Free Mole Calculator
Convert between moles, mass, and molar mass using n = mass ÷ molar mass, and instantly see how many atoms or molecules that is via Avogadro's number.
Enter the two known values — the third is calculated from n = mass ÷ molar mass. Particles = moles × Avogadro's number.
n = m ÷ M · m = n × M · M = m ÷ n. Avogadro's number Nₐ = 6.02214076 × 10²³ /mol. Use grams for mass and g/mol for molar mass; convert mg or kg to grams first.
Quick answer
The number of moles equals mass divided by molar mass: n = m ÷ M. For example, 18 g of water (molar mass 18.015 g/mol) is 18 ÷ 18.015 ≈ 0.9992 mol. Multiply moles by Avogadro's number (6.02214076 × 10²³ /mol) to get the number of particles, so 0.9992 mol ≈ 6.017 × 10²³ molecules.
Formula & method
Moles from mass and molar mass
n = m ÷ M
- n — amount of substance in moles (mol)
- m — mass of the sample in grams (g)
- M — molar mass in grams per mole (g/mol)
Rearranges to m = n × M and M = m ÷ n. Molar mass M is the sum of the atomic masses of every atom in the formula, read from the periodic table.
Number of particles
N = n × Nₐ, where Nₐ = 6.02214076 × 10²³ /mol
- N — number of particles (atoms, molecules, or ions)
- Nₐ — Avogadro constant, exactly 6.02214076 × 10²³ per mole
Since the 2019 SI redefinition, Avogadro's number is an exact, defined value. One mole always contains this many elementary entities.
Examples
- Input
- mass = 18 g, molar mass = 18.015 g/mol
- Result
- ≈ 0.999167 mol (≈ 6.01713 × 10²³ molecules)
- Why
- n = 18 ÷ 18.015 = 0.999167 mol. Multiply by 6.02214076 × 10²³ to get 0.999167 × 6.02214076e23 ≈ 6.01713 × 10²³ water molecules — essentially one mole, since 18 g is close to water's molar mass.
- Input
- moles = 0.25 mol, molar mass = 58.44 g/mol (NaCl)
- Result
- 14.61 g
- Why
- Rearrange to m = n × M = 0.25 × 58.44 = 14.61 g. Weighing out 14.61 g of table salt gives you exactly a quarter mole.
- Input
- mass = 44 g, moles = 1 mol
- Result
- 44 g/mol
- Why
- M = m ÷ n = 44 ÷ 1 = 44 g/mol. A 44 g sample that you know is one mole has a molar mass of 44 g/mol, consistent with carbon dioxide, CO₂ (12.011 + 2 × 15.999 ≈ 44.01 g/mol).
- Input
- mass = 36 g, molar mass = 18.015 g/mol (water)
- Result
- ≈ 1.99833 mol (≈ 1.20343 × 10²⁴ molecules)
- Why
- n = 36 ÷ 18.015 = 1.99833 mol. Twice the mass of the first example gives twice the moles, and 1.99833 × 6.02214076e23 ≈ 1.20343 × 10²⁴ molecules.
When to use this tool
- Preparing a reaction or solution and you need to weigh out a specific number of moles of a reagent.
- Converting a measured mass into moles to balance a chemical equation or apply stoichiometric ratios.
- Estimating the number of atoms, ions, or molecules in a sample using Avogadro's number.
- Back-calculating an unknown molar mass from a known mass and mole count in a lab determination.
Common mistakes
- Confusing molar mass (g/mol, e.g. 18.015 for water) with molecular weight expressed in atomic mass units (u) — the numbers match but the units differ; use g/mol here.
- Forgetting to convert mass to grams. If your sample is in milligrams or kilograms, convert first (1 kg = 1000 g, 1 mg = 0.001 g) before dividing by molar mass.
- Summing the wrong atoms for molar mass — count every atom in the formula, including subscripts (CO₂ is 12.011 + 2 × 15.999, not 12.011 + 15.999).
- Dividing by zero: a molar mass or mole count of 0 makes the formula undefined, so the result is blank until you enter a valid non-zero value.
Frequently asked questions
What is the formula for calculating moles?
Moles equal mass divided by molar mass: n = m ÷ M. Mass is in grams and molar mass is in grams per mole, so the grams cancel and you are left with moles. For example, 18 g of water ÷ 18.015 g/mol ≈ 0.9992 mol.
How do I find the molar mass of a compound?
Add the atomic mass (from the periodic table) of every atom in the chemical formula. For water, H₂O, that is 2 × 1.008 + 15.999 ≈ 18.015 g/mol. For carbon dioxide, CO₂, it is 12.011 + 2 × 15.999 ≈ 44.01 g/mol.
How many particles are in one mole?
Exactly 6.02214076 × 10²³ particles — Avogadro's number. Since the 2019 SI redefinition this is a defined constant, so one mole of any substance contains this many atoms, molecules, or ions. Multiply your mole value by this number to get the particle count.
Why is 18 g of water about 1 mole?
Because water's molar mass is 18.015 g/mol, so 18 ÷ 18.015 ≈ 0.9992 mol — just under one mole. A full mole of water weighs 18.015 g. This is why chemists often treat ~18 g of water as roughly one mole for quick estimates.
What units should I use in the mole calculator?
Use grams for mass and grams per mole (g/mol) for molar mass; the result is in moles. If your mass is in kilograms or milligrams, convert to grams first (1 kg = 1000 g, 1 mg = 0.001 g) so the units are consistent.
Can I work out mass or molar mass instead of moles?
Yes. The same relationship rearranges three ways: n = m ÷ M to find moles, m = n × M to find mass, and M = m ÷ n to find molar mass. Choose which quantity to solve for and enter the other two.
Sources & references
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