Mole Calculator

What a mole counts

A mole is a count, not a weight. It names a specific number of particles, 6.02214076 x 10^23 of them, the same way a dozen names twelve. Chemists count in moles because reactions happen between particles: two hydrogen molecules meet one oxygen molecule to make water, and no scale can weigh a single molecule. The mole lets them weigh grams on a balance while thinking in particle counts.

The number stopped being a measured curiosity in 2019, when the SI redefinition fixed the Avogadro constant at exactly 6.02214076 x 10^23 per mole, as NIST explains in its mole redefinition summary. The value was chosen so that one mole of carbon-12 atoms, the reference isotope, weighs close to 12 grams on a balance.

What ties the count to the scale is molar mass, the weight in grams of one mole of a substance. Water is 18.02 grams per mole, salt is 58.44, carbon is 12.011. Every conversion this calculator performs is one division or one multiplication built from those two kinds of numbers.

The three lines behind every answer

Three relations cover every mole problem:

• Moles = grams / molar mass
• Grams = moles x molar mass
• Particles = moles x 6.02214076 x 10^23

Take a 24.0 gram lump of carbon. Its molar mass is 12.011 grams per mole, so 24.0 / 12.011 = 1.998 mol. Multiply by the Avogadro constant and the lump holds 1.20 x 10^24 atoms. Running the other way, 0.250 mol of water weighs 0.250 x 18.02 = 4.505 g, which is a hair under a teaspoon.

Watch the units in the first line. Molar mass carries grams per mole, so grams divided by grams per mole cancels to moles. If a molar mass is quoted in kilograms per mole, divide the mass by 1000 first and the same three lines hold.

The particle line does not care what the substance is. Moles of helium, moles of electrons and moles of sodium ions all convert to counts with the same constant; only the name of the particle changes.

Molar masses for common substances

A molar mass is built by adding atomic weights from the periodic table. Water takes two hydrogens and one oxygen: 2.016 + 15.999 = 18.015, which rounds to 18.02 grams per mole. The weights themselves come from the Commission on Isotopic Abundances and Atomic Weights, the body that maintains the standard atomic weights.

Calcium carbonate shows the adding-up step for a bigger formula: 40.078 + 12.011 + 3 x 15.999 = 100.086, reported as 100.09. Hydrates trip students here the same way they trip cooks: Epsom salt is magnesium sulfate with seven waters attached, and all seven count toward the molar mass of the crystal you weigh.

Worked examples at homework scale

The table runs the same division across five samples that show up in problem sets. The particle column multiplies each mole count by 6.02214076 x 10^23.

The water row in full: 25 / 18.02 = 1.387 mol, and 1.387 mol holds 8.35 x 10^23 molecules. The baking soda row shows why millimoles exist: 0.500 / 84.01 = 0.005952 mol is easier to say as 5.95 mmol, and even that small pinch holds 3.58 x 10^21 formula units, too many to write out digit by digit.

Atoms, molecules and formula units

One mole of carbon and one mole of salt contain the same number of particles, but the particles are not the same kind of thing. Carbon is an element, so its particles are atoms. Water comes as discrete molecules. Salt has no molecules at all: it is a lattice of sodium and chloride ions, so chemists count formula units, the smallest repeating unit of the lattice. The count is identical in every case; only the label changes.

Getting the label wrong does not change the arithmetic, but it does cost points on a graded set. A safe habit: metals and single elements take atoms, anything with a molecular formula takes molecules, and anything with a metal plus a nonmetal takes formula units. OpenStax Chemistry 2e walks through this naming in its formula mass chapter.

Moles away from the homework set

A 330 milliliter can of soda holds about 2.2 grams of dissolved carbon dioxide, which is 2.2 / 44.01 = 0.050 mol, or 3.01 x 10^22 molecules waiting to fizz. A five gram gold ring contains 5 / 196.97 = 0.0254 mol of gold atoms. Neither label says so, but the counts are there the moment you divide.

Gases add one more bridge: at 0 degrees Celsius and one atmosphere, one mole of any gas fills about 22.4 liters. That is why a mole of steam and a mole of helium take up the same room even though a helium atom weighs far less than a water molecule. The ideal gas law calculator handles the pressure and temperature side of that relation.

Cooking rarely needs moles, and the kitchen pages on this site skip them for good reason. Where the count earns its keep is comparison: two acids, two salts or two sugars behave differently in a recipe because their particles weigh different amounts, and the mole is the only unit that makes that comparison fair.

Mistakes that cost points

• Atomic number instead of atomic mass. Carbon is element 6 but weighs 12.011 grams per mole. Taking the whole number in the corner of the periodic table box instead of the decimal mass below the symbol cuts every answer by half.
• Forgetting diatomic elements. Oxygen in air is O2, so its molar mass is 31.998, not 15.999. Half a class loses this on the first gas problem.
• Rounding mid-calculation. Keep 1.38735 unrounded until the last step; rounding to 1.39 early shifts a particle count by about 1.6 x 10^21 molecules.
• Missing hydrate water. Copper sulfate runs 159.61 grams per mole anhydrous and 249.69 as the pentahydrate, a 56 percent jump for the same blue crystals.
• Wrong particle name. Writing molecules of salt is not a rounding issue, it is a category error: salt has formula units.

None of these are hard; they are habits. Write the molar mass with its units every single time, and most of the list above disappears on its own.

Neighboring tools for the other slices

Each related page on this site takes one slice of the same arithmetic. The grams to moles calculator starts from a kitchen substance list instead of a blank molar mass field. The atoms to moles calculator works from the particle side alone. The molar mass calculator builds a mass from any formula you type, the fastest route for a molecule this page does not list. The molarity calculator adds solution volume, the molality calculator swaps volume for solvent weight, and the mole fraction calculator compares two components of one mixture. For gases, the ideal gas law calculator connects moles to pressure, volume and temperature.