Average atomic mass formula
The average atomic mass is the weighted mean of all isotopes: Σ(isotope mass × fractional abundance). Abundances are entered as decimals between 0 and 1 and should add up to 1. This value is the molar mass you feed into the moles calculator.
Notice there is no division step: the abundances already sum to 1, so the weighting is built in. That is why a periodic-table value sits closer to whichever isotope is more common.
How to use this calculator
Enter each isotope's mass in amu and its fractional abundance (e.g. 19.9% = 0.199). The calculator multiplies and adds them, and warns if your abundances don't total 1. For reaction yield work, pair this with the percent yield calculator.
The most common mistake is entering abundances as percentages — typing 19.9 instead of 0.199 — which inflates the answer roughly a hundredfold. A second trap is using the mass number instead of the measured isotopic mass in amu.
Worked example
Boron has two isotopes: 10.012 amu at 19.9% and 11.009 amu at 80.1%. Average = (10.012 × 0.199) + (11.009 × 0.801) = 10.81 amu, matching the periodic table value.
Interpret the result as a sanity check on your inputs. Because 80.1% of boron atoms are the heavier isotope, the answer must land much nearer 11.009 than 10.012 — and 10.81 does exactly that. Whenever the weighted average falls outside the range spanned by the individual isotope masses, an abundance has been entered wrongly. The same weighted-average logic runs through the percent composition calculator, only with elements in place of isotopes.
Frequently asked questions
- What is average atomic mass?
- It is the weighted average mass of an element's naturally occurring isotopes, weighted by their abundances.
- How do I enter abundance?
- As a decimal fraction between 0 and 1. For example, 80.1% is entered as 0.801.
- Why should abundances sum to 1?
- Together the isotopes make up the whole element, so their fractional abundances must total 1 (100%).
- Is this the same as molar mass?
- For a single element, yes — the average atomic mass in amu equals the molar mass in g/mol.
- What if my element has three or more isotopes?
- Extend the same sum: add one mass × abundance term for every isotope before dividing nothing at all, since the abundances already carry the weighting. This tool handles two isotopes, which covers most textbook problems; for tin or xenon you would add the extra terms by hand and check the abundances still total 1.