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Average Atomic Mass Calculator

Chemistry

Calculate the average atomic mass of an element from its isotope masses and natural abundances. Enter up to 3 isotopes with mass and percent abundance.

34.969 amu
amu
75.77
36.966 amu
amu
24.23
0 amu
amu
0

Average Atomic Mass

35.453
Total Abundance Check
100
Isotope 1 Contribution
26.496
Isotope 2 Contribution
8.957

This calculator computes your Average Atomic Mass, Total Abundance Check, Isotope 1 Contribution, Isotope 2 Contribution from the values you enter.

Inputs
Isotope 1 MassIsotope 1 AbundanceIsotope 2 MassIsotope 2 AbundanceIsotope 3 Mass (optional)Isotope 3 Abundance (optional)
Outputs
Average Atomic MassTotal Abundance CheckIsotope 1 ContributionIsotope 2 Contribution

What is a Average Atomic Mass?

The Average Atomic Mass Calculator computes the weighted average atomic mass of an element from its isotope masses and natural abundances: Ā = Σ(mᵢ × xᵢ) where xᵢ = abundance/100. Enter up to three isotopes with their masses (in amu) and abundance percentages to get the average atomic mass.

Average atomic mass is the value shown on periodic tables — not the mass of any single isotope, but the weighted mean over the element's natural mixture of isotopes. Chlorine's 35.453 amu reflects its 3:1 mixture of ³⁵Cl and ³⁷Cl; bromine's 79.904 amu reflects its near-equal mixture of ⁷⁹Br and ⁸¹Br. The Atomic Mass Calculator provides these pre-computed tabulated values; this calculator shows how they are derived from isotope data.

Understanding average atomic mass connects atomic physics (isotopes and nuclear structure) to macroscopic chemistry (periodic table values and stoichiometry). The same calculation applies to calculating blend averages in mixtures and weighted averages in statistics — but in chemistry it has the specific meaning of the periodic table's atomic weight.

How to use this Average Atomic Mass calculator

  1. Enter Isotope 1 Mass (amu) — the mass of the first isotope (close to but not equal to its mass number). For ³⁵Cl: 34.969 amu.
  2. Enter Isotope 1 Abundance (%) — the natural abundance percentage. For ³⁵Cl: 75.77%.
  3. Repeat for Isotope 2. The calculator works with just 2 isotopes for elements like H, C, N, Cl, Br.
  4. For three-isotope elements (O, Mg, Si, S, Ca), enter Isotope 3 data.
  5. Check Total Abundance — must equal 100% for the average to be valid.
  6. Read Average Atomic Mass and compare to the periodic table value.

Formula & Methodology

Weighted average atomic mass:

Ā = m₁ × (x₁/100) + m₂ × (x₂/100) + m₃ × (x₃/100) where Σxᵢ = 100%

Inverse (two-isotope system):

x₁ = (Ā − m₂) / (m₁ − m₂) × 100% x₂ = 100% − x₁

Worked example — Boron (two isotopes):

¹⁰B: mass = 10.013 amu, abundance = 19.9%
¹¹B: mass = 11.009 amu, abundance = 80.1%

Ā = 10.013 × 0.199 + 11.009 × 0.801   = 1.9926 + 8.8182   = 10.811 amu

This matches the IUPAC standard atomic mass of boron (10.811 g/mol). The predominantly ¹¹B abundance means boron's average mass is closer to 11 than 10. Boron-10 has a very high thermal neutron capture cross-section and is used in boron neutron capture therapy (BNCT) for brain tumours — an active research area at Bhabha Atomic Research Centre (BARC) and the Tata Memorial Centre.

