Mole Calculator
Convert between grams, moles, and number of particles using molar mass and Avogadro’s number.
That is 1.204 × 10²⁴ particles (moles × Avogadro’s number).
To convert grams to moles, divide the mass by the molar mass: moles = mass ÷ molar mass. To get the particle count, multiply moles by Avogadro’s number, 6.02214076 × 10²³. So 36.03 g of water ÷ 18.015 g/mol = 2 mol = 1.204 × 10²⁴ molecules.
What a mole is and how the conversions work
A mole is simply a count: one mole is exactly 6.02214076 × 10²³ particles — atoms, molecules, ions, or formula units. That fixed quantity is Avogadro’s number, the SI defined value. The molar mass of a substance is the mass of one mole in grams per mole, numerically equal to its formula’s atomic-weight sum.
These two constants chain the three quantities together. Mass and moles are linked through molar mass; moles and particle count are linked through Avogadro’s number. Pick the direction you need and the calculator fills in the rest.
N_A = 6.02214076 × 10²³ particles per mole (the exact SI defined value)
Worked example
How many moles and molecules are in 36.03 g of water (molar mass 18.015 g/mol)?
- 1 Find the molar mass. Water, H₂O, has a molar mass of 18.015 g/mol — the sum of two hydrogens (2 × 1.008) and one oxygen (15.999).
- 2 Divide mass by molar mass. 36.03 g ÷ 18.015 g/mol = 2 mol of water.
- 3 Multiply moles by Avogadro’s number. 2 mol × 6.02214076 × 10²³ = 1.204 × 10²⁴ molecules of water.
Molar masses of common substances
Computed from standard atomic weights; use these to convert mass to moles.
| Substance | Formula | Molar mass (g/mol) |
|---|---|---|
| Water | H₂O | 18.015 |
| Table salt | NaCl | 58.44 |
| Carbon dioxide | CO₂ | 44.01 |
| Glucose | C₆H₁₂O₆ | 180.16 |
| Sodium hydroxide | NaOH | 40.00 |
| Sulfuric acid | H₂SO₄ | 98.07 |
Reading the result correctly
Particles means whatever the formula unit is. One mole of CO₂ is 6.022 × 10²³ molecules, but it contains three times as many atoms (one carbon and two oxygens each). Decide whether you want molecules or atoms before scaling.
Keep molar mass precise. Rounding 18.015 to 18 before dividing shifts the mole count by about 0.08% — small, but it compounds in multi-step problems. Carry full precision until the final answer.
Watch the units. Mass must be in grams to pair with g/mol. Convert milligrams or kilograms first, or the moles will be off by a factor of a thousand.