Mole Calculator
18.015 grams of water equals exactly 1 mole, because water has a molar mass of 18.015 grams per mole. This mole calculator handles the core chemistry relationship n = m / M, where n is the amount of substance in moles, m is the mass in grams, and M is the molar mass in grams per mole. Pick what you want to solve for, then enter the two values you know. In moles mode you enter a mass and a molar mass to find how many moles you have. In mass mode you enter moles and a molar mass to find the mass in grams. In molar mass mode you enter a mass and a number of moles to work out the molar mass of the substance. Every result also reports the number of individual particles, atoms, molecules, or formula units, by multiplying the moles by Avogadro's number, 6.02214076 times ten to the twenty third. The tool checks that each value is a finite number greater than zero so you never divide by zero or get a meaningless negative amount.
Quick answer
One mole is the amount of a substance that contains 6.02214076 times ten to the twenty third particles, a value known as Avogadro's number.
What this tells you
- •One mole is the amount of a substance that contains 6.02214076 times ten to the twenty third particles, a value known as Avogadro's number.
- •Moles equal mass in grams divided by molar mass in grams per mole, written as n = m / M.
- •To find mass, rearrange the formula to m = n times M, multiplying moles by molar mass.
- •To find molar mass, rearrange to M = m / n, dividing the mass by the number of moles.
- •Molar mass in grams per mole is numerically equal to the substance's molecular or formula weight in atomic mass units.
- •Multiplying moles by Avogadro's number converts the amount of substance into a raw count of atoms, molecules, or ions.
How to Use
- 11. Choose what you want to solve for in the mode selector: moles, mass, or molar mass.
- 22. In moles mode, enter the mass in grams and the molar mass in grams per mole of your substance.
- 33. In mass mode, enter the number of moles and the molar mass to get the mass in grams.
- 44. In molar mass mode, enter the mass in grams and the number of moles to get the molar mass.
- 55. Read the primary result for the solved quantity, then check the secondary rows for the values you entered and the number of particles counted from Avogadro's number.
How It Works
Formula
n = m / M, m = n × M, M = m / n, particles = n × 6.02214076e23The mole equation ties three quantities together. n is the amount of substance in moles, m is the mass in grams, and M is the molar mass in grams per mole. Starting from n = m / M you can rearrange to solve for whichever value is unknown. Multiply moles by molar mass to recover mass, or divide mass by moles to recover molar mass. Once you know the number of moles, multiplying by Avogadro's number, 6.02214076 times ten to the twenty third, gives the total count of individual particles. The calculator requires every divisor and every entered value to be a finite positive number, since a zero molar mass, a zero mole count, or a negative mass has no physical meaning in this relationship.
Calculation note: values are processed in the order shown above, using the current input units.
Worked Examples
Grams of water to moles
Water has a molar mass of 18.015 grams per mole. Dividing 36.03 grams by 18.015 grams per mole gives 2 moles of water. Multiplying 2 moles by Avogadro's number reports about 1.204e+24 molecules.
Moles of sodium chloride to grams
Table salt, sodium chloride, has a molar mass of 58.44 grams per mole. Multiplying 2 moles by 58.44 grams per mole gives 116.88 grams. This is how you weigh out a target number of moles on a balance.
Finding an unknown molar mass
If a sample weighs 100 grams and you know it contains 2.5 moles, dividing 100 grams by 2.5 moles gives a molar mass of 40 grams per mole, which matches sodium hydroxide.
A small amount of carbon
Carbon has a molar mass of 12.011 grams per mole. Dividing 3 grams by 12.011 grams per mole gives about 0.2498 moles, which corresponds to roughly 1.504e+23 carbon atoms.
Molar Masses of Common Substances
Approximate molar masses you can drop straight into the calculator.
| Substance | Formula | Molar Mass (g/mol) |
|---|---|---|
| Water | H2O | 18.015 |
| Carbon | C | 12.011 |
| Sodium chloride | NaCl | 58.44 |
| Carbon dioxide | CO2 | 44.01 |
| Glucose | C6H12O6 | 180.16 |
| Oxygen gas | O2 | 32.00 |
| Sodium hydroxide | NaOH | 40.00 |
Molar masses are rounded to common textbook values and depend on the standard atomic weights used by your source.
What a mole actually counts
A mole is simply a counting unit, like a dozen or a gross, but scaled up to handle the enormous number of particles in even a tiny sample of matter. One dozen is 12 items. One mole is 6.02214076 times ten to the twenty third items. Chemists use it because atoms and molecules are far too small and far too numerous to count one by one, so grouping them into moles makes the math manageable.
The link between moles and grams is the molar mass. The molar mass of a substance in grams per mole is numerically the same as its molecular or formula weight in atomic mass units, which you get by summing the standard atomic weights of every atom in the formula. Because of this match, weighing out one molar mass in grams always gives you exactly one mole of that substance, no matter how large or small its individual particles are.
This calculator moves freely among the three quantities so you can start from whatever you know. In a lab you often measure mass on a balance and want moles for a reaction ratio. In a homework problem you might know moles and need the mass to weigh out. When identifying an unknown compound, you may measure both mass and moles and solve for the molar mass to narrow down what the substance is.
Common mistakes
- Confusing molar mass with molecular mass units. Molar mass is expressed in grams per mole, while molecular mass is in atomic mass units, even though the two share the same number.
- Entering a molar mass of zero. Molar mass sits in the denominator when solving for moles, so it must be a positive number or the result is undefined.
- Mixing up mass and moles when picking a mode. Double check that the value you type into the mass field is actually in grams, not already a mole count.
- Forgetting to balance the chemical formula before looking up a molar mass. The molar mass depends on the exact formula, so C6H12O6 and CH2O have very different values.
- Assuming particles always means atoms. The particle count applies to whatever unit the formula describes, which may be molecules, ions, or formula units rather than single atoms.
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