Convert between moles and number of particles (atoms, molecules, or ions) using Avogadro's number (6.022 × 10²³), or start from a mass and molar mass. For the broader moles/mass/molar-mass workflow, see the Moles Calculator.
Convert moles ↔ particles
Avogadro's number: 6.02214076 × 10²³ particles per mole. Scientific notation (e.g. 6.022e23) is accepted.
Enter a mass and molar mass to compute the particle count.
Moles—
Particles—
Avogadro's number, precisely
Avogadro's number (NA) is the number of elementary entities — atoms, molecules, ions, or any other specified particle — in exactly one mole of a substance.
Textbook (rounded)6.022 × 10²³
SI-exact (2019 redefinition)6.02214076 × 10²³
Since the 2019 redefinition of the SI base units, the mole is defined by fixing NA to this exact value — it is no longer tied to the mass of carbon-12. This calculator uses the SI-exact value internally.
Atoms, molecules, and ions — same conversion
Avogadro's number converts moles to a count of "elementary entities," and that term covers all three:
Entity type
Example
1 mol contains
Atoms
Iron (Fe)
6.022 × 10²³ Fe atoms
Molecules
Water (H₂O)
6.022 × 10²³ H₂O molecules
Ions
Sodium ion (Na⁺)
6.022 × 10²³ Na⁺ ions
Particle counts for familiar amounts
Amount
Moles
Particle count
1 mole of any substance
1 mol
6.022 × 10²³
12 g of carbon-12 (defines the mole)
1 mol
6.022 × 10²³ atoms
1 mole of gas at STP (22.4 L)
1 mol
6.022 × 10²³ molecules
A grain of table salt (≈1 mg NaCl)
≈1.7 × 10⁻⁵ mol
≈1.0 × 10¹⁹ ion pairs
A drop of water (≈0.05 mL)
≈0.0028 mol
≈1.7 × 10²¹ molecules
Estimated atoms in the human body
—
≈7 × 10²⁷
Figures are order-of-magnitude estimates for intuition — use the Moles ↔ Particles or Mass ↔ Particles tabs above for a precise conversion of your own numbers.
4 min read3 steps6 terms3 examples6 FAQsN = n × N_A
Avogadro's number bridges the microscopic world of atoms and molecules with the macroscopic amounts chemists actually weigh out on a scale.
📋
Walk-through
How to Use This Calculator
3 steps▸
1
Pick a direction
Choose the Moles ↔ Particles tab to convert straight from a mole amount to a particle count (or back), or the Mass ↔ Particles tab if you're starting from a mass and a molar mass instead.
2
Enter your value
Type a mole amount, a particle count, or a mass — scientific notation like 6.022e23 is accepted. The calculator multiplies (or divides) by Avogadro's number, 6.02214076 × 10²³, and updates the result instantly.
3
Read the particle count
The result card shows both the mole amount and the particle count side by side, plus a plain-English line explaining the conversion. Use the Reference tab if you want context for how big that number actually is.
⚡
Reference
Formula & Methodology
2 formulas▸
Moles to particles
N = n × N_A
N is the number of particles (atoms, molecules, or ions), n is the amount in moles, and N_A is Avogadro's number, 6.02214076 × 10²³ particles per mole (the 2019 SI-exact value).
Mass to particles
n = mass ÷ M, then N = n × N_A
When you start from a mass, first divide by the molar mass M (in g/mol) to get moles n, then multiply by Avogadro's number to get the particle count N.
📖
Glossary
Key Terms Explained
6 terms▸
Avogadro's number ↗The number of elementary entities (atoms, molecules, ions, or formula units) in exactly one mole of a substance: 6.02214076 × 10²³, fixed exactly by the 2019 SI redefinition.
Mole ↗The SI base unit for amount of substance. One mole always contains Avogadro's number of elementary entities, regardless of what those entities are.
Particle ↗A general term for the elementary entity being counted — an atom, molecule, ion, or formula unit, depending on the substance.
Atom ↗The smallest unit of a chemical element that retains its properties, e.g. a single iron (Fe) atom.
Molecule ↗Two or more atoms bonded together, e.g. a water molecule (H₂O) made of two hydrogen atoms and one oxygen atom.
Molar mass ↗The mass of one mole of a substance, in grams per mole (g/mol). Used to convert between mass and moles before applying Avogadro's number.
👥
Scenarios
Real-World Examples
3 worked examples▸
🧪
Chemistry student
1 mole of any substance
Moles 1Direction Moles → Particles
1 mol × 6.02214076 × 10²³ = 6.022 × 10²³ particles. This is true no matter what the substance is — 1 mole of iron atoms, 1 mole of water molecules, and 1 mole of sodium ions all contain the same number of particles.
