Avogadro's Number Calculator: Particles to Moles
Convert a specified count of atoms, molecules, ions, electrons or formula units to moles using the exact SI Avogadro constant, with scientific notation.
Find the amount of substance represented by a specified particle count. Choose whether you are counting atoms, molecules, ions, electrons or formula units, then divide by the exact SI Avogadro constant. The chosen entity matters because a molecule and its constituent atoms are different things to count.
How to use this tool
- Enter a nonnegative whole number of entities; scientific notation is accepted.
- Choose the entity that the count represents.
- Read the amount in mol or mmol.
- Keep the entity description with the result when using it in another calculation.
Formula
n = N / N_A; N_A = 6.02214076 × 10^23 mol^-1 exactly
N is the specified entity count and n is amount of substance. Avogadro’s number is the numerical value 6.02214076 × 10^23; Avogadro’s constant includes the unit mol^-1. Neither value is fitted from these inputs.
Example
A sample containing 3.01107038 × 10^23 atoms represents (3.01107038 × 10^23) / (6.02214076 × 10^23) = 0.5 mol of atoms, equivalent to 500 mmol.
Frequently asked questions
Did Avogadro’s constant used to be measured?
Before the revised SI, experiments determined its value. Under the present definition of the mole, its numerical value is fixed exactly. Measurements still have uncertainty when realizing an amount in practice.
What should I select for sodium chloride?
For a bulk NaCl sample, a formula-unit count describes the composition of the lattice. A count of separate sodium ions or chloride ions refers to those entities instead. The selection does not automatically dissociate a compound.
Why are fractional input counts rejected?
This direction accepts a count of whole entities. Zero is valid. A statistical mean or concentration is a different input quantity and should not be silently treated as a literal count.
Can it distinguish every particle in a large number?
No. Above 9,007,199,254,740,991, standard floating-point numbers cannot represent every adjacent integer. Macroscopic entries and twelve-significant-digit displays must be treated as approximate bulk quantities, even though the defining constant is exact.
Sources
Last updated: 2026-10-30