Moles Calculator: Formulas, Examples & Conversions

Use this moles calculator to find the amount of substance from a sample’s mass and molar mass. Enter the mass in grams and molar mass in grams per mole; the calculator returns the amount in moles and the equivalent number of millimoles.

Formula

For a sample with a known mass, calculate moles by dividing the mass by the substance’s molar mass:

n = m / M

• n is amount of substance, in moles (mol).
• m is sample mass, in grams (g).
• M is molar mass, in grams per mole (g/mol).

The units cancel as g ÷ (g/mol) = mol. To express the answer in millimoles, multiply moles by 1,000 because 1 mol = 1,000 mmol. The calculator uses that conversion for its second result.

Worked Example

For the default inputs, the sample mass is 18.015 g and the molar mass is 18.015 g/mol. The example uses water’s molar mass, calculated from the conventional atomic weights H = 1.008 and O = 15.999: 2 × 1.008 + 15.999 = 18.015 g/mol.

1. Apply the formula: n = m / M.
2. Substitute the defaults: n = 18.015 g / (18.015 g/mol) = 1.0000 mol.
3. Convert to millimoles: 1.0000 mol × 1,000 mmol/mol = 1,000.0 mmol.

So the calculator reports 1.0000 mol and 1,000.0 mmol.

Assumptions

• The entered mass is the mass of the substance whose molar mass you entered.
• The sample is treated as pure. If it is a mixture or its purity is known to be below 100%, account for the amount of actual substance separately.
• The formula calculates amount from mass; it does not require assumptions about temperature, pressure, solution volume, or gas behavior.

What a Mole Measures

A mole is the SI unit for amount of substance. One mole contains exactly 6.02214076 × 10²³ specified entities, such as atoms, molecules, ions, or formula units. This fixed number is the Avogadro constant. The word “entities” matters: a mole of oxygen atoms and a mole of oxygen molecules refer to different particles.

The mole connects an invisible particle count to measurable quantities. Atoms and molecules are too small to count individually in an ordinary sample, but a balance can measure mass. Since each substance has a characteristic molar mass, the mass-to-moles formula converts the measured mass into an amount of particles.

Choosing the Right Moles Formula

Mass is a common starting point, but it is not the only one. Choose the relationship that matches what you know:

• Mass: n = m / M. Use mass in grams and molar mass in g/mol.
• Number of particles: n = N / N_A, where N is the particle count and N_A = 6.02214076 × 10²³ entities/mol.
• Solution concentration: n = cV, where c is molar concentration in mol/L and V is solution volume in L.
• Ideal gas: n = PV / RT, when pressure, volume, temperature, and the gas constant use a consistent set of units. This relation assumes ideal-gas behavior.

These formulas are not interchangeable without the corresponding information. For example, volume by itself does not determine moles in a solution; you also need concentration. A gas volume needs suitable pressure and temperature data, or another justified relationship.

Molar Mass and Unit Checks

Molar mass is the mass of one mole of a substance. For a compound, find it by adding the atomic masses for every atom in its formula. For carbon dioxide, CO₂, the calculation using abridged standard atomic weights is 12.011 + 2(15.999) = 44.009 g/mol. A 22.0045 g CO₂ sample therefore contains 22.0045 / 44.009 = 0.50000 mol.

Check the chemical formula and parentheses before calculating: a subscript applies to the element or group immediately before it. If a formula contains a hydrate dot, include the water molecules in the molar mass. For substances whose composition varies, such as some polymers or mixtures, a single exact molar mass may not be appropriate.

Units must also agree. If a mass is entered in milligrams, convert it to grams by dividing by 1,000 before using a molar mass in g/mol. If the molar mass is instead in kg/mol, use a mass in kilograms, or convert the molar mass to g/mol. The unit cancellation is a useful way to catch errors.

Common Errors and Limits

• Using the wrong molar mass: Confirm the substance, formula, and ionic or molecular form. Different forms can have different molar masses.
• Mixing units: Grams divided by g/mol gives moles; milligrams divided directly by g/mol does not.
• Confusing moles with particles: A result of 1 mol means 6.02214076 × 10²³ specified entities, not one entity.
• Rounding too early: Keep extra digits during intermediate steps, then round the final answer to match the precision of the measured mass and molar mass.
• Assuming the sample is pure: Impurities contribute to measured mass but may not contribute to the amount of the target substance. A purity correction requires reliable purity information.

The calculation itself is exact arithmetic for the values supplied, but real measurements and tabulated molar masses have finite precision. Report no more precision than the inputs support. For bench work, follow your lab method, the safety data sheet (SDS) and your supervisor.

Frequently Asked Questions

How do I calculate moles from grams?
Divide the mass in grams by the molar mass in g/mol: n = m / M. The result is in moles.

How do I find molar mass?
Add the atomic masses of all atoms shown in the substance’s chemical formula, including the count represented by each subscript. The result is usually expressed in g/mol.

How many particles are in one mole?
One mole contains exactly 6.02214076 × 10²³ specified entities. Those entities might be atoms, molecules, ions, or formula units.

How do I convert moles to millimoles?
Multiply the number of moles by 1,000. To convert millimoles back to moles, divide by 1,000.

Can I calculate moles from volume alone?
Not in general. For a solution, you need its concentration; for a gas, you need pressure and temperature as well as volume, or other relevant data.

Related

• Molecules to Moles Calculator: Divide by the Avogadro Constant
• Mass to Mole Calculator: Grams to Moles From the Molar Mass
• Moles to Grams Calculator: Mass of a Compound From Moles

in m | Sample mass | g | 18.015 | 0
in mm | Molar mass | g/mol | 18.015 | 0
out n | Amount of substance | mol | m / mm | 4
out nmm | Amount of substance | mmol | n * 1000 | 1