Frequently Asked Questions

Average atomic mass (standard atomic mass) is the weighted mean of the masses of all naturally occurring isotopes of an element, weighted by their natural abundance. It is not a whole number because most elements exist as a mixture of isotopes with different masses (close to but not exactly equal to their mass numbers). Chlorine: 75.77% ³⁵Cl + 24.23% ³⁷Cl gives average = 35.453, not 35 or 37. Carbon: 98.89% ¹²C + 1.11% ¹³C gives average = 12.011, not exactly 12.
Average atomic mass = Σ(mᵢ × xᵢ) where mᵢ is the mass of isotope i (in amu) and xᵢ is its fractional natural abundance (abundance%/100). The sum runs over all naturally occurring isotopes. For two isotopes: Ā = m₁×x₁ + m₂×x₂ = m₁×x₁ + m₂×(1−x₁) if there are only two isotopes and x₁+x₂=1. For three: Ā = m₁x₁ + m₂x₂ + m₃x₃ where x₁+x₂+x₃=1.
Enter the mass (in amu) and abundance (%) for up to 3 isotopes. The calculator computes the weighted average Σ(mᵢ×xᵢ/100) and shows the total abundance percentage (should sum to 100%) as a verification check. The default values are for chlorine: ³⁵Cl (34.969 amu, 75.77%) and ³⁷Cl (36.966 amu, 24.23%) giving 35.453 amu.
Yes — with two isotopes and known masses m₁ and m₂, you can find x₁ (the fractional abundance of isotope 1) from the average mass: x₁ = (Ā − m₂)/(m₁ − m₂). For chlorine: x₁(³⁵Cl) = (35.453 − 36.966)/(34.969 − 36.966) = (−1.513)/(−1.997) = 0.7576 ≈ 75.77%. This inverse calculation is a common JEE and NEET problem type — given two isotope masses and the periodic table atomic mass, find the abundance.
Hydrogen: ¹H 99.985%, ²H (deuterium) 0.015%. Carbon: ¹²C 98.89%, ¹³C 1.11%. Nitrogen: ¹⁴N 99.63%, ¹⁵N 0.37%. Oxygen: ¹⁶O 99.757%, ¹⁷O 0.038%, ¹⁸O 0.205%. Chlorine: ³⁵Cl 75.77%, ³⁷Cl 24.23%. Bromine: ⁷⁹Br 50.69%, ⁸¹Br 49.31%. Boron: ¹⁰B 19.9%, ¹¹B 80.1%. Copper: ⁶³Cu 69.15%, ⁶⁵Cu 30.85%. These are the most common in Indian competitive chemistry problems.
Bromine has two stable isotopes — ⁷⁹Br (50.69%) and ⁸¹Br (49.31%) — in nearly equal proportions, giving Br's average mass of 79.904 amu. This near-equal ratio has an important analytical consequence: organic compounds containing one bromine atom show two peaks of nearly equal intensity in mass spectrometry separated by 2 m/z units (the M and M+2 peaks). This characteristic isotope pattern is a diagnostic test for bromine presence in mass spec — a useful JEE and MBBS pharmacology concept.
For three isotopes, Ā = m₁x₁ + m₂x₂ + m₃x₃ where Σxᵢ = 1. Example — oxygen: ¹⁶O (15.9949 u, 99.757%), ¹⁷O (16.9991 u, 0.038%), ¹⁸O (17.9992 u, 0.205%). Ā = 15.9949×0.99757 + 16.9991×0.00038 + 17.9992×0.00205 = 15.9561 + 0.006460 + 0.03690 = 15.999 u. This matches the tabulated atomic mass of oxygen. This calculator handles up to 3 isotopes; enter 0 abundance for unused third isotope.
Numerically, yes — the standard atomic mass in amu equals the molar mass in g/mol. This is by definition: 1 g/mol ≡ 1 u × N_A, where N_A = Avogadro's number. So Cl atomic mass = 35.453 u means Cl molar mass = 35.453 g/mol. However, conceptually they describe different scales: atomic mass refers to a single atom (in amu), while molar mass refers to one mole of atoms (in g/mol). The [Atomic Mass Calculator](/atomic-mass-calculator/) provides tabulated IUPAC values; this calculator computes them from isotope data.
Natural isotope abundances are measured by mass spectrometry. A sample of the element is ionised and accelerated through a magnetic field; ions of different mass-to-charge ratios are deflected by different amounts and detected separately. The relative peak heights in the mass spectrum directly give the relative abundances. Isotope ratio mass spectrometry (IRMS) can measure variations in natural abundance to parts per thousand — used in food authenticity testing, archaeology, climate science, and geochemistry.
Almost, but not exactly. IUPAC publishes standard atomic weights as ranges (e.g., O = [15.99903, 15.99977]) reflecting natural variation in isotope ratios from different geological sources. Fractionation — slight preferential enrichment of lighter or heavier isotopes in different chemical processes — causes measurable variation. Antarctic ice cores have slightly different ¹⁸O/¹⁶O ratios than equatorial water, recording palaeoclimate information. ¹³C/¹²C ratios differ between C3 and C4 plants (like sugarcane vs wheat), allowing detection of sugar adulteration — used by FSSAI (India's food safety body) in honey adulteration testing.