The Atomic Mass Calculator computes the weighted average atomic mass from the masses and natural abundances of an element's isotopes. Returns the relative atomic mass (Ar) in atomic mass units — the value shown on the periodic table reflecting natural isotopic composition.
10.2112
amu
100
%
10.2112
amu
100
%
The periodic table lists carbon's atomic mass as 12.011 — not exactly 12, and not exactly 13. That decimal arises from the natural mixture of isotopes in Earth's carbon: mostly ¹²C (98.9%) with a small fraction of ¹³C (1.1%) and a trace of ¹⁴C. The calculator for atomic mass computes this isotope-weighted average from the mass and natural abundance of each isotope — the calculation behind every number on the periodic table.
Atomic mass is a weighted average of isotope masses weighted by their fractional natural abundances:
Ar = Σ (isotope mass × fractional abundance)
where fractional abundance = percentage / 100. For chlorine with two stable isotopes:
Ar(Cl) = (34.9689 × 0.7577) + (36.9659 × 0.2423) = 26.496 + 8.959 = 35.455 u — consistent with the periodic table value of 35.45. Note that the abundances must sum to exactly 100% (or 1.0 as fractions); this calculator validates this constraint. Use this online calculator for any element with up to 4 isotopes. The atom calculator finds proton, neutron, and electron counts from atomic and mass numbers.
Two physical facts combine to make atomic masses non-integer:
The atomic mass unit (u) is defined as exactly 1/12 of the mass of a ¹²C atom = 1.66054 × 10⁻²⁷ kg. This definition makes ¹²C exactly 12 u and all other masses slightly non-integer due to binding energy differences.
The periodic table atomic mass is used extensively in stoichiometry:
The molar mass calculator applies the periodic table masses to compute formula or molecular weight for any chemical compound. The atomic and molecular calculators provide the complete chemistry calculation toolkit.
IUPAC (International Union of Pure and Applied Chemistry) publishes the authoritative table of standard atomic weights, updated periodically as measurement precision improves and as natural abundance variations are better characterized. Some elements (like boron, carbon, lithium, and sulfur) have atomic weights expressed as intervals rather than single values because their natural abundance varies measurably across geological sources. Lithium, for example, has been commercially extracted for lithium isotope separation, meaning naturally occurring lithium in some commercial products has a different isotopic composition than pristine geological samples.
The average atomic mass is calculated using the weighted average formula:
M_avg = (m1 x f1) + (m2 x f2) + ... + (mn x fn)
Where m_i is the exact mass of isotope i in atomic mass units (amu), and f_i is the fractional abundance (percentage divided by 100). The fractional abundances of all isotopes must sum to 1.0 (or percentages sum to 100%).
For example, chlorine has two stable isotopes: Cl-35 (mass 34.9689 amu, abundance 75.76%) and Cl-37 (mass 36.9659 amu, abundance 24.24%). The calculation gives: M = 34.9689 x 0.7576 + 36.9659 x 0.2424 = 26.496 + 8.960 = 35.456 amu, which matches the periodic table value of 35.45 amu.
This same principle applies to elements with three or more isotopes. Tin, for instance, has 10 stable isotopes, making it the element with the most stable isotopes. Each isotope's mass is determined experimentally using mass spectrometry, where ions are separated by their mass-to-charge ratio in a magnetic field. The abundances are measured from the relative peak heights in the mass spectrum.
The calculated average atomic mass represents the mass you would expect for a randomly selected atom of the element from a natural sample. This value is what appears on the periodic table and is used in all stoichiometric calculations involving moles and molar masses. The total abundance should equal 100% for a complete calculation. If it does not, some isotopes may be missing from your input. Note that the average atomic mass typically falls between the lightest and heaviest isotope masses, closer to the most abundant isotope's mass.
Inputs
Results
Boron has two stable isotopes: B-10 (mass 10.0129 amu, 80.1% abundance) and B-11 (mass 11.0093 amu, 19.9% abundance). The weighted average of 10.211 amu matches the standard atomic weight of boron (10.81 amu when using more precise abundances of 19.9% for B-10 and 80.1% for B-11). Note: IUPAC lists boron as 10.81 with abundances of ~19.9% B-10 and ~80.1% B-11.
Inputs
Results
Chlorine's two stable isotopes Cl-35 and Cl-37 give a weighted average of 35.453 amu. This explains why chlorine's atomic mass on the periodic table is 35.45 amu, not a whole number. The result is much closer to 35 because Cl-35 is about three times more abundant than Cl-37.
The average atomic mass is a weighted average of the masses of all naturally occurring isotopes. Since isotopes have different masses and non-integer abundances, the weighted average almost always produces a non-integer result. For example, chlorine's average is 35.45 because it is a mixture of Cl-35 (75.76%) and Cl-37 (24.24%).
The mass number is the integer count of protons plus neutrons in a specific isotope (e.g., 12 for Carbon-12). The atomic mass is the precise mass measured in atomic mass units, which includes the mass defect from nuclear binding energy. Carbon-12 has a mass of exactly 12.0000 amu by definition, but other isotopes have non-integer masses.
Isotope abundances are determined using mass spectrometry. A sample is ionized and the ions are separated by their mass-to-charge ratio in a magnetic field. The detector measures the relative number of ions at each mass, giving the natural abundance of each isotope with high precision.
If the total abundance is not 100%, it usually means one or more isotopes are missing from the calculation, or the abundance values are imprecise. For an accurate average atomic mass, all naturally occurring isotopes must be included and their abundances should sum to 100%. Minor isotopes with very low abundance may be negligible.
Yes. Twenty-one elements are monoisotopic, meaning they have only one stable isotope. Examples include fluorine (F-19), sodium (Na-23), aluminum (Al-27), phosphorus (P-31), and gold (Au-197). For these elements, the atomic mass equals the mass of that single isotope.
IUPAC now lists standard atomic weights as intervals (e.g., [10.806, 10.821] for boron) for 14 elements whose isotopic abundances vary significantly depending on the source material. This reflects natural variation in isotope ratios due to geological, biological, or industrial processes.
How helpful was this calculator?
Be the first to rate!
