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Avogadro's Number Calculator

Chemistry
Avogadro constant

NA = 6.022 140 76 × 10²³ mol⁻¹

Exact by definition since the SI redefinition of 20 May 2019.

F = NA · e = 96 485.332 12… C/mol (Faraday constant)

R = NA · kB = 8.314 462 618… J/(mol·K) (Molar gas constant)

Precision

Worked examples

Changes the wording only, never the maths.
Shown in units, e.g. "mol CO₂".

Value of NA to use

Many answer keys use 6.02 × 10²³. The choice changes both the value and the significant figures.

Type in any field below. The one you typed in last is the input; the others are calculated.

molecules

Starting from a mass in grams? Use the Grams to Moles Converter.

Number of entities

6.022 × 10²³ molecules

Rounded to 4 s.f. (from 1.000 mol; NA is exact)

6.022 × 10²³ molecules, written out

602 200 000 000 000 000 000 000

≈ 602.2 sextillion

Counting one per second, this would take 1.91 × 10¹⁶ years, about 1.38 million times the age of the universe.

Factor-label working

Units that appear on top and bottom cancel. Matching pairs share a colour and a strike line.

How big is that number?

Your count on a powers-of-ten ladder, next to things you can picture.

10⁰10³thousand10⁶million10⁹billion10¹²trillion10¹⁵quadrillion10¹⁸quintillion10²¹sextillion10²⁷octillion10³⁰nonillionA dozen: Exactly 12.A dozenSeconds in an 80-year life: 80 years × 31 557 600 s per Julian year = 2.52 × 10⁹ s.Seconds in an 80-year lifeCells in a human body: Estimate: about 3.7 × 10¹³ cells in an adult (Bianconi et al., Annals of Human Biology, 2013).≈ Cells in a human bodySeconds since the Big Bang: 13.787 × 10⁹ years (Planck 2018) × 31 557 600 s per year = 4.35 × 10¹⁷ s.Seconds since the Big BangH₂O molecules in a drop: One drop ≈ 0.05 mL ≈ 0.05 g of water: 0.05 g ÷ 18.015 g/mol × N_A = 1.67 × 10²¹ molecules.H₂O molecules in a dropC atoms in a 1-carat diamond: 1 carat is exactly 0.200 g: 0.200 g ÷ 12.011 g/mol × N_A = 1.00 × 10²² carbon atoms.C atoms in a 1-carat diamondStars in the universe: Estimate: roughly 10²² to 10²⁴ stars in the observable universe; the width reflects uncertain galaxy counts and sizes.≈ Stars in the universeH₂O molecules in a teaspoon: A teaspoon ≈ 5 mL ≈ 5 g of water: 5 g ÷ 18.015 g/mol × N_A = 1.67 × 10²³ molecules.H₂O molecules in a teaspoon1 mole: Exactly 6.022 140 76 × 10²³, fixed by the 2019 SI redefinition.1 moleH₂O molecules in 1 kg: 1 kg (≈ 1 L) of water: 1000 g ÷ 18.015 g/mol × N_A = 3.34 × 10²⁵ molecules.H₂O molecules in 1 kgAtoms in a 70 kg human: Estimate: about 7 × 10²⁷ atoms in a 70 kg adult, most of them hydrogen, oxygen and carbon.≈ Atoms in a 70 kg human

Log scale: each step up is ×10. Solid markers are exact or computed; hollow markers (≈) are estimates.

Hover over or tap a reference marker to see how its value was obtained.

Your 6.022 × 10²³ molecules is about the same as one mole, and 1/56 of the water molecules in 1 kg of water.

About This Tool

Avogadro's Number Calculator – Moles, Particles and the Experiments Behind NA

A mole is a count, like a dozen, only far larger. Avogadro's number says how many entities one mole holds: N_A = 6.022 140 76 × 10²³ mol⁻¹. This Avogadro's number calculator converts between moles and a number of atoms, molecules, ions, formula units or electrons, shows how big the answer really is, and works NA out from the data of three classic lab experiments.

An exact constant since 2019

On 20 May 2019 the SI was redefined so that the mole is fixed by NA itself. The value is now exact by definition, like the speed of light. It was chosen from measurements on nearly perfect spheres of silicon-28, where counting the atoms in a crystal of known density and lattice spacing gives the number per mole. Two familiar constants follow from it: the Faraday constant F = N_A · e and the molar gas constant R = N_A · k_B.

How to convert moles to atoms or molecules

  • N = n × N_A: number of entities from an amount in moles
  • n = N / N_A: moles from a number of entities
  • N_child = k × N: particles inside each entity, such as atoms in a molecule

For example, 2.50 mol of CO₂ contains 2.50 × 6.022 × 10²³ = 1.51 × 10²⁴ molecules. Going the other way, 1.806 × 10²⁴ iron atoms is 1.806 × 10²⁴ / 6.022 × 10²³ = 2.999 mol. Switch on the child level to count what is inside each entity: every CH₄ molecule holds 4 H atoms, so 0.75 mol of methane contains 3.0 mol of hydrogen atoms. The factor-label working shows each step with its units cancelling, ready to copy into homework.

