Mole Calculator
Calculate moles from mass, particle count, solution concentration, or gas conditions. Choose a mode, fill in any two known values, and get the missing quantity with full worked steps.
Formula
Worked example
1) Mass mode: 58.44 g of NaCl (M = 58.44 g/mol) gives n = 1.0000 mol, or 6.022 × 10²³ formula units. 2) Gas mode: 1 atm, 22.414 L, 273.15 K gives n = 1.0000 mol (STP benchmark). 3) Solution mode: 2 mol/L × 0.5 L = 1.000 mol of solute.
How the mole equation works (mass / molar mass mode)
The mole is the SI base unit for amount of substance, defined so that one mole contains exactly 6.02214076 × 10²³ elementary entities, the Avogadro constant. Because counting individual atoms is impossible in the lab, chemists weigh a sample and convert mass to moles using the molar mass M (g/mol). The core equation is n = m / M, and rearranging it gives m = n × M and M = m / n, covering all three unknowns. To find the molar mass of any compound, sum the standard atomic weight of every atom in the formula: water (H₂O) = 2 × 1.008 + 15.999 = 18.015 g/mol. Molar mass in g/mol is numerically identical to the relative formula mass expressed in atomic mass units.
Particle count and the Avogadro constant
The particle count mode converts between a human-scale quantity (moles) and the staggering number of individual entities in a sample. The Avogadro constant N_A = 6.02214076 × 10²³ /mol has been fixed by definition since the 2019 SI revision. Multiply moles by N_A to find how many atoms, molecules, ions, or formula units are present; divide a raw particle count by N_A to recover moles. This mode is especially useful in nuclear physics, semiconductor doping calculations, and any problem where you know a number of particles from a detector rather than a mass.
Solution mode: n = C × V
In solution chemistry, moles link concentration to volume through n = C × V, where C is molarity in mol/L and V is volume in litres. This calculator lets you solve for any one of the three: the moles of solute, the molarity, or the volume needed. Make sure to convert millilitres to litres before substituting (the calculator does this automatically when you pick mL as the unit). The moles you calculate here feed directly into dilution calculations (C1V1 = C2V2), titration stoichiometry, and preparing standard solutions from a solid or concentrated stock.
Ideal gas law mode: PV = nRT
For gases, the ideal gas law PV = nRT connects pressure, volume, temperature, and the number of moles. R = 0.08206 L·atm·mol⁻¹·K⁻¹ is used here, so pressure must be in atm (the calculator converts other units automatically) and temperature must be in Kelvin. At standard conditions (STP: 0 °C, 1 atm) one mole of an ideal gas occupies exactly 22.414 L, a useful benchmark. You can solve for any of the four variables: moles, pressure, volume, or temperature. Remember that real gases deviate from ideal behaviour at high pressures or near the liquefaction point, so treat results as approximations for those conditions.
Why moles matter in stoichiometry
Balanced chemical equations describe reactions in whole-number mole ratios because reactions proceed by whole-number ratios of particles. Converting measured masses, solution volumes, or gas volumes to moles is the essential first step before applying a stoichiometric ratio to predict product yield or reagent requirements. Once the reacting moles are known you can convert back to mass (mass mode), solution concentration (solution mode), or gas volume (gas mode). Mastering these four conversions unlocks limiting-reagent analysis, percent yield, and titration work across all branches of chemistry.
Molar masses of common substances
| Substance | Formula | Molar mass (g/mol) | Common use |
|---|---|---|---|
| Water | H₂O | 18.015 | Solvent reference |
| Sodium chloride | NaCl | 58.44 | Table salt, 1 mol = 58.44 g |
| Glucose | C₆H₁₂O₆ | 180.16 | Energy metabolism |
| Carbon dioxide | CO₂ | 44.01 | Gas law problems |
| Sulfuric acid | H₂SO₄ | 98.08 | Titration standard |
| Calcium carbonate | CaCO₃ | 100.09 | Antacid, back-titrations |
| Ammonia | NH₃ | 17.03 | Fertiliser, buffer solutions |
| Ethanol | C₂H₅OH | 46.07 | Organic chemistry standard |
| Hydrochloric acid | HCl | 36.46 | Common acid titrant |
| Sodium hydroxide | NaOH | 40.00 | Common base titrant |
Approximate molar masses from IUPAC standard atomic weights. Use the exact value when precision matters.
Frequently asked questions
What is the formula for calculating moles from mass?
Moles equal mass divided by molar mass: n = m / M. If you have the moles and molar mass, multiply to get mass (m = n × M). If you have mass and moles, divide to find molar mass (M = m / n). Enter any two values in the mass/molar mass mode and the calculator finds the third.
How do I convert particles to moles?
Divide the number of particles by the Avogadro constant: n = N / (6.02214076 × 10²³). Conversely, multiply moles by the same constant to find particle count. Use the particle count mode in this calculator for instant conversion.
How do I calculate moles in a solution?
Multiply the molar concentration (molarity, in mol/L) by the volume of solution in litres: n = C × V. For example, 2 mol/L in 500 mL (0.5 L) gives 1 mol of solute. Use the solution mode to solve for moles, molarity, or volume.
How do I find moles of a gas using the ideal gas law?
Rearrange PV = nRT to n = PV / (RT). You need pressure in atm, volume in litres, and temperature in Kelvin. The gas constant R is 0.08206 L·atm/mol·K. At STP (0 °C, 1 atm) one mole occupies 22.414 L.
How do I find the molar mass of a compound?
Sum the standard atomic weight of every atom in the chemical formula. For CO₂: one carbon (12.011) plus two oxygens (2 × 15.999) = 44.009 g/mol. Check the reference table below for common substances, or consult the IUPAC periodic table for current atomic weights.
How many particles are in one mole?
Exactly 6.02214076 × 10²³ elementary entities, the Avogadro constant, fixed by definition in the 2019 SI revision. This number applies to atoms, molecules, ions, electrons, or any other specified particle.