Different sample vials beside a balance, representing isotope mixtures conceptually. Original AI-generated editorial artwork produced for GreenCalc.
Suppose a sample contains two hypothetical isotopes with masses 10 u and 11 u. If every fifth atom belongs to the lighter isotope, the average is closer to 11 u. Averaging the two masses as (10 + 11)/2 would describe equal populations, which this sample does not have.
Build the weighted sum
Multiply each isotope mass by its amount fraction, then add the contributions. When abundance is given as a percentage, divide it by 100 first. In symbols, mean mass = Σ(mᵢ × pᵢ/100). The percentages must describe the whole sample.
For the example, the lighter isotope contributes 10 × 0.20 = 2 u, and the heavier isotope contributes 11 × 0.80 = 8.8 u. The total is 10.8 u. These deliberately simplified masses make the weighting visible; they are not a table of natural isotope measurements.
Enter your own data in the Average Atomic Mass Calculator. It accepts up to ten isotope rows and checks that their abundances total 100%.
Why the 100% check matters
A total of 90% leaves one tenth of the sample unaccounted for. A total of 110% counts too much. This tool rejects either case instead of silently changing your inputs. With rounded published abundances, obtain enough precision to make a consistent full composition or state an explicit normalisation method outside this tool.
Do not put 0.20 in a field labelled percent when you mean 20%. That entry describes two tenths of one percent. Keep the units attached to the numbers throughout the calculation.
Use isotope masses, not just isotope labels
Mass numbers such as 10 and 11 are integer nucleon counts. Real isotope masses are not generally exact integers. A homework question may deliberately supply rounded values; a laboratory calculation may require evaluated data with uncertainties. Match the input precision to the question.
The Atomic Mass Calculator gives a nucleon-count approximation. It does not replace an isotope-mass table. Read mass number versus atomic mass if those values appear interchangeable.
Sample average versus standard atomic weight
Your result belongs to the composition you entered. A standard atomic weight describes normal terrestrial materials under a different reporting convention. Natural variation, enrichment and depletion can make a sample-specific average differ from a periodic-table value.
Check the answer before rounding
A weighted average with non-negative fractions must lie between the smallest and largest included isotope masses. In our example, 10.8 u lies between 10 and 11 u. An answer outside that range points to a unit, percentage or transcription error. Keep guard digits during multiplication, then round the final result to suit the input data.
For particle counts behind the isotope labels, use the Atom Calculator. Find the related tools in the Chemistry category.
By GreenCalc · Updated 2026-10-21
Frequently asked questions
Must isotope abundances add to 100%?
Yes. This tool rejects incomplete or excessive totals rather than silently normalising them.
Can an average lie outside the isotope mass range?
Not when all masses are weighted by non-negative fractions summing to one.