If you start from a mass in grams, divide by the molar mass first, or use the Grams to Moles Converter, which does both steps for a chemical formula.

How big is 10²³?

A bare × 10²⁴ is hard to picture, so the result is also written out in full with its zeros grouped in threes, named on the short scale (1.51 septillion), and placed on a powers-of-ten ladder beside things you can imagine: the seconds since the Big Bang, the water molecules in a teaspoon, the atoms in a person. Counting one molecule per second, a single mole would take about 1.9 × 10¹⁶ years, over a million times the age of the universe.

Finding Avogadro's number in the lab

Choose an experiment, enter your measurements, and the calculator grades your result against the exact value:

  • Electroplating: a current I for time t deposits a measured mass Δm of metal, each atom taking z electrons. N_A = (I · t · M) / (z · e · Δm).
  • Fatty-acid monolayer: a drop of dilute oleic or stearic acid spreads into a film one molecule thick. Its thickness h = V / A gives the size of one molecule, and N_A = (M / ρ) · r² / h³.
  • Crystal density: a cubic unit cell of edge a holds Z formula units, so N_A = Z · M / (ρ · a³). The unit-cell drawing shows how corners count ⅛, edges ¼ and faces ½.

Each result comes with the percent error, the ratio to the accepted value, a log-scale gauge, every intermediate step and a lab-report summary you can copy.

Expect the oil-film result to be rough
The monolayer answer depends on the sixth power of the film diameter and on the assumed molecular shape, so being off by a factor of 5 to 10 is normal. Electroplating and crystal data usually land within a few percent.

Significant figures and the value of N_A

The exact constant never limits precision, but many textbooks use 6.02 × 10²³, which caps an answer at 3 significant figures. Pick the value your course uses, and the result is rounded to match your data. Full precision mode shows up to 10 digits instead.

Avogadro's number is not Avogadro's law

The two are often confused. Avogadro's number counts entities per mole. Avogadro's law is a gas law: at the same temperature and pressure, a gas's volume is proportional to its amount, so V₁/n₁ = V₂/n₂. For gas volumes, use an ideal gas law calculator instead.

Frequently Asked Questions

Is the Avogadro's Number Calculator free?

Yes, Avogadro's Number Calculator is totally free :)

Can I use the Avogadro's Number Calculator offline?

Yes, you can install the webapp as PWA.

Is it safe to use Avogadro's Number Calculator?

Yes, any data related to Avogadro's Number Calculator only stored in your browser (if storage required). You can simply clear browser cache to clear all the stored data. We do not store any data on server.

How does this Avogadro's number calculator work?

In Convert mode it multiplies an amount in moles by N_A = 6.02214076 × 10²³ mol⁻¹ to count atoms, molecules or ions, or divides a count by N_A to get moles. In experiment mode it works N_A out from electroplating, oil-film or crystal-density data and grades your result against the exact value.

Why is Avogadro's number exact now?

Since the SI redefinition of 20 May 2019, the mole is defined by fixing N_A at exactly 6.022 140 76 × 10²³ mol⁻¹. The fixed value came largely from X-ray crystal density measurements on near-perfect spheres of silicon-28, the same density-and-lattice method the crystal experiment here uses.

Is Avogadro's number the same as Avogadro's law?

No. Avogadro's number is a count: the number of entities in one mole. Avogadro's law is a gas law: at the same temperature and pressure, a gas's volume is proportional to its amount in moles (V₁/n₁ = V₂/n₂). For gas volumes, use the Ideal Gas Law Calculator.

Why does my answer differ from the answer key?

Many answer keys use N_A = 6.02 × 10²³, which differs from the exact value by about 0.04 % and limits the answer to 3 significant figures. Pick that value under 'Value of N_A to use' to match the key, and check that you kept the same number of significant figures as the data.

Why was my oil-film (monolayer) result so far off?

The result scales with r² · d̄⁶ / V³, so a 10 % error in the film diameter changes N_A by about 77 %, and the cube model ignores that fatty-acid molecules are several times taller than they are wide. Being out by a factor of 5 to 10 is normal for this experiment; the block model with your handout's ratio usually brings it much closer.

How do moles of molecules relate to moles of atoms inside them?

Multiply by the number of those atoms in one molecule. Each CH₄ molecule contains 4 H atoms, so 0.75 mol of CH₄ contains 4 × 0.75 = 3.0 mol of H atoms, or about 1.8 × 10²⁴ H atoms. The same factor works for ions per formula unit, such as 3 ions in each CaCl₂.