Why the mole exists at all
Chemical reactions happen between whole numbers of particles, but you cannot count particles and you cannot weigh one. The mole solves this by fixing a counting unit large enough to be weighable: one mole is exactly 6.02214076 × 10²³ entities, a value the SI fixed by definition in 2019. Molar mass is then simply the mass of that many particles of your substance, in grams.
So the conversion is a unit conversion, no different in principle from feet to metres — except that the factor depends on the substance. One mole of hydrogen gas weighs 2.016 g; one mole of mercury weighs 200.59 g. Both contain the same number of particles. That is the whole idea, and it is why a balanced equation can be read directly in moles but never directly in grams.
You will use this conversion constantly, because it sits at both ends of nearly every quantitative problem. Masses go in, moles do the chemistry, and masses come back out. The mole-ratio calculator handles the middle step; this page handles the two ends.
The equation, and which way to point it
The relationship is n = m ÷ M, where n is the amount in moles, m is the mass in grams and M is the molar mass in grams per mole. Rearranged, m = n × M.
Choose the direction by asking what you are holding. If you are standing at a balance about to weigh a reagent for a recipe that calls for 0.25 mol, you are going from moles to grams, so multiply. If you have already weighed 3.42 g and want to know how much substance that is, you are going from grams to moles, so divide.
The unit algebra will catch a wrong-way error every time. Moles × (grams/mole) leaves grams; the mole units cancel. Grams ÷ (grams/mole) leaves moles. If your answer comes out in mol²/g, you have inverted the factor — a slip that shows up as an answer wrong by the square of the molar mass, which is usually obvious by magnitude.
Molar mass itself comes from the formula: sum each element's standard atomic weight times how many of that element appear. This calculator does that for you from the formula string, or you can type a value if your material is a mixture, a technical grade, or a polymer with an average mass rather than an exact formula. Full detail is on the molar mass calculator.
Worked example: weighing out 0.25 mol of sodium chloride
A procedure calls for 0.25 mol of sodium chloride. Work out what to put on the balance.
- Find the molar mass. Sodium is 22.990 g/mol and chlorine is 35.45 g/mol, so NaCl is 22.990 + 35.45 = 58.44 g/mol.
- Choose the direction. You have moles and want grams, so multiply.
- Multiply. m = 0.25 mol × 58.44 g/mol = 14.61 g.
- Check the particle count. 0.25 × 6.02214076 × 10²³ = 1.506 × 10²³ formula units — that is 1.506 × 10²³ sodium ions and the same number of chloride ions, because each formula unit supplies one of each.
Now the reverse. Your balance settles at 14.58 g rather than 14.61 g, which is normal. Divide: 14.58 ÷ 58.44 = 0.24949 mol. That is 0.2% below target, which matters for a primary standard used in titration and does not matter at all for a buffer you will pH-adjust anyway. Knowing which case you are in is the difference between wasting an afternoon and finishing one.
If this salt is going into solution, carry the mole figure straight to the molarity calculator: 0.24949 mol in 250 mL gives 0.998 mol/L.
Reading the result sensibly
Start with magnitude. For most laboratory salts and organic solids, one mole is somewhere between 40 g and 400 g, so a bench-scale preparation on the order of a gram is a few millimoles. If a calculation tells you to weigh 0.0004 g, you cannot do it directly on a four-place balance — the reading is at the instrument's resolution and the relative error is enormous. Weigh a hundred times more, dissolve it, and take an aliquot.
Then consider significant figures. Molar mass is known to five or six figures; your balance gives four or five. The answer therefore carries the balance's precision, not the molar mass's, so quoting 14.6104 g when the balance reads to 0.01 g is false precision.
Finally, be clear about what one mole contains. A mole of NaCl is a mole of formula units, which is two moles of ions. A mole of O₂ is a mole of molecules, which is two moles of oxygen atoms. Most errors in particle counting come from silently switching between these three senses of "particle".
Molar masses and what one mole weighs
| Substance | Formula | Molar mass (g/mol) | Mass of 0.100 mol (g) |
|---|---|---|---|
| Hydrogen gas | H₂ | 2.016 | 0.2016 |
| Water | H₂O | 18.015 | 1.8015 |
| Sodium hydroxide | NaOH | 39.997 | 3.9997 |
| Carbon dioxide | CO₂ | 44.009 | 4.4009 |
| Sodium chloride | NaCl | 58.440 | 5.8440 |
| Sodium hydrogen carbonate | NaHCO₃ | 84.006 | 8.4006 |
| Sulfuric acid | H₂SO₄ | 98.072 | 9.8072 |
| Calcium carbonate | CaCO₃ | 100.086 | 10.0086 |
| Potassium permanganate | KMnO₄ | 158.032 | 15.8032 |
| Glucose | C₆H₁₂O₆ | 180.156 | 18.0156 |
| Copper(II) sulfate pentahydrate | CuSO₄·5H₂O | 249.677 | 24.9677 |
| Mercury | Hg | 200.590 | 20.0590 |
Every row is the molar mass multiplied by 0.100 — the same single step this calculator performs.
Errors that show up in this conversion
- Dividing when you should multiply. Track the units. Moles × g/mol gives grams; grams ÷ g/mol gives moles.
- Using the anhydrous molar mass for a hydrated reagent. Copper(II) sulfate is 159.60 g/mol anhydrous and 249.68 g/mol as the pentahydrate. Read the bottle, not the name.
- Forgetting that molar mass is substance-specific. There is no universal grams-per-mole figure, and 22.4 is a molar volume for an ideal gas at 0 °C and 1 atm, not a mass.
- Weighing an amount below the balance's usable range. A four-place balance reads to 0.1 mg, so a 20 mg weighing already carries 0.5% uncertainty and a 2 mg weighing carries 5%. Dilute from a larger weighing instead.
- Confusing formula units with atoms. One mole of Ca(NO₃)₂ contains one mole of calcium ions but two moles of nitrate ions and nine moles of atoms.
- Quoting more figures than the balance supports. The molar mass is not the limiting uncertainty; your weighing almost always is.
Related conversions and where this one stops
Three cousins of this conversion cover most of what else you will need. For a solution, concentration replaces molar mass as the bridge: moles = molarity × volume in litres, handled by the molarity calculator. For a gas, the ideal gas law does the same job through PV = nRT, so a volume at a known pressure and temperature converts to moles without any weighing at all. For a reaction, the coefficient ratio converts moles of one species into moles of another, which is the mole-ratio step.
What this calculator deliberately does not do is account for purity. A reagent labelled 98% pure needs 100/98 times the calculated mass to deliver the intended amount of substance, and technical-grade solids are often worse. For assays that matter — titrant standardisation, elemental standards — use a certified primary standard and take the purity from its certificate.
It also treats the molar mass as exact for the substance named. That is a good assumption for a defined compound and a poor one for anything with a distribution of masses. Polymers, humic materials and protein preparations have no single molar mass, only an average whose definition you must state before the arithmetic means anything.
One point of history that explains a common confusion: before 2019 the mole was defined as the number of atoms in exactly 12 g of carbon-12, which made molar mass in g/mol numerically identical to relative molecular mass by definition. The redefinition fixed the Avogadro constant instead, so the two are now equal only to within an experimentally tiny difference — about one part in a billion, which changes nothing you will ever weigh.