Average atomic mass calculator: weighted mean of isotope masses
This average atomic mass calculator multiplies each isotope mass by its fractional abundance and adds the results, as in OpenStax Chemistry 2e. Example: boron is 19.9 % ¹⁰B (10.0129 u) and 80.1 % ¹¹B (11.0093 u), so its average atomic mass is 10.811 u.
How it is calculated
Average atomic mass = Σ (isotope mass × fractional abundance). The atomic mass in the periodic table is a weighted average of all isotopes in a natural sample. Each isotope mass is multiplied by its abundance as a fraction (19.9 % = 0.199), and the products are added.
Examples from OpenStax
| Element | Isotopes (mass, abundance) | Average atomic mass |
|---|---|---|
| boron | ¹⁰B 10.0129 u, 19.9 %; ¹¹B 11.0093 u, 80.1 % | 10.811 u |
| neon (solar wind) | ²⁰Ne 19.9924 u, 91.84 %; ²¹Ne 20.9940 u, 0.47 %; ²²Ne 21.9914 u, 7.69 % | 20.15 u |
| magnesium | ²⁴Mg 23.98 u, 78.70 %; ²⁵Mg 24.99 u, 10.13 %; ²⁶Mg 25.98 u, 11.17 % | 24.31 u |
OpenStax rounds boron to 10.8 u and notes that no single boron atom weighs 10.8 u – each weighs about 10 u or 11 u. Terrestrial neon averages 20.1796 u, slightly more than the solar-wind sample, because abundances depend on origin.
Abundances from the average mass
With two isotopes, call the fraction of the first x; the second is then 1 − x. Chlorine: 34.96885 x + 36.96590 (1 − x) = 35.453 gives x = 0.7576, so 75.76 % ³⁵Cl and 24.24 % ³⁷Cl. Copper with 62.9296 u, 64.9278 u and an average of 63.546 u gives 69.15 % ⁶³Cu and 30.85 % ⁶⁵Cu. Average atomic masses of all elements are listed in the periodic table; for whole compounds use the molar mass calculator.
Frequently asked questions
How do you calculate average atomic mass?
Multiply each isotope mass by its abundance as a decimal and add: 10.0129 × 0.199 + 11.0093 × 0.801 = 10.811 u for boron.
Why is the average atomic mass not a whole number?
Most elements are mixtures of isotopes. The average lies between the isotope masses, closer to the more common one.
How do I find the percent abundance of two isotopes?
Solve m₁x + m₂(1 − x) = average for x. For chlorine 35.453 u gives 75.76 % ³⁵Cl and 24.24 % ³⁷Cl.
What if my abundances do not add up to 100 %?
The calculator still computes the weighted sum but shows a warning. Rounded data, like 78.70 + 10.13 + 11.17 = 100 % for magnesium, should add up exactly.
What is the unit u?
The unified atomic mass unit, 1/12 of the mass of a carbon-12 atom (1.6605 × 10⁻²⁴ g). Older texts call it amu; the dalton (Da) is the same unit.
How exact is the result?
It is calculated exactly from your inputs. Real abundances vary slightly between samples, as the neon example shows (20.15 u against 20.1796 u).
Sources and legal basis
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