How this mole calculator works
Every mole problem is the same three-station railway line, ridden in one direction or the other:
divide or multiply by the molar mass on the left leg, and by 6.02214076 × 1023 on the right leg
Type a formula and the page works out the molar mass for you from the IUPAC atomic weights, the same verified table our molar mass calculator is built on. Then enter whichever amount you actually have: a mass in grams, a mole count, or a particle count, and the other two are computed, with every division and multiplication shown using your numbers. If you already know the molar mass, type it as a plain number instead of a formula and the page uses it as given. And if you enter a mass and a mole count with the formula box empty, the page runs the triangle the third way and tells you what molar mass your numbers imply, which is a fingerprint you can hold up against a periodic table.
The formula
mass = moles × M
particles = moles × NA
M = mass ÷ moles
M is the molar mass in grams per mole, the sum of the atomic weights in the formula. NA is Avogadro's constant, which is exactly 6.02214076 × 1023 per mole: the 2019 redefinition of the SI fixed it by decree, so the moles-to-particles leg of the chain is a definition, not a measurement, and introduces no error at all. Enter any two of mass, moles and molar mass, and the third falls out of the same triangle.
Worked example: a glass of water
How many molecules are in a glass of water? Water is H2O, so its molar mass is 2 × 1.008 + 15.999 = 18.015 g/mol. That is the famous landmark: one mole of water is 18.015 g, the 18.02 your textbook rounds to, and it holds 6.022 × 1023 molecules.
A decent glass holds about 250 g. Moles = 250 ÷ 18.015 = 13.877 mol. Particles = 13.877 × 6.02214076 × 1023 = 8.357 × 1024 molecules, about eight and a third trillion trillion.
For scale: current estimates put the number of stars in the observable universe somewhere between 1022 and 1024. Your glass of water beats even the top of that range, roughly eight times over. Not the number of stars you can see, and not the stars in our galaxy: every star in every galaxy anyone can observe, outnumbered by a drink of water. That is the size of the number chemistry quietly rides on, and why the mole exists at all: nobody wants to do arithmetic on 8,357,000,000,000,000,000,000,000 of anything.
A mole is a count, not a mass
This is the single idea the whole topic hangs on, and the place most confusion starts. A mole is chemistry's dozen: 6.02214076 × 1023 of whatever you are counting. A mole of feathers and a mole of lead weigh wildly different amounts and contain exactly the same number of particles, which is the entire point. The mass of a mole changes from substance to substance; the count never does.
What makes the dozen this particular size? It was chosen so that the count in grams equals the atomic weight in daltons. One atom of carbon weighs about 12 daltons; one mole of carbon weighs about 12 grams. That correspondence is the trick that lets a balance count atoms, and it is why the historical definition was anchored to exactly 12 g of carbon-12: the mole was literally however many atoms that lump contained, a number you had to measure. In 2019 the SI turned the arrangement around. The count itself became the definition, exact by decree, and the 12 g of carbon-12 became merely very close to a mole rather than exactly one. Nothing in any lab changed; the bookkeeping just got honest about which number was fundamental.
Once you hold the count-not-mass idea firmly, the operations stop needing memorisation. Grams to moles divides by the molar mass because the molar mass says how many grams each mole carries, so the grams get shared out. Moles to grams multiplies for the same reason. And moles to particles multiplies by Avogadro's number because that is what a mole means, the way a dozen means twelve.
Molar mass is the bridge, and case is part of the formula
The only substance-specific number in the whole chain is the molar mass, which is why it is the thing to be careful with. This page computes it from the same IUPAC atomic weight table as our molar mass calculator, which also shows the published uncertainties and the percent composition if you want the full story. Two habits worth carrying into any formula you type here. First, capitalisation is load bearing: CO is carbon monoxide at 28.01 g/mol and Co is cobalt at 58.93 g/mol, and this page will not quietly repair one into the other, because a corrected typo becomes a confident wrong answer. Second, a genuinely ambiguous ionic charge like SO42- gets handed back with instructions rather than guessed at: write SO4^2- and the ambiguity disappears.
Where the moles go next is its own arithmetic, and the site covers the usual destinations: dissolving them into a solution is our molarity calculator, and pushing them through a reaction to see what mass should come out the other end is our percent yield calculator.
If it is a gas, moles become liters
Gases get one bonus conversion, because for an ideal gas the volume of a mole does not depend on which gas it is. At 0 °C and 1 atm, one mole of any ideal gas occupies 22.414 L, the figure generations of students have memorised. IUPAC quietly moved its standard pressure to 100 kPa back in 1982, and at that standard the same mole fills 22.711 L, a 1.3% difference that has cost many exam points. Tick the gas option above and the page converts your moles to liters at both standards, so you can quote whichever your course uses.
Two honest boundaries on that number. It is an ideal gas figure, and real gases drift away from it at high pressure and low temperature, which is where our gas law calculator and its warnings take over. And it applies to gases only: a mole of liquid water is about 18 mL, more than a thousand times smaller, because in a liquid the molecules actually touch. If your substance is a solid or a liquid, the liters simply do not apply, which is why this page asks before showing them.