Avogadro's Number Calculator

Avogadro's number (also called Avogadro's constant, symbol N_A) is 6.02214076 x 10^23 per mole, the number of elementary entities (atoms, molecules, ions, or other particles) contained in exactly one mole of a substance. Since the 2019 redefinition of the SI base units, this value is exact by definition, not a measured quantity with experimental uncertainty.

N = n x N_A, where N is the number of particles, n is the amount of substance in moles, and N_A is Avogadro's constant, 6.02214076 x 10^23 per mole. Rearranged, n = N / N_A converts particle count back to moles.

The value comes from defining the mole so that the molar mass of carbon-12 is exactly 12 grams per mole. Historically, Avogadro's number was measured experimentally (through methods like X-ray crystal density and electrolysis) and refined over more than a century. In 2019, the SI redefined the mole using a fixed, exact value of the Avogadro constant, so it is now a defining constant of the unit system rather than a measured result.

Amedeo Avogadro was an Italian scientist who proposed in 1811 that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules, now known as Avogadro's law. He never actually calculated the numerical value of the constant that bears his name, it was first estimated decades later by other scientists, but it was named in his honor for the hypothesis that made the concept of counting particles by mole possible.

The Avogadro's Number Calculator converts between moles and a raw particle count (atoms, molecules, ions) using N = n x N_A, and is meant to explain and demonstrate Avogadro's constant itself. The Grams to Moles Calculator instead converts a mass in grams to moles using a substance's molar mass (n = mass / M), a completely different, mass-based conversion. Use the Avogadro's Number Calculator when you already know or want a mole/particle count; use Grams to Moles when starting from a weighed mass.

The Mole Calculator is a broader hub tool that solves for any missing value among mass, molar mass, and moles, or among moles, volume at STP, and particle count, switching between two calculation modes. This Avogadro's Number Calculator focuses specifically and only on the moles-to-particles relationship, with more explanatory context about the constant itself.

Yes. Avogadro's number applies universally to any substance and any type of particle, atoms of an element, molecules of a compound, ions in solution, electrons, or even non-chemical objects in principle. One mole always means exactly 6.02214076 x 10^23 of whatever entity you are counting.

Exactly 6.02214076 x 10^23 atoms, regardless of which element. One mole of carbon contains the same number of atoms as one mole of gold or one mole of hydrogen, even though their masses differ dramatically because each element has a different atomic mass.

No, they measure completely different things and should not be confused. Avogadro's number is a pure count, the number of particles in one mole, with no units of mass. Molar mass is the mass in grams of one mole of a specific substance, and is different for every substance. They are connected: dividing a sample's mass by its molar mass gives moles, and multiplying moles by Avogadro's number gives the particle count.

Before 2019, the mole was defined in terms of the mass of carbon-12, and Avogadro's constant was a measured quantity with experimental uncertainty determined by methods like the X-ray crystal density (XRCD) method. The 2019 SI redefinition flipped this relationship: the mole is now defined by fixing Avogadro's constant at exactly 6.02214076 x 10^23 per mole, making the constant exact by definition and removing any measurement uncertainty from it.