Molecules to Moles Calculator: Divide by the Avogadro Constant

This calculator converts a count of particles into an amount of substance. Enter the number of molecules, atoms or formula units (scientific notation such as 1e24 or 1 × 10^24 is accepted) and the molar mass; you get the amount in moles and millimoles and the mass of that many particles in grams.

Formula

n = N ÷ N_A, and m = n × M.

• n: amount of substance in moles (mol)
• N: number of particles (molecules, atoms, ions or formula units)
• N_A = 6.02214076 × 10²³ mol⁻¹, the Avogadro constant (exact since the 2019 SI redefinition)
• m: mass in grams; M: molar mass in g/mol
• 1 mol = 1000 mmol

Worked Example

1 × 10²⁴ molecules of water, H₂O, with M = 2 × 1.008 + 15.999 = 18.015 g/mol.

1. n = 1 × 10²⁴ ÷ 6.02214076 × 10²³ = 1.66054 mol
2. In millimoles: 1.66054 × 1000 = 1,660.54 mmol
3. Mass: 1.66054 × 18.015 = 29.915 g

Assumptions

• The count is of one kind of particle. If you count atoms of an element, use the atomic weight of that element as M.
• The molar mass matches the particle you counted: molecules of H₂O use 18.015 g/mol, atoms of hydrogen use 1.008 g/mol.
• N_A is taken as the exact SI value; no rounding to 6.022 × 10²³ is made inside the calculation.

How to read the result

One mole is 6.02214076 × 10²³ particles, so any count below about 10²⁰ gives well under a millimole. The mass line is a check on scale: 10²⁴ water molecules weigh about 30 g, roughly two tablespoons. To go the other way, from grams to particles, use the mass to mole calculator, and use the molar mass calculator to find M from a formula.

Limits and common mistakes

• Typing 10^24 as 1024 is a frequent slip; enter 1e24 or 1 × 10^24.
• Mixing atoms and molecules: 1 mol of O₂ molecules contains 2 mol of O atoms.
• Rounding N_A to 6.0 × 10²³ changes the answer by about 0.4%, which matters when you compare with a precise value.

Frequently Asked Questions

How many moles are 10^24 molecules?

About 1.6605 mol, because 10^24 ÷ 6.02214076 × 10^23 = 1.66054.

What is the formula for molecules to moles?

Moles = number of molecules ÷ 6.02214076 × 10^23.

Does this work for atoms and ions?

Yes. The Avogadro constant counts any specified particle; just use the molar mass of that same particle for the mass line.

Why is the Avogadro constant exact?

Since 2019 the mole is defined by fixing N_A at exactly 6.02214076 × 10²³ mol⁻¹.

in nmol | Number of molecules | - | 1e24 | 0
in mm | Molar mass | g/mol | 18.015 | 0.001
out n | Amount of substance | mol | nmol / 6.02214076e23 | 5
out mmol | Amount in millimoles | mmol | n * 1000 | 2
out m | Mass | g | n * mm | 3