Mole Calculator

Moles = mass ÷ molar mass = particles ÷ 6.02214076 × 10²³ = concentration × volume

n

The amount of substance in moles — the number every route below arrives at. A mole is 6.02214076 × 10²³ entities, which is a definition rather than a measurement

m

The mass you weighed out, in grams. Divide it by the molar mass of the substance to get moles

M

Molar mass: the mass of one mole of the substance, in grams per mole. Type a chemical formula and this page computes it, or type the number from a reagent bottle

N

The number of particles — atoms, molecules, ions or electrons. Divide by Avogadro's number and the count cancels, leaving moles

c

Concentration, in moles per litre. Molarity and volume must both be filled in to make a route; one without the other has nothing to multiply

V

The volume of solution, in litres. Multiply by concentration and you have the moles dissolved in it, whatever the size of the container

Use it whenever a problem gives you something measurable — a weight from the balance, a count of particles, a volume of solution — and the next step wants moles. This conversion sits in the middle of nearly every stoichiometry question, because the coefficients in a balanced equation are ratios of moles and nothing else. It is also the page to use when two of your numbers came from different sources and you want to know whether they agree: fill in both routes and the page will tell you if they differ by more than a percent, which is usually a typo rather than a discovery.

1. One mole of table salt, weighed out

   1. Molar mass of NaCl: 22.990 (Na) + 35.45 (Cl) = 58.44 grams per mole
   2. Divide the mass by it: 58.44 ÷ 58.44 = 1 mole exactly
   3. In millimoles: 1 × 1000 = 1000 mmol
   4. In micromoles: 1 × 10⁶ = 1000000 µmol

   Weighing out the molar mass in grams is the definition of a mole, so this is the one case where the arithmetic is meant to come out at exactly 1 — and it does, because 58.44 g/mol is where the 58.44 grams came from. The three output rows are the same quantity at three scales, not three different results: a lab records this as 1000 mmol and a biochemical assay as 1000000 µmol.

2. A dilution, where the volume is small

   1. Concentration and volume are both given, so the solution route is open
   2. Multiply them: 0.5 mol/L × 0.25 L = 0.125 mol
   3. The litres cancel against the per-litre, leaving moles
   4. In millimoles: 125 mmol, which is how a protocol would write it

   Notice that only these two fields are filled in. Mass and the molar mass are blank and the page does not mind — the routes are independent, and filling in a partial route is not an error. Had the volume been given in millilitres the field would have converted it first, so 0.5 M × 250 mL arrives at the same 0.125 mol.

3. A trace quantity, where two of the three rows read zero

   1. Multiply: 1 × 10⁻⁵ mol/L × 0.001 L = 1 × 10⁻⁸ mol
   2. In moles, to six decimals, that is 0.000000 — the row rounds away
   3. In millimoles it is still 0.000
   4. In micromoles it is 0.01 µmol, and the quantity is visible again

   This is why the third row exists. Ten nanomoles is a real amount in trace analysis and in enzymology, and a panel that answered 0 to all three rows would be saying the solution contains nothing. The row that still reads non-zero is the answer; the two zeros above it are the display running out of decimal places, not a different result.

The three routes are only as good as the data you put in them, and the page does not know which of your numbers is the trustworthy one — it simply reports that they disagree. The one-percent tolerance is deliberate: reagent bottles print molar masses rounded to two decimals (58.44 for salt, where the atomic weights give the same figure, but 18.02 for water where they give 18.015), so a small disagreement is normal and a large one is an error. Avogadro's number is used as the defined value 6.02214076 × 10²³ exactly, so particle counts are converted without any measurement uncertainty — but the particle count itself is almost never known that precisely, and in practice it is a mass or a volume standing in for a count. The particle field accepts up to 10³⁰, which is about 1.7 million moles — a limit against a stuck keyboard rather than any chemical constraint. The third route assumes the concentration is the amount of the substance itself in moles per litre and that the solution is at the temperature its molarity was quoted at; a concentration given in normality or in mass-percent is not the same quantity, and a solution that has expanded in the heat holds fewer moles per litre than its label says. Lastly, the molar mass route says nothing about purity: 58.44 grams of a sample that is only 90% sodium chloride contains 0.9 moles of it, and this page has no way to know that.

How do I work out moles from grams?

Divide the mass in grams by the molar mass in grams per mole. For 58.44 grams of sodium chloride, whose molar mass is 58.44 g/mol, that is 1 mole. The molar mass comes either from the chemical formula, which this page parses and sums for you, or from the number printed on the reagent bottle. Fill in the formula field and leave the molar mass blank to have it computed; fill in both and the page will use your number as long as it agrees with the computed one to within a percent.

What is Avogadro's number, exactly?

6.02214076 × 10²³ per mole, and it is exact by definition — since the 2019 revision of the SI it is a fixed number, not a measured one. One mole of anything contains that many entities, whether they are atoms, molecules, ions or electrons. To go from a particle count to moles, divide by it: 6.022 × 10²³ molecules is 1 mole, and 2 × 10²¹ molecules is 0.003321 mol, or 3.321 mmol. The number is so large that a particle count is rarely measured directly; in practice you weigh or pipette something and let the mass stand in for the count.

Can I use the concentration and volume route with millilitres?

Yes — switch the volume field to mL and it converts to litres before multiplying, so 0.5 mol/L times 250 mL gives the same 0.125 mol as 0.5 times 0.25 L. The concentration field offers M and mM, and mM converts the same way. What does not work is filling in only one of the two: concentration without volume and volume without concentration are both half a route, and the page will say so rather than guess. A concentration in normality, in molality or in mass percent is a different quantity and belongs on its own page.

Why does the answer show 0.000000 in the first row?

Because the quantity is smaller than six decimal places of a mole. Ten nanomoles is 1 × 10⁻⁸ mol, and the moles row shows six decimals, so it reads 0.000000; the millimoles row reads 0.000 for the same reason. The micromoles row shows 0.01, and that is the real answer. The three rows are the same quantity at three scales, so when the top one runs out of room the bottom one is still readable — the alternative, showing 0 everywhere, would say the solution contains nothing.

What happens if I fill in two routes that disagree?

The page refuses to answer and says the two disagree by more than one percent. That is deliberate: the three routes are independent ways of reaching the same number, so a large disagreement means one of the inputs is wrong — a mistyped molar mass, a volume in millilitres entered as litres, a concentration that is really a normality. The one-percent band exists because reagent bottles round: water is printed as 18.02 g/mol on some labels and computed as 18.015 from the atomic weights, and that 0.03% difference is not an error. If you would rather not be checked, fill in a single route and the page will not compare anything.

Does it matter that the molar mass of a hydrate includes the water?

It does, and the formula parser knows: type CuSO4·5H2O and the five waters are included, giving 249.677 g/mol rather than the 159.602 of the anhydrous salt. That difference of 90 grams per mole is most of the compound's mass, so using the wrong one gives an answer that is wrong by more than half. Two cautions. Write the dot — without it, CuSO4 5H2O is a legal but different formula reading forty-six oxygens, and the field rejects that shape rather than guessing. And check the bottle: a hydrated salt that has sat open may have lost some of its water, in which case the formula is right and the sample is not.

• SI Units — Amount of Substance: the mole — National Institute of Standards and Technology (NIST)
• Standard Atomic Weights — abridged to four significant figures — Commission on Isotopic Abundances and Atomic Weights (CIAAW), IUPAC
• IUPAC Gold Book — amount of substance — International Union of Pure and Applied Chemistry (IUPAC)