Atoms to Moles Calculator
Convert atoms to moles, molecules to moles, ions and formula units to moles — and back — plus grams to moles and moles to grams via molar mass. Every atoms-to-moles conversion uses the exact Avogadro constant (6.02214076×10²³ mol⁻¹), with step-by-step working shown.
Mole Conversion Calculator
Atoms to Moles Conversion Formulas
All four conversions in this atoms-to-moles calculator rest on two ideas: the Avogadro constant and molar mass.
How to Convert Atoms to Moles — Worked Examples
Example 1: 1.204×10²⁴ atoms of hydrogen → moles
- Formula: n = N ÷ NA
- Substitute: n = 1.204×10²⁴ ÷ 6.02214076×10²³
- Answer: n = 2.00 mol (3 significant figures)
Example 2: 0.5 mol of CO₂ → molecules
- Formula: N = n × NA
- Substitute: N = 0.5 × 6.02214076×10²³
- Answer: N = 3.011×10²³ molecules
Example 3: 25.0 g of NaCl → moles → formula units
- Grams to moles: n = 25.0 g ÷ 58.44 g/mol = 0.428 mol
- Moles to formula units: N = 0.428 × 6.02214076×10²³
- Answer: N = 2.58×10²³ formula units
Example 4: 3.011×10²³ molecules of H₂O → moles → grams
- Molecules to moles: n = 3.011×10²³ ÷ 6.02214076×10²³ = 0.500 mol
- Moles to grams: m = 0.500 × 18.015 g/mol
- Answer: m = 9.01 g of water
Reference: Particles per Mole for Common Substances
One mole of any substance — atoms, molecules, ions or formula units — always contains exactly 6.02214076×10²³ particles. What differs is the mass of that mole (the molar mass).
| Substance | Formula | Molar mass (g/mol) | Particles per mole |
|---|---|---|---|
| Water | H₂O | 18.015 | 6.02214076×10²³ |
| Sodium chloride | NaCl | 58.44 | 6.02214076×10²³ |
| Carbon dioxide | CO₂ | 44.01 | 6.02214076×10²³ |
| Oxygen | O₂ | 31.998 | 6.02214076×10²³ |
| Glucose | C₆H₁₂O₆ | 180.156 | 6.02214076×10²³ |
| Nitrogen | N₂ | 28.014 | 6.02214076×10²³ |
| Methane | CH₄ | 16.04 | 6.02214076×10²³ |
| Calcium carbonate | CaCO₃ | 100.087 | 6.02214076×10²³ |
| Sulfuric acid | H₂SO₄ | 98.079 | 6.02214076×10²³ |
| Gold | Au | 196.97 | 6.02214076×10²³ |
What Is a Mole in Chemistry?
A mole is the chemist's counting unit for particles too small and numerous to count individually. Just as a "dozen" always means 12, a mole always means 6.02214076×10²³ particles — whether those particles are atoms, molecules, ions, or formula units. The number is called the Avogadro constant (NA).
The mole bridges the invisible world of atoms and the visible world of grams: the molar mass of a substance tells you how many grams one mole weighs (e.g. 18.015 g for water, 58.44 g for table salt). That is why converting grams to moles needs the molar mass, while converting atoms to moles needs only Avogadro's number.
Avogadro's Number: A Short History
The constant is named after Amedeo Avogadro (1776–1856), who proposed that equal volumes of gases contain equal numbers of molecules. The term "Avogadro's number" was coined by Jean Perrin in the early 1900s after his experiments on Brownian motion gave the first solid measurements. For decades the mole was defined by the number of atoms in 12 grams of carbon-12. On 20 May 2019, the SI redefinition fixed the Avogadro constant at exactly 6.02214076×10²³ mol⁻¹ — this atoms-to-moles calculator uses that exact value.
Atoms to Moles — Frequently Asked Questions
How many atoms are in one mole?
Exactly 6.02214076×10²³ — that is the Avogadro constant (Nᴀ). One mole of anything — atoms, molecules, ions, or formula units — always contains 6.02214076×10²³ particles. Since the SI redefinition of 20 May 2019 this number is exact by definition, not a measured value.
How do you convert atoms to moles?
Divide the number of atoms by Avogadro's number: n = N ÷ 6.02214076×10²³. Example: 1.204×10²⁴ atoms of hydrogen ÷ 6.02214076×10²³ mol⁻¹ = 2.00 mol (3 significant figures). Try it in the calculator above.
How many moles are in 3.011×10²³ molecules of water?
3.011×10²³ ÷ 6.02214076×10²³ = 0.500 mol. So 3.011×10²³ water molecules is exactly half a mole of water.
How many molecules are in 2 moles of CO₂?
Multiply by Avogadro's number: N = n × 6.02214076×10²³. For 2 mol of CO₂: 2 × 6.02214076×10²³ = 1.204×10²⁴ molecules of CO₂.
How many atoms are in 0.25 mol of gold?
0.25 mol × 6.02214076×10²³ mol⁻¹ = 1.506×10²³ gold atoms. A quarter mole of any element always holds this many atoms.
How do you convert grams to moles?
Divide the mass by the molar mass: n = m ÷ M. Water has M = 18.015 g/mol, so 18.015 g ÷ 18.015 g/mol = 1.000 mol. Enter 18.015 as the molar mass in the Grams → Moles tab to repeat this.
What is the difference between atoms, molecules, ions and formula units?
They are different kinds of countable particle, but the mole math is identical. Atoms are single atoms (He, Au). Molecules are covalently bonded groups (H₂O, CO₂, O₂). Ions are charged particles (Na⁺, Cl⁻). Formula units are the smallest whole-number ratio in an ionic compound (NaCl). This calculator converts any of them — just pick the particle type.
Why is Avogadro's number 6.022×10²³?
The constant is named after Amedeo Avogadro (1776–1856), who proposed that equal volumes of gases hold equal numbers of molecules. Jean Perrin coined the term after measuring it via Brownian motion in the early 1900s. It was long tied to the atoms in 12 g of carbon-12; on 20 May 2019 the SI redefinition fixed it at exactly 6.02214076×10²³ mol⁻¹ by definition.
How many particles are in half a mole?
Half a mole × 6.02214076×10²³ = 3.011×10²³ particles — atoms, molecules, ions or formula units, whichever you are counting.
How many moles is 1.204×10²⁴ atoms of hydrogen?
1.204×10²⁴ ÷ 6.02214076×10²³ = 2.00 mol of hydrogen atoms (3 significant figures).
How do you convert moles to grams?
Multiply by the molar mass: m = n × M. Table salt has M = 58.44 g/mol, so 0.5 mol × 58.44 g/mol = 29.22 g of NaCl.
How many significant figures should I use in mole conversions?
Report the same number of significant figures as your least precise input. Example: 2.50 mol (3 s.f.) × 6.02214076×10²³ = 1.51×10²⁴ particles — quoted to 3 significant figures. Set 2–6 significant figures in the calculator above.
How many formula units are in 0.10 mol of NaCl?
0.10 mol × 6.02214076×10²³ mol⁻¹ = 6.022×10²² formula units of NaCl.
How many atoms are in 1 gram of hydrogen?
Two steps. First grams to moles: 1.000 g ÷ 1.008 g/mol = 0.9921 mol. Then moles to atoms: 0.9921 × 6.02214076×10²³ = 5.974×10²³ hydrogen atoms.
Free tool by NRTechStudio