# Average Atomic Mass Calculator URL: https://speedycalculator.com/calculators/chemistry/average-atomic-mass/ Last updated: 2026-10-30 > The average atomic mass calculator weights each isotope’s mass by its natural abundance to give the mean atomic mass of an element, for two to twelve isotopes. It can also run backwards and find the abundances of two isotopes from a known average. ## Inputs - Calculate - Isotope data - Isotopes – one per line: label (optional), mass in u, abundance — Example line: "Cl-35 34.968853 75.76". Separate numbers with spaces, commas or tabs. - Abundances are given as - Mass of isotope 1 (u) - Mass of isotope 2 (u) - Average atomic mass (u) ## Results - Average atomic mass - Molar mass - Abundance of isotope 1 - Abundance of isotope 2 - Sum of the abundances entered - Contribution of each isotope - Isotope abundances - How it was calculated ## Formula ``` Average atomic mass = Σ fᵢ·mᵢ = f₁m₁ + f₂m₂ + … + fₙmₙ (fᵢ = abundance as a fraction) Two isotopes from the average: f₂ = (M̄ − m₁)/(m₂ − m₁), f₁ = 1 − f₂ ``` ## Explanation Most elements are a mixture of isotopes. Natural chlorine, for example, is about three quarters chlorine-35 and one quarter chlorine-37. A sample of the element therefore behaves as if every atom had the same, average mass – the number printed on the periodic table and used for molar masses. That average is a weighted mean: each isotope’s mass counts in proportion to how common it is. Multiply each isotopic mass by its abundance written as a fraction (75.76% → 0.7576), add up the products, and you have the average atomic mass in daltons, numerically equal to the molar mass in g/mol. Because rare isotopes contribute little, the average sits close to the most abundant isotope – 35.45 for chlorine, much nearer 35 than 37. Type one isotope per line (an optional label, the mass and the abundance), or load one of the built-in elements with NIST isotope data. If the abundances do not add up to 100%, they are scaled automatically. The second mode solves the classic textbook problem in reverse: given two isotope masses and the average, how abundant is each? ### How to use the Average Atomic Mass Calculator - **Calculate** - **Isotope data** - **Isotopes – one per line: label (optional), mass in u, abundance** — Example line: "Cl-35 34.968853 75.76". Separate numbers with spaces, commas or tabs. - **Abundances are given as** - **Mass of isotope 1 (u)** - **Mass of isotope 2 (u)** - **Average atomic mass (u)** Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server. ### How it works Each line is read as label (optional), mass in u and abundance in % (or as a fraction). The abundances are divided by their total so they sum to 1, each mass is multiplied by its fraction, and the products are added. In the reverse mode the two-isotope equation M̄ = f₁m₁ + (1 − f₁)m₂ is solved for the fractions. ### Worked example Gallium has two stable isotopes: ⁶⁹Ga, 68.925574 u with 60.108% abundance, and ⁷¹Ga, 70.924703 u with 39.892%. Converting the percentages to fractions and multiplying: 68.925574 × 0.60108 = 41.4298 u and 70.924703 × 0.39892 = 28.2933 u. Their sum, **69.7231 u**, matches the standard atomic weight of gallium, 69.723. Reverse problem: copper’s average atomic mass is 63.546 u and its isotopes weigh 62.929597 u and 64.927789 u. The abundance of ⁶⁵Cu is (63.546 − 62.929597)/(64.927789 − 62.929597) = 0.616403/1.998192 = 0.3085, so copper is 30.85% ⁶⁵Cu and 69.15% ⁶³Cu. ### Built-in isotope data (NIST) ElementIsotopes (mass in u, abundance)AverageLithium⁶Li 6.015123 (7.59%), ⁷Li 7.016003 (92.41%)6.940Boron¹⁰B 10.012937 (19.9%), ¹¹B 11.009305 (80.1%)10.811Neon²⁰Ne 19.992440 (90.48%), ²¹Ne 20.993847 (0.27%), ²²Ne 21.991385 (9.25%)20.180Magnesium²⁴Mg 23.985042 (78.99%), ²⁵Mg 24.985837 (10.00%), ²⁶Mg 25.982593 (11.01%)24.305Silicon²⁸Si 27.976927 (92.223%), ²⁹Si 28.976495 (4.685%), ³⁰Si 29.973770 (3.092%)28.085Chlorine³⁵Cl 