Average Atomic Mass Calculator
Work out an element’s average atomic mass from its isotope masses and abundances. Pick any of 84 elements to load NIST isotope data, or type your own, then solve for unknown abundances or an unknown isotope mass and compare with the standard atomic weight.
How to Use
- Choose what to work out: the average mass, two unknown abundances, or one unknown isotope mass.
- Pick an element to load its isotope masses and natural abundances (NIST), or choose Custom and type one isotope per line: a label, the mass in u and the abundance, such as Cl-35 34.96885 75.76.
- Set whether the abundances are percentages or fractions. Write ? for each value you want solved: two abundances, or one mass.
- For the two solving modes enter the known average atomic mass; picking an element fills in its standard atomic weight.
- Read the result, the comparison with the standard atomic weight or the measured value, and the bar chart of the isotopes. Show Work lists every mass × abundance product.
Worked Example
Chlorine from its isotopes. NIST gives chlorine-35 a mass of 34.968852682 u and an abundance of 75.76%, and chlorine-37 36.965902602 u and 24.24%. The weighted average is 0.7576 × 34.968852682 + 0.2424 × 36.965902602 = 26.49240 + 8.96053 = 35.45294 u, inside the CIAAW range of 35.446 to 35.457.
Working backwards. If you only know chlorine’s atomic weight, 35.45, and the two isotope masses, the Cl-35 fraction is x = (35.45 − 36.965902602) ÷ (34.968852682 − 36.965902602) = −1.51590 ÷ −1.99705 = 0.75907, so 75.91% Cl-35 and 24.09% Cl-37. The small gap from the measured 75.76% comes from rounding the average to four figures.
The common mistake: averaging without the abundances. Adding the two masses and dividing by 2 gives 35.96738 u, as if the isotopes were equally common. Chlorine-35 is three times as common, so the right answer, 35.45294 u, sits much closer to 35. Using the mass numbers 35 and 37 instead of the real masses is a smaller slip: 35.4848 u.
Show Work
Formulas
Isotopes, Aston’s Mass Spectrograph and Atomic Weights
Frederick Soddy introduced the word “isotope” in 1913 for forms of an element with the same chemistry but different masses, and in the same year J. J. Thomson found that neon gave two parabolas in his positive-ray apparatus. Francis Aston built the first mass spectrograph in 1919, confirmed neon-20 and neon-22, and went on to show that chlorine is a mixture of masses 35 and 37, which is why its atomic weight is not close to a whole number. He received the 1922 Nobel Prize in Chemistry.
Since 1961 atomic masses have been measured on the carbon-12 scale, with one unified atomic mass unit defined as one twelfth of the mass of a carbon-12 atom. The IUPAC Commission on Isotopic Abundances and Atomic Weights (CIAAW) reviews the standard atomic weights, and since 2009 it has given intervals rather than single values for elements whose isotope mix varies in nature. The isotope masses and abundances this tool loads are NIST’s values (atomic weights and isotopic compositions), via the PubChem periodic table; the standard atomic weights and intervals are CIAAW’s.
About This Tool
This calculator works out the abundance-weighted average of any set of isotopes and compares it with the element’s standard atomic weight, including whether it falls inside the CIAAW interval. It loads the NIST masses and natural abundances for all 84 elements that have them, or takes your own rows, so textbook problems with made-up isotopes work too. It also runs the problem backwards: two unknown abundances from a known average, or one unknown isotope mass, with a note on how strongly rounding in the average affects the answer.
If your abundances don’t add up to 100%, the average is still found by dividing by their total, and you are told. Everything runs in your browser; nothing is sent anywhere.
Related tools: Interactive Periodic Table, Molar Mass Calculator, and Oxidation Number Calculator.
Frequently Asked Questions
How do you calculate average atomic mass?
Multiply each isotope’s mass by its abundance as a fraction and add the results. For chlorine, 0.7576 × 34.968852682 + 0.2424 × 36.965902602 = 26.49240 + 8.96053 = 35.45294 u, which matches the standard atomic weight of 35.45 and sits inside its range of 35.446 to 35.457.
How do you find the percent abundance of two isotopes from the average?
Call one abundance x and the other 1 − x, so x × m₁ + (1 − x) × m₂ = average and x = (average − m₂) ÷ (m₁ − m₂). For copper, with Cu-63 at 62.92959772 u, Cu-65 at 64.92778970 u and an average of 63.546 u, x = −1.38179 ÷ −1.99819 = 0.69152: 69.152% Cu-63 and 30.848% Cu-65.
Why isn’t an atomic mass a whole number?
For two reasons. Most elements are a mixture of isotopes, so the average falls between their masses: chlorine’s 35.45 lies between 35 and 37. And even a single isotope is not a whole number of mass units, because of nuclear binding energy: Cl-35 is 34.968852682 u, not 35. Only carbon-12 is exactly 12 u, by definition.
Why do some elements have an atomic weight range?
Their isotope mix varies measurably between natural sources, so the IUPAC Commission on Isotopic Abundances and Atomic Weights (CIAAW) gives an interval. Chlorine is [35.446, 35.457], hydrogen [1.00784, 1.00811] and lead, whose isotopes partly come from uranium and thorium decay, [206.14, 207.94]. 14 of the elements here have an interval; 35.45 is the conventional value for chlorine.
What is the difference between mass number, isotope mass and atomic weight?
The mass number is the count of protons and neutrons, 37 for chlorine-37. The isotope mass is what that atom actually weighs, 36.965902602 u. The atomic weight is the abundance-weighted average over the element’s isotopes, 35.45 for chlorine. Using mass numbers instead of isotope masses gives 0.7576 × 35 + 0.2424 × 37 = 35.4848, off by 0.032.
How do I use the Average Atomic Mass Calculator?
Simply type your numbers and read the result, which refreshes the instant you change something. There is nothing to submit and nothing to wait for.
Does it cost anything or need an account?
No. The tool is completely free, there is no account to create, and it keeps working offline after the page first loads.
Is anything I type uploaded?
No. The tool works entirely on your device, so the values you enter never leave your browser.
Common Use Cases
Mass spectra
A molecule with one chlorine shows two peaks 2 u apart in a 75.76 : 24.24 ratio, 3.13 : 1, the familiar M and M+2 pattern.
Homework problems
An element with 19.9% at 10.013 u and 80.1% at 11.009 u averages 10.81080 u: boron.
Reverse problems
Copper’s 63.546 u gives 69.152% Cu-63, within 0.002 percentage points of the NIST 69.15%.
Nuclear fuel
Natural uranium is 0.7204% U-235; enriched to 4% U-235 with the rest U-238, its average mass drops to 237.93051 u.
Checking data
Solving Cl-37’s mass back from 35.45 u gives 36.9538 u, 0.0121 u off, because each 0.01 u of rounding in the average moves it by 0.0413 u.
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