An average atomic mass calculator finds the weighted average mass of an element from its isotopes. Most elements occur as a mixture of isotopes, atoms with the same number of protons but different numbers of neutrons. The mass printed on the periodic table is not the mass of a single atom, but the average over that natural mixture, weighted by how common each isotope is.
Weighting matters because a rare heavy isotope should not count as much as a common light one. A simple average of isotope masses would give each isotope equal weight, regardless of abundance, and would usually be wrong. A weighted average multiplies each isotope mass by its fractional abundance, so common isotopes dominate the result, as they should.
What this calculator does
For isotopes with masses m1, m2, and so on, and percent abundances a1, a2, and so on, average atomic mass = (m1 x a1 + m2 x a2 + …) / 100, when abundances are given as percentages that sum to 100. If abundances are given as decimals that sum to 1, the division by 100 is omitted and the formula is m1 x f1 + m2 x f2 + … . The calculator below uses the percentage form with two isotopes, the most common textbook case, and it assumes the two percentages sum to 100.
Carbon is the classic example. Carbon-12 has a mass of 12.00 and an abundance of about 98.93 percent, while carbon-13 has a mass of about 13.003 and an abundance of about 1.07 percent. The weighted calculation gives an average near 12.01, which is the value shown on the periodic table. A simple average of 12 and 13 would give 12.50, which is far from the true average because carbon-13 is rare.
Formula
Average atomic mass = (mass1 x abundance1 + mass2 x abundance2) / 100, for abundances in percent summing to 100.
How to use it
- List each isotope with its mass and its percent abundance.
- Check that the abundances sum to about 100. If they do not, a third isotope may be missing or a percentage was copied wrong.
- Multiply each mass by its abundance.
- Add the products and divide by 100.
- Compare the result with the periodic table value. It should be close, within rounding and abundance precision.
Try the calculator
Worked example
Calculate the average atomic mass of carbon from carbon-12 at mass 12.00 with 98.93 percent abundance, and carbon-13 at mass 13.003 with 1.07 percent abundance. First product: 12.00 x 98.93 = 1,187.16. Second product: 13.003 x 1.07 = 13.91. Sum = 1,201.07. Divide by 100 = 12.01. The result, 12.01 atomic mass units, matches the periodic table value for carbon to two decimal places. The calculation shows why the average is much closer to 12 than to 13: the heavier isotope is only about 1 percent of natural carbon.
If the abundances were reversed, with carbon-13 at 98.93 percent, the average would be near 13, which confirms that abundance, not just mass, controls the weighted result.
How to check your answer
Check that abundances sum to 100 before dividing. If they sum to 99 or 101 due to rounding, the result will be slightly off, and the gap should be noted.
Compare with the periodic table. A large difference usually means an abundance was entered as a decimal instead of a percentage, or the reverse.
Use isotope masses, not mass numbers alone, when precision matters. Carbon-13 mass is 13.003, not exactly 13, although the difference is small.
Common mistakes
- Taking a simple average of isotope masses without weighting by abundance.
- Entering abundances as decimals, such as 0.9893, into a formula that expects percentages, which divides the result by 100 a second time.
- Using mass numbers instead of precise isotope masses when the problem gives precise masses.
- Omitting a minor isotope and then wondering why the average does not match the periodic table.
Frequently asked questions
Why is average atomic mass not a whole number?
Because it is a weighted average over isotopes with different masses. Most elements are mixtures, so the average falls between isotope masses and is rarely a whole number.
What is the difference between mass number and isotope mass?
Mass number is the whole-number count of protons plus neutrons. Isotope mass is the measured mass, which is close to but not exactly the mass number.
Can average atomic mass change?
Only if the isotopic composition of the sample changes. Natural abundances are fairly stable, so the periodic table value is stable for most purposes, but a specially prepared sample could differ.
