Atomic Mass Calculator
Atomic Mass Calculator
Click an element to append it to the formula
Supports (), [], hydrates (·), and isotope notation [13]C. Case-sensitive: Co ≠ CO.
Enter a Chemical Formula
Type a chemical formula such as H2O, Ca(OH)2, or CuSO4·5H2O to see the molar mass, elemental composition chart, and step-by-step breakdown.
Calculate molar mass, elemental composition, and mole conversions for any chemical formula using IUPAC 2021 atomic weights
The Atomic Mass Calculator is an essential chemistry tool for students, teachers, laboratory technicians, pharmacists, and anyone working with chemical quantities. It instantly computes the molar mass (also called molecular weight) of any compound by parsing the chemical formula and summing the IUPAC 2021 standard atomic weights of all constituent elements. Whether you are preparing a solution, balancing a stoichiometric equation, or studying for a chemistry exam, this calculator provides accurate results with a full step-by-step breakdown of each element's contribution. Molar mass is defined as the mass of one mole of a substance, expressed in grams per mole (g/mol). For a pure element, it equals the standard atomic weight listed on the periodic table. For a compound, it is calculated by multiplying each element's atomic weight by its count in the formula and summing the products. For example, water (H₂O) has a molar mass of 2 × 1.008 + 1 × 15.999 = 18.015 g/mol. This value is fundamental to converting between measurable masses and the number of moles in the mole concept — the cornerstone of quantitative chemistry. The formula parser built into this calculator handles the full complexity of chemical notation. It correctly processes nested parentheses for coordination compounds such as Ca(OH)₂ and Al₂(SO₄)₃, square brackets for coordination complexes like K₃[Fe(CN)₆] and K₄[Fe(CN)₆], and hydrate notation with a middle dot or period separator such as CuSO₄·5H₂O. Isotope notation using the square-bracket prefix format — for example [¹³]C for carbon-13 — is also supported. The parser is case-sensitive, so Co (cobalt) is correctly distinguished from CO (carbon monoxide), and Fe (iron) from FE (which would be an error). Charge notations are gracefully ignored. This tool supports three calculation modes. The primary Formula Mode accepts any chemical formula and produces the molar mass, an elemental composition table sorted by descending mass contribution, a donut chart showing each element's share of the total mass, the Hill formula (organics ordered C, H, then alphabetically), the empirical formula derived by reducing atom ratios to the smallest integers, and a mole-mass-particles converter. The Average Atomic Mass Mode allows you to calculate the weighted average atomic mass of an element from two to five isotopes by entering each isotope's mass in atomic mass units and its natural abundance as a percentage. The Proton/Neutron Mode provides a quick approximation of atomic mass from the mass number (A = Z + N), where Z is the number of protons and N is the number of neutrons. The elemental composition feature is particularly useful in analytical chemistry, where knowing the exact mass percentage of each element in a compound is required for quantitative analysis, empirical formula derivation from combustion data, and verifying the purity of synthesized compounds. The mass percent of element E is calculated as: %E = 100 × (n_E × AW_E) / M, where n_E is the atom count, AW_E is the atomic weight, and M is the total molar mass. The integrated mole-mass converter in the results panel lets you immediately convert between moles and grams once the molar mass is known. Enter either the number of moles or the mass in grams, and the calculator outputs both the other quantity and the number of particles (molecules, formula units, or atoms) using Avogadro's number — 6.02214076 × 10²³ mol⁻¹. This bidirectional converter covers the three quantities that define the mole concept: amount (mol), mass (g), and particle count (N). All 118 elements are included in the database, using the 2021 IUPAC standard atomic weights — the most current international values for conventional reporting. For elements with radioactive isotopes only (such as technetium, promethium, and the transuranic elements), the most stable isotope mass is used as the conventional value, consistent with IUPAC practice. Additional productivity features include preset compound buttons for the most commonly encountered chemicals in educational and laboratory settings (water, glucose, sodium chloride, sulfuric acid, calcium hydroxide, caffeine, aspirin, and more), adjustable decimal precision from 2 to 6 significant figures, one-click copy of results to clipboard, CSV export for lab notebooks and spreadsheets, and a print button for generating paper reports.
