Avogadro's Number Calculator

Chemists deal with numbers of atoms and molecules so vast that counting them individually is hopeless, so they group particles into moles, and Avogadro's number is the bridge between the two, this calculator converting freely in both directions. Enter a number of moles and it tells you how many particles that is; enter a number of particles and it tells you how many moles. Everything updates as you type. Avogadro's number, 6.022 times ten to the twenty-third, is one of the fundamental constants of chemistry: it is simply the count of particles in one mole of any substance. The mole was chosen so that this number of particles of an element weighs, in grams, the same as the element's relative atomic mass, which is what makes the mole the natural counting unit that ties the invisible world of atoms to the measurable world of grams in the lab. To turn moles into particles you multiply by Avogadro's number, and to turn particles back into moles you divide by it, a pair of operations so common in chemistry that having them at your fingertips saves constant fiddling with scientific notation and exponents, where small slips are easy to make. The particles being counted might be atoms for an element, molecules for a covalent compound, or formula units and ions for an ionic compound, but the conversion is always the same. That makes the tool genuinely useful for chemistry students learning the mole concept, particle counting and the link between moles and mass, for checking homework and lab calculations, and for anyone who needs to move quickly between an amount in moles and a raw count of particles. The constant used is the modern value of Avogadro's number. The method and a worked example are explained clearly below.

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Moles to particles

1.2044e+24
particles

Particles to moles

0.999977
moles

How it works

Avogadro's number is N = 6.022 times 10 to the 23 particles per mole. The number of particles is the moles times N. The number of moles is the particles divided by N. Scientific notation, like 6.022e23, is accepted in the inputs.

Worked example

For 2 moles: the particles are 2 times 6.022 times 10 to the 23, which is about 1.204 times 10 to the 24 particles. Going the other way, 6.022 times 10 to the 23 particles is exactly 1 mole.

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Frequently asked questions

What is Avogadro's number?

Avogadro's number is 6.022 times 10 to the 23, the number of particles in one mole of a substance. A mole of any substance contains this many atoms, molecules or ions, which is how chemists count the unimaginably large numbers of particles in a sample.

How do you convert moles to particles?

Multiply the number of moles by Avogadro's number, 6.022 times 10 to the 23. So 2 moles contain 2 times 6.022 times 10 to the 23, which is about 1.204 times 10 to the 24 particles. To go back, divide the particles by Avogadro's number.

What counts as a particle?

It depends on the substance: for an element it is usually atoms, for a molecular compound it is molecules, and for an ionic compound it can be formula units or ions. A mole always contains Avogadro's number of whichever particle you are counting.