Avogadro's Number Calculator

The Avogadro's constant calculator connects the measurable world with that which cannot be directly counted. By inputting mass, amount of substance (number of moles), molar mass and total number of particles it converts these quantities using a constant value into each other.

The Avogadro constant is an extremely important bridge in chemistry. It tells us how many atoms, molecules or ions are contained in one mole of any substance, thus allowing the conversion from measured grams to incredibly large numbers of particles.

What is the Avogadro constant?

The Avogadro constant is the number of particles in one mole of a substance. Since the redefinition of SI base units in 2019, it has been defined precisely as:

A particle can be anything. In chemistry it usually refers to atoms, molecules or ions but it could also be a grain of sand, a fuel tank or a piece of pizza.

If there are $6.02214076 \times 10^{23}$ of them, then you have one mole.

This name is dedicated to the Italian scientist Amedeo Avogadro who was born in 1776. At the age of 35, he postulated that at equal pressure and temperature, an equal number of molecules are contained in equal volumes of gas. This insight later became part of the equation of state for ideal gases, but it wasn't until much later that this constant received its current name.

Formula for use in calculation tools:

Two simple relationships can be used to perform all calculations, both of which relate to the number of moles.

The first relationship is between amount of substance (number of moles) and number of particles.

The second relationship is between mass and amount of substance via the molar mass. The molar mass is the number of grams per mole.

Combining these two relationships allows one to directly calculate the number of particles from a measured mass.

In this case, N stands for the number of particles, n for the amount of substance (in moles), m for mass in grams, M for molar mass in grams per mole and N_A for Avogadro's constant. By rearranging one of the equations, the missing quantity can be calculated.

Instructions for using the calculator:

Select the desired calculation process. The first mode directly links amount of substance to particle number. Another mode uses molar mass to convert between mass and amount of substance. A further mode converts both mass and particle number simultaneously.

In one of the modes enter known values and leave unknown fields blank. The calculator will automatically fill in the unknown fields, also showing other derived quantities such as number of particles or mass per individual particle. Avogadro's constant is a fixed value so does not need to be entered.

Example calculation:

Let's say we have 18.015 grams of water, with a molar mass of 18.015 g/mol. Dividing the mass by the molar mass gives us exactly one mole.

When multiplied by the Avogadro constant, this molar quantity contains approximately $6.022 \times 10^{23}$ water molecules.

The mass of a single water molecule can also be calculated using the same constant. By dividing the molar mass by the Avogadro constant, one obtains a mass of about $2.99 \times 10^{-23}$ grams per molecule.

Overview: Conversion of amount of substance to particle number

The number of particles is the product of the amount of substance and a constant quantity, so it changes in direct proportion to the amount of substance. The following table shows some common amounts of substances.

Applications of Avogadro's constant

All calculations in analytical chemistry are based on this constant. It allows for weighing reactants, determining the number of molecules involved, adjusting coefficients in chemical equations to reflect actual mass or calculating the number of dissolved ions in a solution.

It also provides a sense of scale that is hard to grasp using other methods. A single tablespoon of water contains more than $10^{24}$ molecules, a number which exceeds the number of stars in the observable universe. This figure can also be directly derived from Avogadro's constant.

This calculator should be used for general educational purposes only. If accuracy is required, please always check the periodic table or a reliable reference source to confirm molar mass.