Understanding Atomic and Molar Mass
What Is Atomic Mass and Molar Mass?
Atomic mass (also called atomic weight) is the mass of a single atom, measured in atomic mass units (u or Da), where 1 u = 1/12 the mass of a carbon-12 atom. The standard atomic weight listed on the periodic table is a weighted average across all naturally occurring isotopes of an element. For example, chlorine has two main isotopes — Cl-35 (75.77% abundance) and Cl-37 (24.23% abundance) — giving a standard atomic weight of 35.45 u. Molar mass is the mass of exactly one mole (6.02214076 × 10²³ entities) of a substance, expressed in grams per mole (g/mol). Its numerical value equals the standard atomic weight in u. For water (H₂O): molar mass = 2(1.008) + 15.999 = 18.015 g/mol.
How Is Molar Mass Calculated from a Formula?
The molar mass M of a compound is calculated by summing the products of each element's atom count and atomic weight: M = Σ(n_i × AW_i), where n_i is the number of atoms of element i in one formula unit and AW_i is its standard atomic weight. For sulfuric acid (H₂SO₄): M = 2(1.008) + 32.06 + 4(15.999) = 2.016 + 32.06 + 63.996 = 98.072 g/mol. For hydrated compounds like CuSO₄·5H₂O: the five water molecules are added separately, giving M = 63.546 + 32.06 + 4(15.999) + 5[2(1.008) + 15.999] = 249.685 g/mol. This calculator handles all these cases automatically through its recursive formula parser.
Why Molar Mass Matters in Chemistry
Molar mass is the conversion factor between the amount of substance (moles) and the mass that can be weighed on a balance. Stoichiometry — the quantitative study of reactants and products in chemical reactions — depends entirely on mole ratios derived from balanced equations. However, in the real world, chemists measure grams, not moles. The relationship m = n × M (mass equals moles times molar mass) bridges these scales. In pharmaceuticals, molar mass governs drug dosage calculations and formulation. In environmental chemistry, it quantifies pollutant concentrations. In materials science, it determines composition and properties of alloys and polymers. Every quantitative chemistry calculation, from preparing a 0.1 M buffer solution to titrating an unknown acid, requires accurate molar mass values.
Limitations and Notes on Atomic Weights
Standard atomic weights from IUPAC represent averages across naturally occurring isotope distributions and may vary slightly depending on geographic origin of samples. For isotopically enriched materials, isotopically labeled compounds (e.g., deuterium-labeled solvents), or specific isotopes used in nuclear medicine or spectroscopy, use the isotopic mass of the specific isotope rather than the standard atomic weight. This calculator's Average Atomic Mass Mode supports this use case. For transuranic elements (atomic numbers 93–118), the listed atomic weight is the most stable known isotope, as no stable isotopes exist. Empirical formulas are derived by dividing all atom counts by their greatest common divisor — this gives the simplest integer ratio but may not represent the molecular formula.
Formulas
The molar mass M (g/mol) is the sum of each element's atom count nᵢ multiplied by its standard atomic weight AWᵢ. For example, H₂SO₄: M = 2(1.008) + 32.06 + 4(15.999) = 98.072 g/mol.
The mass percentage of element E in a compound equals its total mass contribution (atom count × atomic weight) divided by the compound's molar mass, multiplied by 100.
The average atomic mass is the sum of each isotope's mass mⱼ (in amu) multiplied by its fractional natural abundance fⱼ. For Cl: Ā = 0.7577 × 34.969 + 0.2423 × 36.966 = 35.45 amu.
