The Avogadro Number Calculator converts between moles, number of particles, and mass using Avogadro's constant (6.02214076 × 10²³ mol⁻¹). Solves all three variants of the fundamental stoichiometry relationship — the bridge between the atomic scale and the weighable laboratory scale in chemistry.
6.022141e+23
6.02214076e+23
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6.022141e+23
6.022141e+23
6.02214076e+23
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6.022141e+23
Avogadro's number is arguably the most important constant in chemistry — the scaling factor that transforms imperceptibly small atoms into weighable, measurable quantities. One mole of carbon-12 atoms weighs exactly 12 grams; one mole of water weighs 18.015 grams; one mole of any substance contains exactly 6.02214076 × 10²³ constituent entities. The calculator for Avogadro's number converts fluently between moles, particle counts, and masses for any element or compound.
Since the 2019 SI redefinition of the mole, Avogadro's constant Nₐ is defined as an exact number:
Nₐ = 6.02214076 × 10²³ mol⁻¹ (exact by definition)
The three fundamental conversions:
For 5.00 g of NaCl (M = 58.44 g/mol): n = 5.00/58.44 = 0.0856 mol; N = 0.0856 × 6.022 × 10²³ = 5.15 × 10²² formula units. Use this online calculator for any substance. The mole calculator provides extended stoichiometric conversions including gram-to-mole and mole-to-gram.
The magnitude of Nₐ is not arbitrary — it is determined by the historical choice of the gram as the mass unit and the atomic mass unit (u) as the atomic scale reference. One gram equals exactly Nₐ atomic mass units; equivalently, Nₐ is the number of 12C atoms in exactly 12 grams of pure carbon-12. Had chemists historically chosen the kilogram as the base mass unit, Avogadro's number would be 6.022 × 10²⁶ — a thousand times larger. The number's magnitude reflects a historical convention that locked in when the metric system was standardized in the 19th century, long before the atomic scale was well understood. The Planck constant calculator and physical constants calculators provide related fundamental constant calculations.
The mole concept underlies every quantitative calculation in chemistry:
Before the 2019 redefinition, Nₐ was a measured quantity with experimental uncertainty. Key historical determinations: Jean Perrin's Brownian motion experiments (1908, Nobel Prize 1926) gave Nₐ ≈ 6.0 × 10²³; X-ray crystallography of NaCl crystals in the 1920s gave values consistent with 6.022 × 10²³; the most precise pre-2019 value (6.022140857 × 10²³) came from silicon sphere measurements using X-ray diffraction and atom interferometry in the Avogadro project. The 2019 SI redefinition froze this value exactly, making the mole a counting unit rather than a mass-based unit for the first time.
Select the conversion type: moles to number of particles (N = n × NA), particles to moles (n = N/NA), mass to atoms (using N = (m/M) × NA where M is molar mass), or atoms to mass (m = N × M/NA). The exact SI value NA = 6.02214076 × 10²³ mol⁻¹ is used throughout.
One mole of any gas at STP (0 °C, 1 bar) occupies 22.414 liters. One mole of water has mass 18.015 g. The number NA ≈ 6.022 × 10²³ is so large that even a tiny amount of substance contains an astronomical number of particles — a single drop of water (0.05 mL, ~2.8 × 10²¹ molecules) contains more molecules than there are grains of sand on all Earth's beaches.
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1 g of hydrogen ÷ 1.008 g/mol ≈ 0.992 mol, containing 5.97 × 10^23 hydrogen atoms. Nearly one full mole.
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1 trillion (10^12) gold atoms have mass 3.27 × 10^-10 g = 0.327 nanograms. Measurable with a microbalance but invisible to the naked eye.
The Italian scientist Amedeo Avogadro proposed in 1811 that equal volumes of ideal gases at the same temperature and pressure contain equal numbers of molecules (Avogadro's hypothesis). The number itself was determined much later by various methods — Josef Loschmidt (1865), Jean Perrin (1909) — but named in honor of Avogadro's foundational contribution. Perrin won the 1926 Nobel Prize for his experimental determination.
Early determinations came from Loschmidt's estimate of molecular sizes from viscosity (1865), Perrin's Brownian motion measurements (1909), Millikan's oil drop experiment combined with electrochemistry (1913), and X-ray diffraction of crystals where the atomic spacing is known from geometry. All methods converged on approximately 6 × 10²³, confirming the atomic theory of matter.
The Loschmidt constant nL = NA/Vm = 2.6867774 × 10²⁵ m⁻³ is the number density of molecules in an ideal gas at standard conditions (273.15 K, 101.325 kPa). It equals Avogadro's number divided by the molar volume. It is used in atmospheric physics and kinetic theory.
The molar mass M (in g/mol) of any element numerically equals its atomic mass A (in u). This is because 1 u is defined as 1/12 the mass of C-12, and 1 mole of C-12 = 12.000 g by the old SI definition. In the new SI, the mole is defined by fixing NA, and the C-12 molar mass is 11.9999... g/mol — extremely close to 12 but no longer exactly 12.
The Faraday constant F = NA × e = 6.02214076 × 10²³ × 1.602176634 × 10⁻¹⁹ C = 96,485.33212 C/mol. It is the electric charge per mole of elementary charges (electrons or protons). One faraday of charge deposits one equivalent weight of any substance in electrolysis — Faraday's law of electrolysis.
6.022 × 10²³ atoms ÷ 10⁶ atoms/s = 6.022 × 10¹⁷ seconds ≈ 19.1 billion years — longer than the age of the universe (13.8 billion years). Even at 10¹² (one trillion) atoms per second, it would take 19,000 years. This illustrates why Avogadro's number represents such an incomprehensible quantity.
The molar volume Vm is the volume occupied by one mole of a substance. For ideal gases at STP (0°C, 1 bar), Vm = RT/P = 22.414 L/mol. For liquid water at 25°C, Vm = 18.015 g/mol ÷ 0.997 g/mL = 18.07 mL/mol. The ratio of gas to liquid molar volume (~1240:1) reflects the large intermolecular spacing in gases.
In X-ray crystallography, the unit cell dimensions are measured directly, giving the volume per formula unit. Combined with the measured density and molar mass, NA can be determined: NA = (Z × M)/(ρ × Vcell), where Z is the number of formula units per unit cell. This was one of the earliest precise determinations of NA.
The atomic mass unit u = 1/NA grams = 1.66053906660 × 10⁻²⁷ kg. So 1 u = 1 g/NA. This means the mass of one atom of element X in grams is its atomic mass divided by NA. For carbon-12: mass = 12 u = 12/(6.022 × 10²³) g = 1.993 × 10⁻²³ g per atom.
Since the 2019 SI redefinition, NA is exactly 6.02214076 × 10²³ mol⁻¹ by definition — it has zero uncertainty by construction. Before 2019, the CODATA 2018 recommended value had a relative uncertainty of 4.6 × 10⁻¹⁰, making it one of the most precisely known fundamental constants. The 2019 redefinition fixed this value exactly, transferring the uncertainty to the molar mass of C-12.
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