⚗️
Lab prep
Particles from a mass of water
Mass 18 gMolar mass 18.015 g/mol
18 g ÷ 18.015 g/mol ≈ 0.99917 mol, then 0.99917 mol × 6.02214076 × 10²³ ≈ 6.017 × 10²³ water molecules — almost exactly one mole because 18 g of water is close to its molar mass.
🔬
Quick sanity check
Atoms in a gram of carbon
Mass 1 gMolar mass 12.011 g/mol
1 g ÷ 12.011 g/mol ≈ 0.0833 mol, then × 6.02214076 × 10²³ ≈ 5.014 × 10²² carbon atoms in a single gram — illustrating just how small atoms are relative to everyday mass.
🔗
Reference
Cite This Calculator
APA & MLA▸
Use either format to cite this calculator in a paper, report, or resource list.
Avogadro's number bridges the microscopic world of atoms and molecules with the macroscopic amounts chemists actually weigh out on a scale. This calculator converts directly between a mole amount and a particle count, or starts from a mass and molar mass — for chemistry students, lab work, or anyone who needs a fast, precise particle count without doing the exponent math by hand.
How the conversion works
▸
The relationship is a single multiplication: N = n × NA, where n is the amount in moles and NA is Avogadro's number. Since the 2019 SI redefinition, NA is fixed at exactly 6.02214076 × 10²³ — it no longer depends on the mass of a carbon-12 sample the way it historically did. This calculator uses that SI-exact value internally, though results are commonly rounded to 6.022 × 10²³ for everyday chemistry.
When you're starting from a mass instead of a mole amount, the Mass ↔ Particles tab first solves n = mass ÷ molar mass, then applies the same N = n × NA relationship to get the particle count.
Avogadro's Number Calculator vs. the Moles Calculator
▸
If you already know a mole amount (or a particle count) and just want the fast conversion, this page is the quickest path — enter one number, get the other, with scientific notation on both sides. The Moles Calculator is the broader tool: it solves for moles from mass and molar mass, lets you solve for any of the three (mass, moles, or molar mass) when you know the other two, and includes its own moles ↔ particles conversion as one of several modes. Use this page when Avogadro's number is the whole point of the calculation; use the Moles Calculator when you're working through a full mass/molar-mass/moles problem and particles are just the last step.
Why the mole is defined this way
▸
The mole exists so chemists can count atoms and molecules by weighing them. A single atom is far too small to weigh individually, but a mole of atoms — 6.022 × 10²³ of them — is a workable, weighable quantity for almost any element or compound. That is the entire reason Avogadro's number is so large: it has to bridge the gap between atomic-scale mass units and gram-scale lab measurements.
Limits and edge cases
▸
This calculator assumes you already know (or can look up) the correct molar mass for the Mass ↔ Particles tab — an incorrect molar mass will silently produce a wrong particle count, since the math itself can't detect that error. It also treats "particles" generically: it does not distinguish between atoms, molecules, and ions, since Avogadro's number applies identically to all three. For compound stoichiometry (converting between reactants and products in a chemical equation), use the Stoichiometry Calculator instead — this tool only handles the moles-particles-mass relationship for a single substance.
❓
Questions
Frequently Asked Questions
6 questions▸
What is the value of Avogadro's number?+
Avogadro's number is 6.02214076 × 10²³ per mole, exact by definition since the 2019 SI redefinition. It is commonly rounded to 6.022 × 10²³ for everyday chemistry calculations.
How do I convert moles to particles?+
Multiply the mole amount by Avogadro's number: N = n × 6.02214076 × 10²³. For example, 2 moles of any substance contains 2 × 6.02214076 × 10²³ ≈ 1.204 × 10²⁴ particles.
How do I convert from mass to particles?+
First divide the mass by the substance's molar mass to get moles (n = mass ÷ molar mass), then multiply that mole amount by Avogadro's number to get the particle count. The Mass ↔ Particles tab does both steps automatically.
What units does this calculator use?+
Mass is entered in grams (g), molar mass in grams per mole (g/mol), and the mole amount in mol. The particle count is a plain (unitless) count of atoms, molecules, or ions, typically displayed in scientific notation.
Does Avogadro's number apply to atoms and molecules the same way?+
Yes. Avogadro's number counts "elementary entities," a category that includes atoms, molecules, ions, and formula units alike. One mole of iron atoms, one mole of water molecules, and one mole of sodium ions all contain exactly the same number of particles.
How is this different from the Moles Calculator?+
This page is the fast, single-purpose Avogadro's-number converter — enter a mole amount, particle count, or mass, and get the particle count immediately, with a built-in Reference tab for context. The Moles Calculator is the broader tool for solving mass/molar-mass/moles problems generally, with moles ↔ particles as one of its several modes. If Avogadro's number is the whole calculation, use this page; if you're working through a fuller moles problem, use the Moles Calculator.
📄
Save & share
Get a branded PDF of your results
Download a one-page PDF of your numbers instantly. Add your email to also get our occasional calculator tips — no spam, unsubscribe anytime. Privacy.