.99 x 10^-23 g. A single iron atom: 55.845 / (6.022 x 10^23) = 9.27 x 10^-23 g. These masses are also expressible in atomic mass units (amu or Da), where 1 amu = 1.66054 x 10^-24 g.

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How This Calculator Works

Avogadro's number NA = 6.02214076 x 10^23 mol^-1 is the bridge between the macroscopic world of grams and the microscopic world of atoms and molecules. Given moles, the calculator multiplies by NA to get the number of particles. Given grams, it first divides by molar mass to get moles, then multiplies by NA. Given a number of particles, it divides by NA to get moles.

What Is Avogadro's Number

Avogadro's number is the count of elementary entities in one mole of substance. It is named after Amedeo Avogadro, the Italian scientist who first proposed that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules. The value 6.02214076 x 10^23 was fixed exactly by the 2019 SI redefinition of the mole.

Why 6.022 x 10^23

The mole was historically defined so that 12 grams of carbon-12 contained exactly one mole of atoms. The number of atoms in that sample was measured by many experimental methods - X-ray crystallography, electrochemistry, and oil-drop experiments - and converged on approximately 6.022 x 10^23. The 2019 SI revision locked the number exactly and redefined the mole accordingly.

Scale of Avogadro's Number

To appreciate the scale: if you had 6.022 x 10^23 sand grains, they would cover the entire surface of Earth in a layer about 80 meters deep. If you stacked that many pennies, the tower would reach from the Sun to Alpha Centauri and back roughly 75 billion times. Atoms are extraordinarily small, which is why so many of them fit in a single gram of material.

Avogadro's Number in the Modern SI

Since May 2019, the mole is defined by fixing NA to exactly 6.02214076 x 10^23 mol^-1. This makes the mole consistent with the kilogram, which is now defined by the Planck constant. The practical effect for chemistry is negligible, but the conceptual shift is important: the mole no longer depends on a physical artifact or isotope standard.

Avogadro's Number Calculator

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