# Avogadro’s number calculator

## How to use our Avogadro’s number calculator?

The Avogadro’s number calculator is very easy to use and works in two different ways. You can first determine the number of particles by knowing the amount of moles or you can get the number of moles if you know the number of particles of the chemical substance.

The Avogadro’s number is fixed and can’t be changed. When you set the number of moles, the calculator will directly show the number of elementary elements. These elements can be atoms, molecules,… in function of the chemical substance used for the calculation.

If you set the number of particles, the calculator will directly give the number of moles corresponding to this number of elements for the chemical substance.

**table of contents:**

- What represent the Avogadro’s number?
- Avogadro’s number value
- Avogadro’s number units
- Avogadro’s number symbol
- Avogadro’s number formula
- Relation with other formulas
- Why it is called Avogadro’s number?

## What represent the Avogadro’s number?

The Avogadro’s number (also called Avogadro’s constant because it has a unit) is the number of elementary elements contain in one mole. These elementary elements can be atoms, ions, molecules, … This means that one mole of carbon has the same amounts of atoms as 1 mole of lead. Or 1 mole of water has the same amount of molecules as the amounts of atoms of 1 mole of Mercury.

## Avogadro’s number value

Until the 20th May of 2019, the Avogadro number was defined as the number of atoms of carbon in 12 grams of Carbon 12. The measured value was 6.022 140 857 x 10^{23} mol^{-1}.

Since the 20th May 2019, the Avogadro number has become a constant fixed by convention to 6.022 140 76 x 10^{23} mol^{-1}.

## Avogadro’s number unit

The Avogadro’s constant has a SI unit which is mol^{-1}.

## Avogadro’s number symbol

The usual symbol of the Avogadro’s constant is *N _{A}*.

## Avogadro’s number formula

The number of elementary entities of a chemical substance can be calculated with the following formula:

*N = N*_{A} x n

where

*N*is the number of elementary entities of a chemical substance*N*is the Avogadro’s number (mol_{A}^{-1})*n*is the amount of the chemical substance in moles (mol)

## Relation with other formulas

### Molar mass and atomic mass

The Avogadro’s number is also the conversion factor between the molar mass and the atomic mass unit:

*M* = 1 g/mol = *N _{A}* x u

where

*M*is the molar mass (kg/mol)*N*is the Avogadro’s number (mol_{A}^{-1})*u*is the atomic mass (kg)

### Molar gas constant and Boltzmann constant

The Avogadro’s constant also interacts in the formula of the molar gas constant and the Boltzmann constant:

*R* = *N _{A}* x

*k*

_{B}where

*R*is the molar gas constant in (J / K^{-1}mol^{-1})*N*is the Avogadro’s number (mol_{A}^{-1})is the Boltzmann constant (J K*k*_{B}^{-1})

### Faraday constant and the elementary charge

Finally, the Avogadro’s number is also present in the relation between the Faraday constant and the elementary charge:

F = *N _{A}* x

*e*

where

- F is the Faraday constant (C mol
^{-1}) *N*is the Avogadro’s number (mol_{A}^{-1})*e*is the elementary charge (C)

## Why it is called Avogadro’s number?

It is named after the Italian physicist and chemist Amedeo Avogadro (9 August 1776 – 9 July 1856), which also defined the Avogadro’s law.