This average atomic mass calculator computes the weighted average printed on the periodic table: Σ (isotope mass × fractional abundance) across an element’s naturally occurring isotopes. Enter up to four isotopes with their percent abundances and get the standard atomic weight.

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Why the Periodic Table Prints Fractions

No carbon atom weighs 12.011 u and no chlorine atom weighs 35.45 u — those table entries are population averages over each element's isotope mix, and this weighted sum is the entire computation: each isotope contributes its exact mass times its natural abundance fraction. Chlorine is the cleanest demonstration: just two isotopes, ³⁵Cl (34.96885 u, 75.77%) and ³⁷Cl (36.96590 u, 24.23%), summing to 0.7577(34.96885) + 0.2423(36.96590) = 35.45 u — pulled toward 35 because the light isotope dominates 3:1. Carbon plays it subtler: ¹²C at 98.93% with ¹³C (13.003355 u) at 1.07% gives 11.8736 + 0.1391 = 12.011 u, the small excess over 12 being almost entirely the ¹³C contribution. Boron is the drama case students meet next: ¹⁰B (19.9%) and ¹¹B (80.1%) yield 10.81 — visibly between the mass numbers because the mix is genuinely contested.

Two professional notes keep the number honest. First, "average atomic mass" (standard atomic weight, maintained by CIAAW) is defined for a specified natural source — a few elements (S, Cl, Tl…) show small real variations between sources, and since 2009 a dozen elements carry INTERVAL standard weights rather than single values; the conventional single numbers this calculator reproduces remain the working values for essentially all chemistry. Second, the weighted average is what molar mass means for elements: 35.45 g per mole of chlorine atoms, the bridge between this isotope arithmetic and every stoichiometry calculation downstream. The mass spectrometer, incidentally, measures the inputs directly — peak positions give the isotope masses, peak areas the abundances — so this page's computation runs the instrument's data backwards into the table entry.

Worked Examples (Verified)

  • Chlorine (defaults): 26.496 + 8.957 = 35.45 u.
  • Carbon: 0.9893(12.000000) + 0.0107(13.003355) = 12.011 u.
  • Boron: 0.199(10.0129) + 0.801(11.0093) = 1.993 + 8.818 = 10.81 u.

Atomic Mass Discipline

  • Use exact isotope masses (34.96885), not mass numbers (35) — the mass-number version is a rough estimate that misses by ~0.1 u on chlorine.
  • Abundances must total ~100%: the calculator prints your entered total so a forgotten isotope is visible rather than silent.
  • The result is a per-atom average AND the molar mass in g/mol — the same number serves both because Avogadro's number is defined to make it so.
  • Monoisotopic elements (F, Na, P, Al…): the "average" is the single isotope's mass — no weighting needed or possible.
  • For mass-spec problems, reverse the flow: given the average and two isotope masses, solve for abundances (the classic two-unknown algebra setup).

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Frequently Asked Questions

What is average atomic mass?

The abundance-weighted mean mass of an element's naturally occurring isotopes: Σ(isotope mass × fractional abundance). It's the value printed on the periodic table (chlorine 35.45, carbon 12.011) and doubles as the molar mass in grams per mole. No individual atom need have this mass — it describes the population. Enter isotope masses and percent abundances above to compute it.

How is chlorine's atomic mass 35.45 if isotopes are 35 and 37?

Because the isotopes aren't 50/50 and their masses aren't exactly 35/37. Natural chlorine is 75.77% ³⁵Cl (exact mass 34.96885 u) and 24.23% ³⁷Cl (36.96590 u): 0.7577 × 34.96885 + 0.2423 × 36.96590 = 35.45. The 3:1 dominance of the light isotope pulls the average much closer to 35 than to 37. This exact two-isotope case is preloaded as the calculator's defaults.

Average atomic mass vs mass number vs atomic mass — differences?

Mass number is a COUNT (protons + neutrons: 35 for ³⁵Cl, an integer per atom). Atomic mass (isotopic mass) is one isotope's measured mass (34.96885 u — slightly less than 35 because of nuclear binding energy, the mass defect). Average atomic mass is the abundance-weighted population mean (35.45 u for chlorine) used for molar masses. Confusing the three is the standard first-month chemistry error; this page computes the third from the second.

Why aren't standard atomic weights whole numbers?

Two compounding reasons: isotope masses themselves aren't whole (binding energy converts a little mass via E = mc² — only ¹²C is exactly 12, by definition), and most elements mix several isotopes in lopsided proportions. A few elements are effectively monoisotopic (fluorine 18.998, sodium 22.990) and print near-whole values; the rest carry their mixture fractions openly. Hydrogen (1.008) is the extreme: mostly ¹H with a whisper of ²H.

Do abundances vary by source?

Slightly, for some elements: isotope ratios fractionate in nature and industry, so CIAAW now publishes interval atomic weights for a dozen elements (H, Li, B, C, N, O, Si, S, Cl, Tl and others) — sulfur spans [32.059, 32.076], for instance. For laboratory and classroom purposes the conventional single values (this calculator's outputs) are used universally; isotope geochemistry is the field that exploits the variations themselves as tracers.

How does a mass spectrometer measure this?

It ionizes the sample, separates ions by mass-to-charge ratio, and records peaks: positions give each isotope's mass, relative peak intensities give the abundances. Feed those two columns into the weighted sum (this calculator) and you reproduce the standard atomic weight — which is precisely how the table's values were established and how unknown samples get identified in analytical labs.

What if abundances don't add to 100%?

Then the weighted sum is a partial sum, not the element's atomic weight — usually a missing minor isotope (harmless if it's a 0.01% species, significant if it's boron's second isotope). The calculator displays the entered total beside the result so the check is one glance. For exact work use a complete isotope table (NIST lists all stable isotopes and abundances per element).

Is this average atomic mass calculator free?

Yes — free, instant, no sign-up. Enter up to four isotopes' masses and percent abundances for the weighted average atomic mass in u.