Avogadro's Number Calculator

About Avogadro's Number Calculator

Avogadro's number (6.022 × 10²³) is the number of particles in one mole. One mole of any substance contains this many atoms/molecules.

How to use this calculator

1. Enter the amount in moles if you want the number of particles, or enter the number of particles if you want moles.
2. Use the formula to multiply by Avogadro's number, which is \(6.022\\times10^{23}\) particles per mole.
3. Read the result as the total count of particles or the amount in moles, depending on the direction of the conversion.
4. Check your units, because moles and particle counts are not the same thing.

The formula explained

The formula \(N = n \\times N_A\) computes the number of particles \(N\) from the number of moles \(n\). If you are converting back to moles, divide by \(N_A\) instead.

• N = number of particles
• n = number of moles
• \(N_A\) = Avogadro's number, \(6.022\\times10^{23}\) particles per mole

Step by step method

1. Start with the amount you know, either \(n\) in moles or \(N\) in particles.
2. If you know moles, multiply by \(N_A\) to find particles. If you know particles, divide by \(N_A\) to find moles.
3. Write the answer with the correct unit, particles or moles.

Worked example

Problem. How many molecules are in \(2.5\) moles of water?

1. Use \(N = n \\times N_A\).
2. Substitute \(n = 2.5\) and \(N_A = 6.022\\times10^{23}\): \(N = 2.5 \\times 6.022\\times10^{23}\).
3. Compute \(N = 1.5055\\times10^{24}\), so the number of molecules is \(1.51\\times10^{24}\) molecules.

Tips and common mistakes

• Make sure you know whether you are counting atoms, molecules, or ions, because the calculator gives a particle count, not a mass.
• Use scientific notation for very large answers, since particle counts are usually enormous.

Frequently asked questions