Average Atomic Mass Calculator
Find the abundance-weighted average atomic mass of any element using up to five isotopes. Load a built-in preset for chlorine, boron, carbon and more, enter custom masses and percent abundances, let the calculator normalise any rounding gaps, and optionally reverse-solve for one unknown abundance when you already know the average.
Formula
Worked example
Chlorine has two isotopes: 35Cl (34.96885 amu, 75.77%) and 37Cl (36.96590 amu, 24.23%). Average = 34.96885 x 0.7577 + 36.96590 x 0.2423 = 26.503 + 8.957 = 35.460 amu, matching the periodic-table value of 35.45 amu.
What average atomic mass means
The average atomic mass of an element is the abundance-weighted mean of the masses of its naturally occurring isotopes. Isotopes are atoms of the same element with the same number of protons but different numbers of neutrons, so they differ in mass. Because most elements exist as a mixture of isotopes in nature, the mass printed on the periodic table is not the mass of any single atom; it is the population average across a typical sample. That average is almost never a whole number, which is the first hint that you are looking at a weighted mean rather than a physical atom. The formula is: average mass equals the sum of each isotope mass multiplied by its fractional (not percent) abundance.
Standard forward calculation
To compute the average atomic mass, convert each percent abundance to a decimal fraction by dividing by 100, multiply each fractional abundance by the corresponding isotope mass, and add the products together. For chlorine, that is 34.96885 times 0.7577 plus 36.96590 times 0.2423, giving 35.460 amu. If your abundances do not quite sum to 100% due to rounding, the normalise option rescales them proportionally so the result stays a true weighted mean. Using the more precise NIST masses rather than rounded textbook values will bring your answer within 0.001 amu of the accepted periodic-table figure.
Reverse solve: finding an unknown abundance
Sometimes a problem gives you the average atomic mass and all but one isotope abundance, then asks you to find the missing value. Rearranging the formula gives: f_unknown = (average mass - sum of known weighted terms) / m_unknown. For example, if you know chlorine averages 35.45 amu and 35Cl has 75.77% abundance, you can solve: f_37 = (35.45 - 34.96885 x 0.7577) / 36.96590 = 0.2423, confirming the 24.23% value. Switch the mode selector to "Find unknown abundance" to access this automatically. The calculator identifies which isotope has its abundance field left blank and solves for that one.
Multi-isotope elements and element presets
Many elements have more than two stable isotopes. Tin has ten, and magnesium has three. This calculator supports up to five isotopes via the "Number of isotopes" dropdown, covering the vast majority of homework and laboratory problems. The preset menu loads NIST-published masses and abundances for eight common elements (Cl, B, C, Cu, Br, Ga, Mg, Sn) so you can verify your data against accepted values or simply explore. Abundances are taken from the NIST Atomic Weights and Isotopic Compositions table, which publishes best-estimate values with stated uncertainties. When precision matters, use the full NIST masses rather than the rounded values in textbooks.
Why atomic mass is not exactly a whole number
A proton and a neutron each have a mass close to 1 amu, so you might expect an atom with 18 nucleons to have exactly 18 amu. Three effects push it away from an integer. First, nuclear binding energy is equivalent to a small mass deficit per nucleon (this is the energy released when the nucleus forms). Second, electron masses add a tiny contribution. Third, and most importantly for the periodic table value, the element is a mixture of isotopes, so the average sits between the individual isotope masses rather than at any one of them. Chlorine atoms come in two flavours, mass roughly 35 and 37, and the 75/25 mixture pulls the average to 35.45, not 36.
NIST isotope data for selected elements
| Element | Isotope | Mass (amu) | Abundance (%) |
|---|---|---|---|
| Chlorine | 35Cl | 34.96885268 | 75.77 |
| Chlorine | 37Cl | 36.96590259 | 24.23 |
| Boron | 10B | 10.01293700 | 19.9 |
| Boron | 11B | 11.00930540 | 80.1 |
| Carbon | 12C | 12.00000000 | 98.93 |
| Carbon | 13C | 13.00335484 | 1.07 |
| Copper | 63Cu | 62.92959750 | 69.15 |
| Copper | 65Cu | 64.92778950 | 30.85 |
| Bromine | 79Br | 78.91833710 | 50.69 |
| Bromine | 81Br | 80.91628970 | 49.31 |
| Magnesium | 24Mg | 23.98504170 | 78.99 |
| Magnesium | 25Mg | 24.98583700 | 10.00 |
| Magnesium | 26Mg | 25.98259300 | 11.01 |
Isotopic masses and natural percent abundances from NIST Atomic Weights and Isotopic Compositions (2023). Use these to verify your inputs.
Frequently asked questions
What is the difference between atomic mass and average atomic mass?
Atomic mass (or isotopic mass) refers to the mass of one specific isotope, measured in atomic mass units. It is nearly a whole number because each proton and neutron contributes roughly 1 amu, with a small adjustment for nuclear binding energy. Average atomic mass is the abundance-weighted mean of all naturally occurring isotopes of an element and is the value listed on the periodic table. Because most elements are mixtures of isotopes in nature, the average is rarely a whole number and usually does not equal the mass of any single isotope.
Do the isotope abundances have to add up to 100%?
In nature, the abundances of all stable isotopes of an element sum to exactly 100%. When you enter abundances that total a slightly different amount due to rounding or an omitted trace isotope, this calculator can normalise them by dividing each by the total, preserving the correct proportions. Turn on "Normalise abundances" for this behaviour. If you are entering fewer than all natural isotopes, the normalisation step is essential for a meaningful answer.
How do I find a missing isotope abundance if I know the average mass?
Switch the mode to "Find unknown abundance (reverse solve)". Enter the masses of all isotopes, the abundances of all but one, and the known average atomic mass. Leave the unknown abundance field blank. The calculator rearranges the weighted-average formula: f_unknown = (average - sum of known weighted terms) / m_unknown. It displays the solved abundance and the full step-by-step derivation.
Why is chlorine's average atomic mass 35.45 and not 36?
Chlorine has two main isotopes: 35Cl at about 75.77% and 37Cl at about 24.23%. The weighted average is 34.969 x 0.7577 + 36.966 x 0.2423, which equals approximately 35.45 amu. Because the lighter isotope is roughly three times more common, the average is pulled close to 35 rather than landing midway between 35 and 37. A simple arithmetic mean of 36 would only apply if both isotopes were equally abundant.
What is the most precise source for isotope masses and abundances?
The National Institute of Standards and Technology (NIST) publishes the Atomic Weights and Isotopic Compositions table, which gives best-estimate isotopic masses to eight or more decimal places along with stated uncertainties. The International Union of Pure and Applied Chemistry (IUPAC) Commission on Isotopic Abundances and Atomic Weights reviews and publishes recommended standard atomic weights, noting that some elements (such as carbon and lead) have natural-abundance ranges that depend on the sample source.
Can I enter abundances as decimal fractions instead of percentages?
Yes. Change "Abundance entered as" to "Decimal fraction". Instead of typing 75.77, type 0.7577. The calculator converts automatically. Decimal fractions are used in some analytical chemistry and mass spectrometry literature, so having both options avoids transcription errors when copying values from reference tables.