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Particles to Moles Converter
↔ Convert mol to particles instead

Common Conversions

particles mol
602200000000000000000 0.001
6.022e+21 0.01
6.022e+22 0.1
1.204e+23 0.2
3.011e+23 0.5
6.022e+23 1
1.204e+24 2
3.011e+24 5
6.022e+24 10
6.022e+25 100
6.022e+26 1000

Why this conversion matters in chemistry

Cryo-EM particle-yield math is a typical place to need it. A grid prepared from 3 µL of 2 µM protein solution holds about 6 × 10⁻¹² mol = 6 pmol of protein — many orders of magnitude more than the few thousand 2D projection particles selected during data processing. The conversion shows how vanishingly little of the input contributes to the final structure. The ratio of 1/Nₐ mol per particle is exact through the 2019 SI redefinition of Avogadro's number. Mostly it's a unit-system step between counting-based techniques (digital PCR, single-molecule fluorescence, particle counting) and mole-scale chemistry arithmetic.

Formula

mol = particles / 6.02214 × 10²³

Worked Examples

6.022 × 10²³ particles = 1 mol

Avogadro's number itself — the conversion anchor.

3.011 × 10²³ particles = 0.5 mol

Half a mole — useful for limiting-reagent stoichiometry.

1.204 × 10²⁴ particles = 2 mol

Two moles — twice Avogadro's number of particles.

6.022 × 10²⁰ particles = 0.001 mol

One millimole — about a typical small-scale benchtop reaction.

Frequently Asked Questions

How do I convert particles to moles?
Divide by Avogadro's number, 6.02214 × 10²³ /mol. So 1.806 × 10²⁴ molecules becomes 3 mol. Works for atoms, molecules, ions, or formula units — any discrete entity.
What is Avogadro's number?
Nₐ = 6.02214076 × 10²³ /mol — exact since 2019. The figure was historically chosen so that 12 g of carbon-12 contains Nₐ atoms; the 2019 redefinition reversed that, fixing Nₐ as the defining constant and letting the mole follow.
Can individual atoms be counted?
Not practically for macroscopic amounts — even 1 µg of carbon holds about 5 × 10¹⁶ atoms. The mole concept lets weighable quantities (grams) stand in for countable numbers, bridging the atomic and macroscopic worlds.
Does the type of particle matter?
No. One mole always contains 6.022 × 10²³ entities, whether atoms, molecules, ions, electrons, or photons. But specify what's being counted — 1 mol of H₂ contains 2 mol of H atoms, and the distinction matters for stoichiometry.