Mass (g) equals moles times molar mass. Number of particles N equals moles times Avogadro's number (Nₐ = 6.02214076 × 10²³ mol⁻¹).
Reference Tables
Common Elements — Standard Atomic Weights (IUPAC 2021)
| Element | Symbol | Atomic Number | Atomic Weight (g/mol) |
|---|---|---|---|
| Hydrogen | H | 1 | 1.008 |
| Carbon | C | 6 | 12.011 |
| Nitrogen | N | 7 | 14.007 |
| Oxygen | O | 8 | 15.999 |
| Sodium | Na | 11 | 22.990 |
| Sulfur | S | 16 | 32.06 |
| Chlorine | Cl | 17 | 35.45 |
| Calcium | Ca | 20 | 40.078 |
| Iron | Fe | 26 | 55.845 |
| Copper | Cu | 29 | 63.546 |
Molar Mass of Common Compounds
| Compound | Formula | Molar Mass (g/mol) |
|---|---|---|
| Water | H₂O | 18.015 |
| Sodium Chloride | NaCl | 58.443 |
| Glucose | C₆H₁₂O₆ | 180.156 |
| Sulfuric Acid | H₂SO₄ | 98.072 |
| Calcium Carbonate | CaCO₃ | 100.086 |
| Ethanol | C₂H₅OH | 46.069 |
| Aspirin | C₉H₈O₄ | 180.158 |
| Caffeine | C₈H₁₀N₄O₂ | 194.191 |
Worked Examples
Molar Mass of Calcium Hydroxide — Ca(OH)₂
Identify atom counts: Ca = 1, O = 2, H = 2
Ca contribution: 1 × 40.078 = 40.078 g/mol
O contribution: 2 × 15.999 = 31.998 g/mol
H contribution: 2 × 1.008 = 2.016 g/mol
Sum: M = 40.078 + 31.998 + 2.016 = 74.092 g/mol
Mass %: Ca = 54.09%, O = 43.19%, H = 2.72%
Average Atomic Mass of Chlorine from Isotopes
Convert abundances to fractions: f₁ = 0.7577, f₂ = 0.2423
Cl-35 contribution: 0.7577 × 34.969 = 26.496 amu
Cl-37 contribution: 0.2423 × 36.966 = 8.957 amu
Sum: Ā = 26.496 + 8.957 = 35.453 amu
Mole-Mass Conversion — How Many Grams in 3.5 mol of NaCl?
Molar mass of NaCl: 22.990 + 35.453 = 58.443 g/mol
Mass: m = n × M = 3.5 × 58.443 = 204.55 g
Particles: N = n × Nₐ = 3.5 × 6.022 × 10²³ = 2.108 × 10²⁴ formula units
How to Use the Atomic Mass Calculator
Select a Mode
Choose Formula Mode to calculate molar mass from a chemical formula, Isotope Mode to compute the weighted average atomic mass from isotope data, or Proton/Neutron Mode to find the mass number from proton and neutron counts. The most commonly used mode is Formula Mode.
Enter or Select a Formula
In Formula Mode, type a chemical formula in the input field — for example H2O, NaCl, Ca(OH)2, K3[Fe(CN)6], or CuSO4·5H2O. You can also click one of the preset compound buttons to fill the formula automatically. The input field shows a green indicator when the formula is valid and a red error message if an unknown element symbol is detected.
Read the Composition Results
The molar mass appears as the main result. Below it you will find the Hill formula, empirical formula, total atom count, and a full elemental composition table with a color-coded donut chart showing each element's share by mass. Horizontal bars let you quickly compare each element's contribution. The step-by-step box shows the arithmetic for each element.
Convert Moles and Export
Use the Mole-Mass-Particles Converter section to convert between moles, grams, and particle count using Avogadro's number. Enter either moles or grams and the other value is calculated instantly. Use the copy, export CSV, or print buttons to save your results for lab reports, homework, or notebooks.
Frequently Asked Questions
What is the difference between atomic mass and molar mass?
Atomic mass is the mass of a single atom measured in atomic mass units (u or Da), where 1 u = 1.66053906660 × 10⁻²⁷ kg. The standard atomic weight listed on the periodic table is a weighted average across all naturally occurring isotopes. Molar mass is the mass of one mole (6.022 × 10²³ entities) of a substance, expressed in grams per mole (g/mol). The numerical value of molar mass equals the standard atomic weight in u — so the molar mass of carbon is 12.011 g/mol, and the molar mass of water is 18.015 g/mol. In everyday chemistry practice, the terms are often used interchangeably when referring to compounds.
How do I enter complex formulas like hydrates or coordination compounds?
This calculator supports the full range of standard chemical notation. For parenthesised groups, use round brackets: Ca(OH)2, Al2(SO4)3. For coordination compounds with square brackets, use: K3[Fe(CN)6]. For hydrates, use either a middle dot (·) or a period (.): CuSO4·5H2O or CuSO4.5H2O. For isotope notation, use the square-bracket prefix: [13]C for carbon-13 or [2]H for deuterium. The parser is case-sensitive: Co (cobalt, atomic number 27) is different from CO (carbon monoxide, two separate atoms). If your formula contains a charge such as SO4²⁻, the charge characters are ignored and the formula parsed normally.
What is the Hill formula and why is it useful?
The Hill formula is a standardized way of ordering element symbols in a molecular formula, devised by Edwin A. Hill in 1900 and widely used in chemistry databases and literature. For organic compounds (those containing carbon), carbon is listed first, hydrogen second, then all other elements in alphabetical order. For compounds without carbon, all elements are listed in alphabetical order. For example, glucose C₆H₁₂O₆ in Hill order is C₆H₁₂O₆. This standardization allows consistent indexing and searching in chemical databases like CAS, PubChem, and chemical journals. This calculator always displays the Hill formula alongside any formula you enter.
How is the average atomic mass calculated in Isotope Mode?
The average atomic mass is the weighted average of all isotope masses, weighted by their fractional natural abundance. The formula is: Ā = Σ(f_j × m_j), where f_j is the fractional abundance (abundance percentage ÷ 100) and m_j is the mass of isotope j in atomic mass units. For example, chlorine has two stable isotopes: Cl-35 with mass 34.969 u and abundance 75.77%, and Cl-37 with mass 36.966 u and abundance 24.23%. Average mass = (0.7577 × 34.969) + (0.2423 × 36.966) = 26.496 + 8.957 = 35.453 u, which matches the standard atomic weight of chlorine (35.45 u). Enter the isotope masses and abundances in Isotope Mode to perform this calculation.
What atomic weight values does this calculator use?
This calculator uses IUPAC 2021 standard atomic weights — the most current internationally recommended values as published by the International Union of Pure and Applied Chemistry. These values are weighted averages across the natural isotope abundances of each element as they occur in the Earth's crust, atmosphere, and oceans. For elements that have no stable isotopes (technetium, promethium, and all transuranic elements from neptunium onward), the atomic weight of the most stable known isotope is used, consistent with IUPAC practice. Results may differ very slightly from older periodic tables, which may use values from IUPAC 2013 or earlier revisions.
How do I use the Mole-Mass-Particles Converter?
After calculating the molar mass of a compound in Formula Mode, a converter section appears in the results. Enter either the number of moles or the mass in grams — the other value is computed automatically. The particle count is also shown, calculated by multiplying the moles by Avogadro's number (6.02214076 × 10²³ mol⁻¹). For example, entering 2 moles of water (molar mass 18.015 g/mol) gives 36.030 g and 1.204 × 10²⁴ water molecules. Entering 58.44 g of NaCl (molar mass 58.443 g/mol) gives approximately 1.000 mol and 6.022 × 10²³ formula units. This converter is ideal for stoichiometry problems and solution preparation.