What this calculator does
The atomic mass on the periodic table is a weighted average across naturally occurring isotopes. Carbon is 98.93% carbon-12 and 1.07% carbon-13, giving 12.011 amu.
This is why periodic table masses are rarely near whole numbers. Chlorine sits at 35.453 because it is roughly three quarters chlorine-35 and one quarter chlorine-37, and no individual chlorine atom has that mass. The tabulated value describes a population, not a particle.
The formula
Each isotope mass is multiplied by its fractional abundance and the products are summed. Abundances are entered as percentages and divided by 100 internally, so they should total 100. The calculator reports the sum so you can check, and flags it if it is meaningfully off.
| Term | Meaning |
|---|---|
| Atomic mass unit (amu) | One twelfth the mass of a carbon-12 atom, by definition. |
| Isotope | Atoms of the same element with different neutron counts and therefore different masses. |
| Natural abundance | The percentage of an element found as a given isotope in nature. |
| Mass number | The whole-number count of protons plus neutrons, which is close to but not equal to the isotope mass. |
The inputs explained
| Field | What to enter |
|---|---|
| Mass of each isotope, amu (comma-separated) | Isotope masses in amu, comma separated. These are close to but not exactly the mass numbers. |
| Natural abundance of each isotope, % (comma-separated) | Natural abundance of each isotope as a percentage, in the same order. These should sum to 100. |
When to use it
Checking a periodic table value
The tabulated mass should reproduce from the isotope data, which is a useful verification.
Working with enriched material
Isotopically enriched samples have a different average mass from the natural one, which affects every mole calculation.
Interpreting mass spectra
Isotope patterns in a spectrum reflect these abundances directly.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
What do the isotope data give for each element?
Three elements with their natural isotope distributions.
| Isotope masses (amu) | Average atomic mass | Isotopes entered | Sum of abundances |
|---|---|---|---|
| 12, 13.003 | 12.011 amu | 2 | 100.0% |
| 10.013, 11.009 | 10.024 amu | 2 | 100.0% |
| 34.969, 36.966 | 34.990 amu | 2 | 100.0% |
Questions
Why is chlorine 35.45 rather than 35 or 37?
Because it is a mixture. About 75.76% is chlorine-35 and 24.24% is chlorine-37, and the weighted average falls between them at 35.453. No single chlorine atom weighs 35.45; the figure describes the natural mixture.
Why are isotope masses not whole numbers?
Because of nuclear binding energy. Mass is lost when nucleons bind together, by an amount corresponding to the binding energy. Carbon-12 is exactly 12 only because the amu is defined from it; every other isotope departs slightly from its mass number.
Do abundances need to total 100?
They should, and the calculator reports the sum so you can check. If they do not, either an isotope has been omitted or a figure is wrong, and the resulting average will be proportionally off. Minor isotopes below 0.1% are sometimes left out of tables.
Does the average atomic mass ever change?
Slightly, depending on source. Elements whose isotopes fractionate in nature, such as carbon, oxygen and sulfur, vary measurably between samples. This is the basis of isotope ratio analysis, and it is why some elements now have their atomic masses published as intervals.
For converting mass to moles, see the grams to moles calculator. For particle counts, see the Avogadro’s number calculator.