Mole Calculator
Calculate mole with our free science calculator. Uses standard scientific formulas with unit conversions and explanations.
Calculator
Adjust values & calculateConversion Details
Formula
The number of moles equals the mass of a substance divided by its molar mass. The number of particles equals moles multiplied by Avogadro's number (6.022 x 10^23). For gases at STP, the volume in liters equals moles multiplied by 22.414 L/mol.
Last reviewed: December 2025
Worked Examples
Example 1: Mass of Water to Moles
Example 2: Moles of CO2
Background & Theory
The Mole Calculator applies the following established principles and formulas. Chemistry is the science of matter's composition, structure, properties, and transformations. At the heart of quantitative chemistry lies the mole concept. One mole of any substance contains exactly 6.022×10²³ entities (Avogadro's number, Nₐ), and the molar mass of an element or compound in grams per mole is numerically equal to its atomic or molecular mass in atomic mass units. This allows chemists to convert between measurable mass and the number of reacting particles. Stoichiometry uses balanced chemical equations to relate the amounts of reactants and products. A balanced equation conserves both mass and charge. Molarity, the most common concentration unit, is defined as M = n/V, where n is moles of solute and V is volume of solution in liters, giving units of mol/L. Acidity and basicity are quantified by the pH scale, defined as pH = −log₁₀[H⁺], where [H⁺] is the molar concentration of hydrogen ions. Pure water at 25°C has pH 7.00; acids have lower values and bases higher values. Each unit change represents a tenfold change in hydrogen ion concentration. Gas behavior is described by the ideal gas law PV = nRT, where P is pressure in pascals, V is volume in cubic meters, n is moles, R = 8.314 J/(mol·K), and T is temperature in kelvin. Special cases include Boyle's Law (P₁V₁ = P₂V₂ at constant temperature) and Charles's Law (V₁/T₁ = V₂/T₂ at constant pressure). Thermochemistry quantifies heat changes in reactions through enthalpy, H. Hess's Law states that the total enthalpy change for a reaction is the sum of enthalpy changes for any sequence of steps leading to the same overall reaction, making it possible to calculate enthalpies for reactions that cannot be measured directly. Electron configuration describes the distribution of electrons in atomic orbitals according to the Aufbau principle, Pauli exclusion principle, and Hund's rule. Periodic trends including atomic radius, ionization energy, and electronegativity arise systematically from electron configuration and nuclear charge, enabling chemists to predict and rationalize chemical behavior across the periodic table.
History
The history behind the Mole Calculator traces back through the following developments. Chemistry's roots lie in alchemy, the medieval practice combining proto-scientific experimentation with mystical aims. Alchemists developed practical techniques including distillation, calcination, and the preparation of acids, building a body of empirical knowledge despite their theoretical misunderstandings. Modern chemistry is conventionally dated to Antoine Lavoisier (1743–1794), often called the father of modern chemistry. Lavoisier demonstrated the law of conservation of mass in 1789, showing that matter is neither created nor destroyed in chemical reactions. He identified oxygen's role in combustion, dismantling the phlogiston theory, and co-authored the first systematic chemical nomenclature, establishing the language still used today. John Dalton proposed the first modern atomic theory in 1803, asserting that all matter is composed of indivisible atoms, that atoms of the same element are identical in mass, and that compounds form from fixed ratios of different atoms. This provided a physical basis for Lavoisier's conservation law and Proust's law of definite proportions. Dmitri Mendeleev published his periodic table in 1869, arranging the 63 known elements by atomic mass and revealing repeating patterns of chemical behavior. He boldly left gaps for undiscovered elements and predicted their properties with remarkable accuracy, predictions confirmed by the subsequent discovery of gallium, scandium, and germanium. Ernest Rutherford's gold foil experiment in 1911 revealed the nuclear model of the atom: a tiny, dense, positively charged nucleus surrounded by electrons. Niels Bohr refined this in 1913 with a quantized model of electron orbits that explained the hydrogen emission spectrum. Quantum chemistry and molecular orbital theory, developed through the 1920s and 1930s, provided the full quantum mechanical description of chemical bonding. The latter 20th century saw the rise of computational chemistry, enabling molecular simulation at unprecedented scale. The green chemistry movement, articulated in the 12 Principles of Green Chemistry in 1998, reoriented the field toward sustainability, waste reduction, and benign chemical design, reflecting chemistry's growing awareness of its environmental responsibilities.
Frequently Asked Questions
Sources & References
Formula
Moles = Mass (g) / Molar Mass (g/mol)
The number of moles equals the mass of a substance divided by its molar mass. The number of particles equals moles multiplied by Avogadro's number (6.022 x 10^23). For gases at STP, the volume in liters equals moles multiplied by 22.414 L/mol.
Worked Examples
Example 1: Mass of Water to Moles
Problem: How many moles are in 36 grams of water (H2O, molar mass 18.015 g/mol)?
Solution: Moles = mass / molar mass\nMoles = 36 / 18.015 = 1.999 mol\nParticles = 1.999 x 6.022 x 10^23 = 1.2038 x 10^24\nVolume at STP = 1.999 x 22.414 = 44.80 L
Result: 1.999 moles of water
Example 2: Moles of CO2
Problem: Calculate moles in 100 grams of carbon dioxide (CO2, molar mass 44.01 g/mol).
Solution: Moles = 100 / 44.01 = 2.272 mol\nParticles = 2.272 x 6.022 x 10^23 = 1.369 x 10^24\nVolume at STP = 2.272 x 22.414 = 50.93 L
Result: 2.272 moles of CO2
Frequently Asked Questions
What is a mole in chemistry?
A mole is a fundamental unit in chemistry that represents exactly 6.02214076 x 10^23 particles (atoms, molecules, ions, or other entities). This number is known as Avogadro's number. One mole of any substance contains the same number of particles, just as one dozen always means twelve items. The mole bridges the gap between the atomic scale and the laboratory scale, allowing chemists to count atoms by weighing substances. For example, one mole of water (H2O) has a mass of about 18.015 grams.
How many atoms are in one mole?
One mole contains exactly 6.02214076 x 10^23 particles, a value known as Avogadro's number or Avogadro's constant. This enormous number was chosen so that one mole of carbon-12 atoms has a mass of exactly 12 grams, linking the atomic mass unit to grams. To put this number in perspective, if you had a mole of sand grains, they would cover the entire surface of the Earth to a depth of several kilometers. Despite its size, Avogadro's number is a precisely defined constant in the SI system since 2019.
What is a mole and why is it used in chemistry?
A mole is 6.022 x 10^23 particles (Avogadro's number). It allows chemists to count atoms and molecules by weighing them. One mole of any element weighs its atomic mass in grams. For example, one mole of carbon weighs 12 grams and contains 6.022 x 10^23 carbon atoms.
Is my data stored or sent to a server?
No. All calculations run entirely in your browser using JavaScript. No data you enter is ever transmitted to any server or stored anywhere. Your inputs remain completely private.
How do I get the most accurate result?
Enter values as precisely as possible using the correct units for each field. Check that you have selected the right unit (e.g. kilograms vs pounds, meters vs feet) before calculating. Rounding inputs early can reduce output precision.
How do I verify Mole Calculator's result independently?
The Formula section on this page shows the equation used. You can reproduce the calculation manually or in a spreadsheet using those steps. Compare your answer against the worked examples in the Examples section, which use known reference values so you can confirm the calculator is behaving as expected.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy