Atomic Mass Calculator

Common isotopic mass numbers

Atomic Mass Calculator: Complete Guide

The atomic mass of a specific isotope is approximately equal to its mass number -- the total count of protons and neutrons. The LazyTools atomic mass calculator computes A = Z + N for any isotope and also shows the more precise unbound nuclear mass using proton mass (1.007276 amu) and neutron mass (1.008665 amu). The difference between the calculated unbound mass and the actual nuclear mass is the nuclear binding energy, expressed through Einstein's E=mc2.

Mass number vs exact isotopic mass

The mass number A is the integer sum of protons and neutrons -- an approximation that is exact enough for most chemistry calculations. The exact isotopic mass is measured by mass spectrometry and differs slightly from A due to nuclear binding energy. For C-12 (defined as exactly 12.000000 amu by convention): A = 12, exact mass = 12.000000. For C-13: A = 13, exact mass = 13.003355 amu. For Fe-56: A = 56, exact mass = 55.934939 amu. The difference (56 vs 55.934939) reflects the mass equivalent of the binding energy holding 56 nucleons together. In general chemistry courses, A is used as the atomic mass for isotopes; the exact isotopic mass is used in mass spectrometry and nuclear chemistry.

How to calculate mass number

Formula: A = Z + N, where Z = atomic number (number of protons) and N = number of neutrons. Examples: Carbon-12: Z=6, N=6, A=12. Carbon-14: Z=6, N=8, A=14. Chlorine-35: Z=17, N=18, A=35. Chlorine-37: Z=17, N=20, A=37. Uranium-238: Z=92, N=146, A=238. Iron-56: Z=26, N=30, A=56. Lead-208: Z=82, N=126, A=208. The mass number determines which isotope is being described and is used in nuclear notation (superscript left of the element symbol).

Atomic mass units (amu) and the dalton

The atomic mass unit (amu), also called the unified atomic mass unit (u) or dalton (Da), is defined as exactly 1/12 the mass of one carbon-12 atom = 1.66054 x 10^-27 kg. One proton = 1.007276 amu. One neutron = 1.008665 amu. One electron = 0.000549 amu (usually neglected). The dalton is widely used in biochemistry and mass spectrometry: a protein with a molecular weight of 50,000 Da has a mass of 50 kDa. For atoms, 1 amu = 1 g/mol by Avogadro's number, which is why the molar mass of C-12 is exactly 12 g/mol.

Atomic mass in the periodic table

The atomic mass printed on the periodic table is the standard atomic weight -- a dimensionless quantity equal to the weighted average of the atomic masses of all naturally occurring isotopes. Chlorine: (0.7577 x 34.969) + (0.2423 x 36.966) = 35.45. Bromine: (0.5069 x 78.918) + (0.4931 x 80.916) = 79.90. The standard atomic weight changes slightly over time as isotopic abundance measurements are refined. IUPAC publishes the current recommended values. For a specific isotope, the mass number (A) is used; for chemical calculations involving natural samples, the standard atomic weight is used.

Nuclear binding energy and mass defect

When protons and neutrons combine to form a nucleus, energy is released and the nucleus has less mass than the sum of its parts -- this is the mass defect. For Fe-56: sum of unbound nucleons = 26 x 1.007276 + 30 x 1.008665 = 26.189 + 30.260 = 56.449 amu. Actual mass of Fe-56 nucleus = 55.935 amu. Mass defect = 56.449 - 55.935 = 0.514 amu. Binding energy = 0.514 x 931.5 MeV/amu = 478.9 MeV. Binding energy per nucleon = 478.9/56 = 8.55 MeV/nucleon -- one of the highest values on the binding energy curve, explaining why iron is the endpoint of stellar nucleosynthesis.

Common atomic mass calculation questions

What is the mass number of an atom with 26 protons and 30 neutrons? A = 26 + 30 = 56 (iron-56). What is the mass number of uranium-235? U has Z=92 and A=235, so N=235-92=143. What isotope has 6 protons and 8 neutrons? Z=6 is carbon, N=8, A=14: carbon-14 (used in radiocarbon dating). What is the mass number of the most stable isotope of lead? Pb-208 (Z=82, N=126, A=208). The atom calculator and atomic mass calculator together answer any combination of these exam question types.

How to use this chemistry calculator effectively

All LazyTools chemistry calculators run entirely in your browser -- no data is sent to a server, no account is required, and results appear instantly. The tools are designed for chemistry students, educators and professionals who need quick, accurate answers during study sessions, lab work or problem-set solving. Each calculator shows the underlying formula alongside the result so you can verify the calculation method and understand the chemistry, not just get a number. Copy the result to your clipboard for use in lab reports, assignments or messages with one click.

Related chemistry topics and further study

Chemistry calculators are most useful when paired with a solid understanding of the underlying concepts. This calculator addresses one specific quantitative aspect of chemistry -- the formula, units and typical values are described in the article above. For a deeper understanding, pair this tool with a standard university-level general chemistry textbook such as Atkins, Zumdahl, or Chang and Overby. The LazyTools chemistry suite covers all major quantitative topics in general, physical, organic and biochemistry -- see the related tools section below for the calculators most commonly used alongside this one.

Mass spectrometry and atomic mass measurement

Atomic masses are measured by mass spectrometry, in which atoms are ionised, accelerated through a magnetic field, and separated by their mass-to-charge ratio (m/z). A time-of-flight mass spectrometer measures the time taken for ions to travel a fixed distance -- lighter ions arrive first. The result is a mass spectrum showing peaks at each isotopic mass, with peak heights proportional to natural abundance. For chlorine: two peaks at m/z = 35 and m/z = 37, in the ratio 3:1 (approximately). Modern instruments achieve mass accuracy to parts per million, making mass spectrometry the definitive method for measuring exact isotopic masses. The values in atomic mass tables -- such as those published by the Commission on Isotopic Abundances and Atomic Weights (CIAAW) -- are derived from these measurements.

Atomic mass in stoichiometry and molar mass

The atomic mass of an element in amu is numerically equal to its molar mass in grams per mole by Avogadro's number (6.022 x 10^23). Carbon-12 has a mass of exactly 12 amu per atom, and exactly 12.000 g/mol for one mole of C-12 atoms. For the standard atomic weight of carbon (12.011 amu), one mole of natural carbon weighs 12.011 g. This equivalence between amu and g/mol is fundamental to stoichiometry: it allows the atomic masses read from the periodic table to be used directly as molar masses in gram-per-mole units, making it possible to convert between mass and moles of any element or compound. For a specific isotope such as C-13, the molar mass is 13.003 g/mol.

Nuclear physics applications of atomic mass

In nuclear physics, precise atomic masses are essential for calculating Q-values (energy released in nuclear reactions), binding energies, and predicting whether reactions are exothermic or endothermic. The Q-value of a reaction is Q = (sum of reactant masses - sum of product masses) x 931.5 MeV/amu. For alpha decay of U-238: the Q-value is approximately 4.27 MeV, calculated from the exact masses of U-238, Th-234 and He-4. Nuclear engineers use tabulated atomic masses to model fuel cycles, criticality calculations and radioactive decay chains. The LazyTools atomic mass calculator provides the mass number for any specified isotope, which serves as the starting point for these more detailed nuclear calculations. For students and educators, the mass number and exact isotopic mass provided by the LazyTools calculator are sufficient for all standard nuclear chemistry problems encountered in A-level and undergraduate general chemistry curricula. The tool is available at no cost, requires no installation and works on any device with a modern browser, making it suitable for use in the classroom, the laboratory or while studying at home.

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