How to Calculate Moles: Formula and Examples

This calculator finds the amount of substance in moles from a sample’s mass and molar mass. Enter the mass in grams and molar mass in grams per mole to get moles, plus the equivalent number of particles. Use it for chemistry study and lab-planning arithmetic; the result depends on having the correct formula and units.

Formula

The amount in moles equals sample mass divided by molar mass:

n = m / M

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

The particle count is N = n × N_A, where N is the number of particles and Avogadro’s constant, N_A = 6.02214076 × 10²³ mol⁻¹ exactly. “Particles” means the relevant entities: atoms, molecules, ions, or formula units. The first calculator result is moles; the second is the corresponding particle count.

Worked Example

Suppose a sample has the calculator’s default mass of 10 g and a molar mass of 58.44 g/mol.

1. Write the mass and molar mass with units: m = 10 g; M = 58.44 g/mol.
2. Divide mass by molar mass: n = 10 g / (58.44 g/mol) = 0.1711157 mol, approximately.
3. Round the amount to the calculator’s four decimal places: 0.1711 mol.
4. Find the particle count using the unrounded amount: N = 0.1711157 mol × 6.02214076 × 10²³ mol⁻¹ ≈ 1.0303 × 10²³ particles.

The particle count is shown to zero decimal places in the calculator; for a very large result, scientific notation is a clearer way to report it. The molar mass in this example is a generic input value, not a claim about a particular sample. For a real compound, calculate or look up its molar mass from its chemical formula and the applicable atomic weights.

Assumptions

• The sample’s mass and molar mass refer to the same chemical substance and specified entity.
• The sample is sufficiently pure for its stated molar mass to apply. If it is a mixture, the calculation gives no separate amount for each component.
• The entered mass is in grams and molar mass is in grams per mole. The calculator does not convert other units.
• The result is a calculated amount, not a measurement of purity or reaction yield.

What You’ll Need

• A measured sample mass, with its unit known.
• The substance’s correct chemical formula and molar mass, in g/mol.
• A calculator or this page’s calculator. For a lab sample, use the balance and measurement approach specified by your lab method.

Step-by-Step

1. Identify the substance. Check its chemical formula and whether the quantity refers to atoms, molecules, ions, or formula units. Do not use the molar mass of a related compound, hydrate, or salt form by mistake.
2. Find its molar mass. For a formula, multiply each element’s atomic weight by the number of its atoms, then add the contributions. For example, water, H₂O, has M = 2 × 1.008 + 15.999 = 18.015 g/mol using these abridged standard atomic weights. Include all atoms shown in parentheses and any waters of crystallization in a hydrate.
3. Measure or obtain the sample mass. Record the mass in grams. If your measurement is in milligrams, convert it using 1 g = 1000 mg; if it is in kilograms, use 1 kg = 1000 g. Keep enough digits to reflect the measurement rather than rounding early.
4. Enter the values. Put the mass in the Sample mass field and the molar mass in the Molar mass field. Confirm that the units match the labels: g and g/mol.
5. Read the amount in moles. The calculator divides the mass by molar mass. Check the unit cancellation: g ÷ (g/mol) = mol. This is the amount of substance in the sample.
6. Use the particle count only if needed. The second result multiplies moles by Avogadro’s constant. It estimates the number of specified entities in that amount; it is not a count of different chemical species in a mixture.
7. Report appropriate precision. Keep unrounded values for later calculations when possible. Round the final answer to a precision supported by the least precise measured or supplied value, and state units.

Common Mistakes

• Mixing units: Dividing milligrams directly by a molar mass in g/mol makes the result 1000 times too small. Convert the mass to grams first.
• Using the wrong molar mass: Similar names can refer to different formulas, salts, hydrates, or isotopic compositions. Verify the exact substance and formula.
• Counting atoms instead of molecules: Moles of a compound count molecules or formula units. To find moles of a particular atom in it, multiply by the number of that atom in each formula unit.
• Rounding too soon: Early rounding can shift the final result, especially in multi-step stoichiometry. Carry extra digits and round once at the end.
• Treating a mixture as pure: If a weighed sample contains impurities or multiple components, mass divided by one molar mass does not give the amount of the target compound unless its actual mass is known.

Tips

• Write the equation with units before calculating. If the units do not reduce to mol, check the setup.
• Use the formula’s subscripts when calculating molar mass; a missing subscript changes the answer.
• For a solution, do not confuse moles with molarity. Moles are an amount; molarity is moles per litre of solution.
• Keep the unrounded mole value for reaction ratios, limiting-reactant calculations, or concentration calculations, then round the reported result.
• For bench work, follow your lab method, the safety data sheet (SDS) and your supervisor.

Troubleshooting

• The answer seems 1000 times too large or small: Check whether the mass was entered in g rather than mg or kg, and whether the molar mass is in g/mol rather than kg/mol.
• The result is unexpectedly high or low: Recheck the chemical formula, parentheses, hydrate waters, and molar mass. Then confirm that the mass belongs to the same substance.
• The calculator rejects an entry: Mass cannot be negative, and molar mass must be positive. Enter a valid nonnegative mass and a positive molar mass.
• The sample is a solution or mixture: First determine the mass of the specific substance whose moles you need. If only the total mixture mass is known, more composition information is required.
• You need moles from a different measurement: The mass formula is not the right route for every problem. For a solution, use concentration and volume; for a gas, use an appropriate gas-law relationship and its stated conditions.

Frequently Asked Questions

What is a mole?
A mole is the SI unit for amount of substance. One mole contains exactly 6.02214076 × 10²³ specified entities.

What is the basic formula for calculating moles?
For a sample with known mass and molar mass, use n = m / M, with mass in grams and molar mass in g/mol.

Can I calculate moles from milligrams?
Yes. Convert milligrams to grams by dividing by 1000, then divide by molar mass in g/mol.

How do I calculate molar mass?
Add the atomic weights of all atoms in the chemical formula, multiplying each element’s atomic weight by its subscript.

How do I convert moles to molecules?
Multiply moles by 6.02214076 × 10²³ entities per mole. Specify whether those entities are molecules, atoms, ions, or formula units.

Can this formula find moles in an impure sample?
Not by itself. You need the mass of the target substance or its proportion in the sample; applying one molar mass to the total mass assumes the sample is that substance.

Related

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

in m | Sample mass | g | 10 | 0
in mm | Molar mass | g/mol | 58.44 | 0.001
out n | Amount of substance | mol | m / mm | 4
out p | Number of particles | particles | n * 6.02214076e23 | 0