34.968853 (75.76%), ³⁷Cl 36.965903 (24.24%)35.453Copper⁶³Cu 62.929597 (69.15%), ⁶⁵Cu 64.927789 (30.85%)63.546Bromine⁷⁹Br 78.918338 (50.69%), ⁸¹Br 80.916290 (49.31%)79.904 ### Tips - Type formulas with normal capitals and numbers, e.g. Ca(OH)2 or CuSO4·5H2O – brackets and hydrates work. - Atomic masses are IUPAC standard atomic weights; radioactive elements use the mass number of their longest-lived isotope. - Electronegativity values are on the Pauling scale. - Everything is calculated in your browser. ### Common mistakes to avoid - Writing CO (carbon monoxide) when you mean Co (cobalt) – capitals matter. - Forgetting to multiply the bracket contents by the subscript after the bracket. - Mixing up atomic number (protons) and mass number (protons + neutrons). ## Worked example Inputs — Calculate: Average atomic mass from isotopes; Isotope data: My own isotopes (below); Isotopes – one per line: label (optional), mass in u, abundance: Ga-69 68.925574 60.108 Ga-71 70.924703 39.892; Abundances are given as: Percent (75.76). Results — **Average atomic mass = 69.723067 u**; Molar mass = 69.7231 g/mol; Sum of the abundances entered = 100 %; Contribution of each isotope = Isotope Mass (u) Abundance Fraction Contribution (u) ───────────────────────────────────────────────────────────── Ga-69 68.925574 60.108% 0.60108 41.429784 Ga-71 70.924703 39.892% 0.39892 28.293283 Total 100% 1 69.723067; How it was calculated = Average = Σ fᵢ·mᵢ = 0.6011 × 68.9256 + 0.3989 × 70.9247 = 69.72307 u.. ## Key terms - **Isotope**: Atoms of the same element with different neutron numbers and therefore different masses. - **Natural abundance**: The fraction of an element’s atoms that are a given isotope, as found on Earth. - **Weighted average**: A mean in which each value counts in proportion to its weight – here, its abundance. - **Relative atomic mass**: The average mass of an element’s atoms relative to 1/12 of a carbon-12 atom (also called atomic weight). ## FAQ **How do you calculate average atomic mass?** Multiply each isotope’s mass by its abundance as a decimal and add the results. Chlorine: 34.968853 × 0.7576 + 36.965903 × 0.2424 = 26.4924 + 8.9605 = 35.4529 u. **Why is the average atomic mass not a whole number?** It is a weighted mean of several isotopes, and each isotopic mass is itself slightly different from a whole number because of nuclear binding energy. **Is average atomic mass the same as molar mass?** Numerically yes: an average atomic mass of 35.45 u means one mole of the element weighs 35.45 g. **What if my percentages do not add up to 100%?** Published abundances are rounded, so they may sum to 99.99% or 100.01%. The calculator divides by the actual total, which keeps the weights consistent; check your data if the total is far from 100%. **How do I find the abundance of two isotopes from the average?** Let the abundance of the heavier isotope be x: M̄ = m₁(1 − x) + m₂x, so x = (M̄ − m₁)/(m₂ − m₁). For copper, (63.546 − 62.9296)/(64.9278 − 62.9296) = 0.3085, so 30.85% ⁶⁵Cu and 69.15% ⁶³Cu. **Can I use mass numbers instead of exact isotope masses?** For a rough answer, yes – 35 × 0.7576 + 37 × 0.2424 = 35.48 for chlorine. Exact masses give 35.453, so the shortcut is off by about 0.03 u. **Which element has the most stable isotopes?** Tin, with ten stable isotopes from ¹¹²Sn to ¹²⁴Sn. Up to twelve isotopes fit in this calculator. **What formula does the Average Atomic Mass Calculator use?** Average atomic mass = Σ fᵢ·mᵢ = f₁m₁ + f₂m₂ + … + fₙmₙ (fᵢ = abundance as a fraction). ## Sources - [NIST – Atomic weights and isotopic compositions for all elements](https://www.nist.gov/pml/atomic-weights-and-isotopic-compositions-relative-atomic-masses) - [IUPAC Commission on Isotopic Abundances and Atomic Weights – Standard atomic weights](https://www.ciaaw.org/atomic-weights.htm) - [OpenStax – Chemistry 2e](https://openstax.org/details/books/chemistry-2e)