Last updated: July 3, 2026
Avogadro's Number Calculator
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Quick Answer
Avogadro's number is the exact count of particles in one mole: 6.02214076 × 10²³ mol⁻¹. This calculator converts moles to particles, particles to moles, mass to particles, and particles to mass using molar mass where needed.
Avogadro's number is exactly six point zero two two one four zero seven six times ten to the twenty-third particles per mole. Multiply moles by this value to find particles, or divide particles by it to find moles.
Key Takeaways
- Avogadro's number is exactly 6.02214076 × 10²³ mol⁻¹.
- Particles from moles use N = n × N_A.
- Moles from particles use n = N / N_A.
- Particles from mass require n = mass / molar mass before multiplying by N_A.
- Mass from particles uses mass = (N / N_A) × molar mass.
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Formula
N = n × N_A; n = N / N_A; n = mass / molar mass; mass = (N / N_A) × molar mass
Where:
- N=Number of particles(particles)
- n=Amount of substance(mol)
- N_A=Avogadro constant(mol⁻¹)
- m=Sample mass(g)
- M=Molar mass(g/mol)
Worked Examples
Two moles of particles
Find the number of entities in 2 mol of any substance.
- 1Use the exact constant N_A = 6.02214076 × 10²³ mol⁻¹.
- 2Multiply moles by Avogadro's number: N = 2 × 6.02214076 × 10²³.
- 3N = 1.204428152 × 10²⁴ particles.
Half a mole from particle count
Convert 3.011 × 10²³ particles into moles.
- 1Use n = N ÷ N_A.
- 2n = 3.011 × 10²³ ÷ 6.02214076 × 10²³.
- 3n ≈ 0.5 mol, so the sample contains about half a mole.
Water molecules in 18.015 g
Use water's molar mass to convert grams to molecules.
- 1Convert mass to moles: n = 18.015 g ÷ 18.015 g/mol = 1 mol.
- 2Multiply by Avogadro's number: N = 1 × 6.02214076 × 10²³.
- 3The sample contains 6.02214076 × 10²³ water molecules.
Introduction
Avogadro's number, more precisely the Avogadro constant, links the microscopic world of atoms and molecules to measurable laboratory amounts. One mole contains exactly 6.02214076 × 10²³ specified entities. This calculator converts between moles, particles, and grams using the exact SI value from the BIPM SI Brochure. It pairs naturally with the molar ratio calculator, molarity calculator, and mass-based stoichiometry workflows.
What is Avogadro's number?
Avogadro's number is the number of elementary entities in one mole: exactly 602,214,076,000,000,000,000,000. Chemists use it for atoms, molecules, ions, electrons, formula units, or any specified particles. Since the 2019 SI redefinition, this value is exact rather than experimentally rounded.
1 mol atoms = 6.02214076 × 10²³ atoms.
1 mol molecules = 6.02214076 × 10²³ molecules.
The symbol is N_A, and the unit is mol⁻¹.
The mole is an SI base unit for amount of substance.
Avogadro's number formulas
The core conversion is N = n × N_A, where N is the particle count and n is moles. Rearranging gives n = N / N_A. If a problem starts with grams, first convert mass to moles using n = mass / molar mass, then multiply by N_A. If you know particles and need mass, use mass = (N / N_A) × molar mass.
Always specify the entity counted: atoms, molecules, ions, or formula units can have different chemical meanings.
How to calculate particles from moles or mass
Start by identifying which quantity you know. Direct mole problems use one multiplication. Mass problems need the molar mass calculator first, because grams must become moles before particles can be counted. For example, 18.015 g of water divided by 18.015 g/mol gives 1 mol, which contains N_A water molecules.
Enter moles directly, or enter mass plus molar mass.
Convert mass to moles when needed: n = m / M.
Multiply moles by N_A to find particles.
Use scientific notation for particle counts above 10²¹.
Keep significant figures consistent with the measured mass or molar mass.
Common mole and particle values
The table shows reference conversions that make mental checks easier. The same N_A applies to every substance; only molar mass changes when converting to or from grams.
| Quantity | Moles | Particles |
|---|---|---|
| 1 mole | 1 mol | 6.02214076 × 10²³ |
| Half mole | 0.5 mol | 3.01107038 × 10²³ |
| 2 moles | 2 mol | 1.204428152 × 10²⁴ |
| 1 dozen equivalent | 12 particles | 1.99264688 × 10⁻²³ mol |
Why Avogadro's number matters in stoichiometry
Balanced equations compare substances in moles, while experiments often measure grams and particle models count individual entities. Avogadro's number is the conversion bridge. After converting grams to moles, coefficients from the molar ratio calculator can predict reactants or products, and concentration tools such as the mass percent calculator describe mixtures.
Never apply balanced-equation coefficients directly to grams or particles without converting through moles.
Accuracy, exactness, and notation
The Avogadro constant is exactly 6.02214076 × 10²³ mol⁻¹ by SI definition, as summarized by NIST constants. Your final uncertainty usually comes from measured mass, molar mass, purity, or rounding, not from N_A itself. For teaching background, Chemistry LibreTexts discusses the mole concept and particle counting in introductory stoichiometry.
Use exponential notation to avoid losing zeros.
Distinguish atoms from molecules in formulas such as O versus O₂.
Use molar mass in g/mol when mass is entered in grams.
Round final answers to match the least precise measured input.
Quick Reference Card
Avogadro's Number — Quick Reference
Quick reference • Avogadro's Number Calculator
N = n × N_A; n = N / N_A; N = (mass / molar mass) × N_AValid range: Any non-negative amount; typical chemistry problems use 10⁻⁶ to 10² mol
Common Values
⚠ Watch Out
- •Do not confuse atoms with molecules; 1 mol O₂ contains 1 mol molecules but 2 mol oxygen atoms.
- •Use molar mass in g/mol when mass is entered in grams.
- •Scientific notation prevents mistakes with 23 zeros.
- •Report significant figures based on measured inputs, even though N_A is exact.
Pro Tips
- →For grams to particles, always convert grams to moles first.
- →Use the chemical formula to decide whether entities are atoms, molecules, ions, or formula units.
- →Keep the exact N_A value during calculation and round only the final result.
- →Check mass conversions by converting the final moles back to grams.
FAQs
What is Avogadro's number?
Avogadro's number is exactly 6.02214076 × 10²³ particles per mole. It tells how many specified entities are present in one mole of a substance.
How do I convert moles to particles?
Multiply moles by the Avogadro constant: N = n × 6.02214076 × 10²³. For example, 2 mol contains 1.204428152 × 10²⁴ particles.
How do I convert particles to moles?
Divide the particle count by Avogadro's number: n = N / N_A. A count of about 3.011 × 10²³ particles is about 0.5 mol.
How do I find particles from grams?
First divide mass by molar mass to get moles, then multiply by Avogadro's number. The formula is N = (mass / molar mass) × N_A.
Is Avogadro's number exact?
Yes. Since the 2019 SI redefinition, N_A is fixed exactly at 6.02214076 × 10²³ mol⁻¹. Measurement uncertainty comes from your sample data, not from the constant.
Does one mole always have the same mass?
No. One mole always has the same number of particles, but its mass depends on molar mass. One mole of water is about 18.015 g; one mole of carbon-12 atoms is 12 g.