Average atomic mass calculator
List the isotopes, get the weighted average; or go from the average back to the abundances.
How do you calculate average atomic mass?
Multiply the mass of each isotope by its fractional abundance and add the results: average mass = Σ (isotope mass × abundance ÷ 100). OpenStax Chemistry 2e, Example 2.4 (neon): 91.84% of ²⁰Ne at 19.9924 u, 0.47% of ²¹Ne at 20.9940 u and 7.69% of ²²Ne at 21.9914 u give 18.361 + 0.0987 + 1.691 = 20.15 u. That is the pre-filled example. The u is the atomic mass unit, one-twelfth of the mass of a carbon-12 atom (also written amu).
How do I find percent abundance from the average atomic mass?
For an element with two isotopes of masses m₁ and m₂ and an average mass M, the fraction of the first is x = (M − m₂) ÷ (m₁ − m₂), and the second is 1 − x. OpenStax Example 2.5: chlorine-35 (34.96885 u) and chlorine-37 (36.96590 u) with M = 35.453 u give 75.76% and 24.24%. Their copper problem (62.9296 u and 64.9278 u, M = 63.546 u) gives 69.15% copper-63 and 30.85% copper-65. The average has to lie between the two isotope masses.
What if the abundances don’t add up to 100?
Abundances rounded to two decimals can add up to 99.99 or 100.01, so the calculator divides by their total when it is within 0.5 of 100. A bigger gap means an isotope is missing or a value is mistyped: the message shows how much is left to add. If you typed fractions like 0.7576, multiply them by 100 — the calculator wants percent.
Why is my answer slightly different from the periodic table?
For some elements the isotope mix varies by source, so IUPAC publishes an interval rather than one number: chlorine 35.446–35.457, boron 10.806–10.821, lithium 6.938–6.997 (CIAAW, 2024). OpenStax Chemistry 2e, Exercise 25, uses exactly this: boron from Turkey (10.807 u) is 20.3% boron-10 and from the US (10.819 u) is 19.1%. Periodic tables show one abridged value, 35.45 for chlorine, 10.81 for boron, 6.94 for lithium, and the comparison box lets you check your result against it.
What is the difference between mass number, isotopic mass and atomic mass?
The mass number is a whole count of protons plus neutrons (35 or 37 for chlorine). An isotopic mass is the measured mass of one isotope in u, close to that whole number but not equal to it, such as 34.96885 u. The average atomic mass is the abundance-weighted mean over the isotopes found in nature, which is why chlorine’s is 35.45 rather than a whole number (OpenStax Chemistry 2e, Section 2.3).
Worked example: magnesium with three isotopes
NIST lists magnesium-24 at 23.985042 u (78.99%), magnesium-25 at 24.985837 u (10.00%) and magnesium-26 at 25.982593 u (11.01%). Each contribution is mass × abundance ÷ 100: 18.9458, 2.4986 and 2.8607 u. They add up to 24.305 u, which sits inside the IUPAC interval for magnesium (24.304 to 24.307). The simple average of the three masses, 24.984 u, is a wrong answer because it ignores that most atoms are magnesium-24. The weighted result always lies between the lightest and the heaviest isotope and is pulled toward the most abundant one.
Worked example: boron's two isotopes, both ways
Forward: boron-10 is 10.01294 u at 19.9% and boron-11 is 11.00931 u at 80.1%, so the weighted mean is 10.811 u. Backward: from the periodic-table value 10.81 u, x = (10.81 − 11.00931) ÷ (10.01294 − 11.00931) gives 20.0% boron-10 and 80.0% boron-11. Because the isotope mix varies from sample to sample, these two answers differ in the last digit, which is the reason IUPAC gives boron as an interval.
Common mistakes with average atomic mass
Using mass numbers (10 and 11) instead of isotopic masses (10.01294 and 11.00931 u), which makes the result slightly off. Entering abundances as fractions when the field wants percent. Averaging the isotope masses without weights. Reporting too many digits: the answer cannot be more precise than the abundances, so two or three decimals are enough. Using this calculator for a molecule: the molar mass of a compound is the sum of the atomic masses of its atoms, which is a separate calculation.
Sources and related calculators
Sources: OpenStax Chemistry 2e, Section 2.3 “Atomic Structure and Symbolism” (Examples 2.4 and 2.5 and the chapter 2 exercises); isotope masses and compositions from the NIST physical measurement laboratory table “Atomic Weights and Isotopic Compositions”; standard atomic weight intervals from IUPAC (CIAAW). Related: molar mass calculator, electron configuration calculator, molarity calculator and dilution calculator.