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)
| Element | Isotopes (mass in u, abundance) | Average |
|---|---|---|
| Lithium | ⁶Li 6.015123 (7.59%), ⁷Li 7.016003 (92.41%) | 6.940 |
| Boron | ¹⁰B 10.012937 (19.9%), ¹¹B 11.009305 (80.1%) | 10.811 |
| Neon | ²⁰Ne 19.992440 (90.48%), ²¹Ne 20.993847 (0.27%), ²²Ne 21.991385 (9.25%) | 20.180 |
| Magnesium | ²⁴Mg 23.985042 (78.99%), ²⁵Mg 24.985837 (10.00%), ²⁶Mg 25.982593 (11.01%) | 24.305 |
| Silicon | ²⁸Si 27.976927 (92.223%), ²⁹Si 28.976495 (4.685%), ³⁰Si 29.973770 (3.092%) | 28.085 |
| Chlorine | ³⁵Cl 34.968853 (75.76%), ³⁷Cl 36.965903 (24.24%) | 35.453 |
| Copper | ⁶³Cu 62.929597 (69.15%), ⁶⁵Cu 64.927789 (30.85%) | 63.546 |
| Bromine | ⁷⁹Br 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).
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 − f₂Worked 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).
Frequently asked questions
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).