Average Atomic Mass Calculator
Inputs
| Isotope 1 mass | 34.969 g/mol |
|---|---|
| Isotope 1 abundance | 75.8 % |
| Isotope 2 mass | 36.966 g/mol |
| Isotope 2 abundance | 24.2 % |
Average Atomic Mass Calculator
Compute the average atomic mass of an element from the masses and natural abundances of its two isotopes. The atomic mass shown on the periodic table is the abundance-weighted mean of each isotope mass: m̄ = m₁·(a₁/100) + m₂·(a₂/100).
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What average atomic mass means
The atomic mass printed under each element on the periodic table is almost never a whole number. That is because most elements occur as a mixture of isotopes — atoms with the same number of protons but different numbers of neutrons. The tabulated value is the abundance-weighted mean of the masses of those isotopes:
mˉ=m1⋅100a1+m2⋅100a2| Symbol | Quantity | Unit |
|---|---|---|
| m̄ | Average atomic mass | u (g/mol) |
| m₁, m₂ | Isotope masses | u (g/mol) |
| a₁, a₂ | Natural abundances | % |
Each isotope mass is given in unified atomic mass units (u), and because one mole of any isotope weighs its atomic mass in grams, the value in u is numerically equal to the molar mass in g/mol. The abundances are entered as percentages and should add up to 100%.
Worked example
Chlorine occurs as two stable isotopes. Chlorine-35 has a mass of 34.96885 u and makes up 75.77% of chlorine atoms; chlorine-37 has a mass of 36.96590 u and makes up the remaining 24.23%. The average atomic mass is:
mˉ=34.96885×0.7577+36.96590×0.2423=35.4527 uRounded to two decimals this is 35.45 u — exactly the value the periodic table lists for chlorine.
Why it is a weighted mean
A weighted mean is not the same as a plain average of the two masses. The simple midpoint of 34.96885 and 36.96590 would be about 35.97 u, but chlorine-35 is roughly three times more common than chlorine-37, so the average is dragged down toward 35. The more abundant an isotope is, the more it pulls the result toward its own mass. The answer always lands somewhere between the lightest and heaviest isotope.
How abundances are measured
Natural abundances come from mass spectrometry, which separates ions by their mass-to-charge ratio and records how many atoms fall into each isotope peak. The relative peak heights give the abundances, and the peak positions give the isotope masses. These abundances stay nearly constant across ordinary terrestrial samples, which is why a single periodic-table value serves for everyday chemistry calculations.
| Element | Main isotopes (abundance) | Average atomic mass |
|---|---|---|
| Chlorine | ³⁵Cl (75.77%), ³⁷Cl (24.23%) | 35.45 u |
| Copper | ⁶³Cu (69.17%), ⁶⁵Cu (30.83%) | 63.55 u |
| Boron | ¹⁰B (19.9%), ¹¹B (80.1%) | 10.81 u |
Using the result
The average atomic mass is what you reach for when converting between grams and moles or when adding up a molar mass from a chemical formula. Because it already blends the isotopes in their natural proportions, you can treat an element as if every atom had that single mass — no need to track individual isotopes for routine stoichiometry. If you need the value for a different element, replace the two isotope masses and abundances with the published figures for that element.
Frequently Asked Questions (FAQ)
How do you calculate average atomic mass?
Multiply each isotope’s mass by its fractional abundance and add the products together. With abundances written as percentages the formula is m̄ = m₁·(a₁/100) + m₂·(a₂/100). For example, chlorine is 75.77% chlorine-35 (34.96885 u) and 24.23% chlorine-37 (36.96590 u), giving m̄ = 34.96885 × 0.7577 + 36.96590 × 0.2423 = 35.45 u. The result is a weighted mean, so it always lies between the two isotope masses and sits closer to the more abundant one.
What is the difference between atomic mass and mass number?
The mass number is an integer — the total count of protons and neutrons in a single nucleus (35 for chlorine-35). The atomic mass is the measured mass of that isotope in unified atomic mass units (34.96885 u for chlorine-35), which is close to but not exactly the mass number because of the binding energy holding the nucleus together. The average atomic mass on the periodic table averages those measured masses over an element’s naturally occurring isotopes, so it is rarely a whole number.
Why is chlorine’s atomic mass 35.45 and not a whole number?
Chlorine is a mixture of two stable isotopes: chlorine-35 makes up about 75.77% of atoms and chlorine-37 about 24.23%. Because chlorine-35 is roughly three times more common, the weighted average is pulled toward 35 but not all the way there, landing at 35.45 u. The periodic-table value is never the mass of any single atom — it is the average a typical sample of the element would show, reflecting the natural blend of isotopes.
What does isotope abundance mean?
Natural abundance is the fraction of an element’s atoms that are a given isotope, as found in nature. It is usually quoted as a percentage and the abundances of all an element’s isotopes add up to 100%. Abundances are remarkably constant across most terrestrial samples, which is why a single periodic-table mass works for everyday chemistry. In this calculator the two abundances you enter should sum to 100%; a warning appears if they do not.
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