The Average Atomic Mass Calculator computes the weighted average atomic mass of any element from up to three isotopes using mass and natural abundance. Used in chemistry to understand how the decimal values on the periodic table arise from the natural isotopic mixture of each element.
64.5447
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64.5447
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Pick up any periodic table and you will see that chlorine's atomic mass is 35.45 — not a whole number, and not the mass of any single chlorine atom that has ever existed. It is a weighted average of two stable isotopes that nature provides in a fixed ratio. The calculator for average atomic mass reconstructs this calculation from isotope data, illuminating the physical meaning behind every decimal place on the periodic table.
Average atomic mass is the sum of each isotope's mass multiplied by its fractional natural abundance:
Ā_r = Σ (m_i × f_i)
where m_i is the mass of isotope i in atomic mass units (u) and f_i is its fractional abundance (percentage ÷ 100). All fractional abundances must sum to exactly 1.000 (100%). For chlorine:
This online calculator handles up to three isotopes simultaneously. The atomic mass calculator covers the same calculation with a slightly different interface focused on two-isotope systems.
A classic chemistry problem inverts the formula: given the average atomic mass and one isotope's mass and abundance, find the second isotope's mass or abundance. If you know the average atomic mass (from periodic table) and one isotope's data, set up: Ā_r = m₁f₁ + m₂f₂, where f₁ + f₂ = 1. Substituting f₂ = 1 − f₁: Ā_r = m₁f₁ + m₂(1 − f₁). Solving for f₁: f₁ = (Ā_r − m₂) / (m₁ − m₂). For boron (Ā_r = 10.81 u): given ¹⁰B (10.013 u) and ¹¹B (11.009 u): f(¹⁰B) = (10.81 − 11.009) / (10.013 − 11.009) = 0.201 = 20.1%. Check: ¹⁰B = 19.9%, ¹¹B = 80.1% — very close to the accepted values.
Some elements have many stable isotopes, making the average atomic mass calculation more complex:
For elements with many isotopes, this calculator computes the three-isotope case which covers most teaching and textbook problems. The molar mass calculator uses average atomic masses to compute formula masses for chemical compounds. The atomic and molecular calculators provide the complete toolkit for atomic composition calculations.
IUPAC publishes standard atomic weights as intervals for elements whose isotopic composition varies meaningfully in natural materials. Lithium is the most notable example — industrial lithium extraction for batteries has depleted the lighter ⁶Li isotope from some commercial lithium sources, shifting the average atomic mass. Carbon isotopic composition varies slightly between biological and geological samples, which is the physical basis of stable isotope ecology and food authenticity testing. For most chemical calculations, the standard atomic weight is precise enough; for isotope-sensitive work, specific isotopic compositions must be used.
The average atomic mass is computed using the general weighted average formula:
M_avg = sum(m_i x f_i) for all isotopes i
Where m_i is the exact isotopic mass in atomic mass units (amu) and f_i is the fractional natural abundance (percentage / 100). This calculator supports up to three isotopes, set unused isotope masses to 0.
The deviation from the nearest integer shows how far the average deviates from a whole number. Elements with one dominant isotope (like carbon, 98.9% C-12) have very small deviations, while elements with two similarly abundant isotopes (like bromine, roughly 50/50 Br-79 and Br-81) have large deviations near 0.5.
Isotopic masses are determined by mass spectrometry and are expressed relative to carbon-12, which is defined as exactly 12.0000 amu. Individual isotope masses are close to but not exactly equal to their mass numbers due to the nuclear binding energy (mass defect). The unified atomic mass unit (u or amu) equals 1/12 of the mass of a carbon-12 atom, approximately 1.6605 x 10^-27 kg.
The average atomic mass result should closely match the value on the periodic table for the element in question. The total abundance should be 100% for a complete data set. The deviation metric reveals how representative any single isotope is of the element's listed mass. A small deviation (near 0) means the average is close to a whole mass number, indicating one isotope strongly dominates. A large deviation (near 0.5) indicates roughly equal contributions from isotopes with different mass numbers, as seen with copper and bromine.
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Copper has two stable isotopes: Cu-63 (69.17%) and Cu-65 (30.83%). The weighted average of 63.546 amu matches the periodic table value. The high deviation of 0.454 reflects the significant contribution of Cu-65 pulling the average away from 64.
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Silicon has three stable isotopes dominated by Si-28 at 92.23%. The average of 28.086 amu is very close to 28, reflected in the small deviation of 0.086. This is typical of elements where one isotope strongly predominates.
The number of stable isotopes varies from 0 (for elements like technetium and promethium, which have no stable isotopes) to 10 (tin has 10 stable isotopes, the most of any element). Most elements have between 1 and 4 stable isotopes. About 21 elements are monoisotopic with only one stable form.
Brackets indicate that the element has no stable isotopes. The number shown is the mass number of the longest-lived or most commonly encountered radioactive isotope. For example, [209] for bismuth indicates Bi-209, its longest-lived isotope with a half-life of 1.9 x 10^19 years.
Natural processes like radioactive decay, nuclear reactions in stars, mass-dependent fractionation during geological processes, and biological isotope effects can alter local isotopic ratios. For example, the ratio of O-18 to O-16 varies with temperature and is used in paleoclimatology to reconstruct ancient climates.
Modern Penning trap mass spectrometers can measure atomic masses with relative uncertainties of 10^-11 or better. The AME2020 (Atomic Mass Evaluation) database contains precise mass values for over 3,500 nuclides, including both stable and radioactive species.
Yes, but with a caveat. Radioactive isotopes are continuously decaying, so their abundance in a sample changes over time. The calculator works for any set of masses and abundances you provide, but the result only represents the average at the time of measurement for radioactive species.
One atomic mass unit (amu or u) equals exactly 1/12 the mass of a carbon-12 atom, which is approximately 1.6605 x 10^-24 grams. Avogadro's number (6.022 x 10^23) of atoms with an average mass of M amu will have a total mass of M grams. This is the bridge between atomic-scale masses and laboratory-scale masses.
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