Last updated: July 3, 2026
Average Atomic Mass Calculator
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Quick Answer
Average atomic mass, or standard atomic weight, is the abundance-weighted mean of an element's isotope masses: Ar = Σ(mᵢ × abundanceᵢ/100). It explains why periodic-table values such as chlorine 35.45 u and carbon 12.011 u are not usually whole numbers. The calculator supports up to four isotopes and flags totals that do not sum to about 100%.
To calculate average atomic mass, multiply each isotope's exact mass by its fractional abundance, then add the products. For chlorine, 34.969 times 0.7577 plus 36.966 times 0.2423 gives about 35.45 unified atomic mass units.
Key Takeaways
- Average atomic mass is a weighted average of isotope masses, not a simple arithmetic mean.
- Convert percent abundance to fractional abundance by dividing by 100 before multiplying by isotope mass.
- Periodic-table atomic masses are often non-integers because most elements are natural isotope mixtures.
- A complete natural-abundance calculation should have total abundance very close to 100%.
- The answer in u has the same numerical value as the element's molar mass in g/mol.
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Formula
Ar = Σ(fᵢ × mᵢ), where fᵢ = abundanceᵢ / 100
Where:
- Ar=Average atomic mass (relative atomic mass)(u)
- mᵢ=Exact mass of isotope i(u)
- aᵢ=Percent abundance of isotope i(%)
- fᵢ=Fractional abundance of isotope i(dimensionless)
Worked Examples
Chlorine: why the table shows 35.45 u
³⁵Cl and ³⁷Cl are mixed in nature, so the periodic-table mass is closer to ³⁵Cl because ³⁵Cl is more abundant.
- 1Convert every percent abundance to a fraction by dividing by 100.
- 2Multiply each exact isotope mass by its fractional abundance to get that isotope's contribution.
- 3Add the contributions to obtain Ar = 35.45 u after rounding.
- 4Confirm the entered abundances sum to 100%, so the periodic-table comparison is meaningful.
Boron standard atomic weight
Natural boron is mostly ¹¹B with a smaller ¹⁰B contribution, producing a value near 10.81 u.
- 1Convert every percent abundance to a fraction by dividing by 100.
- 2Multiply each exact isotope mass by its fractional abundance to get that isotope's contribution.
- 3Add the contributions to obtain Ar = 10.81 u after rounding.
- 4Confirm the entered abundances sum to 100%, so the periodic-table comparison is meaningful.
Copper weighted average
Copper's atomic weight lies closer to ⁶³Cu because ⁶³Cu is more abundant than ⁶⁵Cu.
- 1Convert every percent abundance to a fraction by dividing by 100.
- 2Multiply each exact isotope mass by its fractional abundance to get that isotope's contribution.
- 3Add the contributions to obtain Ar = 63.55 u after rounding.
- 4Confirm the entered abundances sum to 100%, so the periodic-table comparison is meaningful.
Carbon: non-integer natural mass
Even though ¹²C is exactly 12 u, the small natural amount of ¹³C raises natural carbon to about 12.011 u.
- 1Convert every percent abundance to a fraction by dividing by 100.
- 2Multiply each exact isotope mass by its fractional abundance to get that isotope's contribution.
- 3Add the contributions to obtain Ar = 12.011 u after rounding.
- 4Confirm the entered abundances sum to 100%, so the periodic-table comparison is meaningful.
Silver isotope pair
Silver has two common stable isotopes with similar abundances, giving an average near the midpoint.
- 1Convert every percent abundance to a fraction by dividing by 100.
- 2Multiply each exact isotope mass by its fractional abundance to get that isotope's contribution.
- 3Add the contributions to obtain Ar = 107.87 u after rounding.
- 4Confirm the entered abundances sum to 100%, so the periodic-table comparison is meaningful.
Introduction
The average atomic mass of an element is the number printed on most periodic tables: an abundance-weighted mean of the exact masses of its naturally occurring isotopes. This is why chlorine is about 35.45 u instead of exactly 35 or 37, and why carbon is 12.011 u even though ¹²C is exactly 12 u. Enter up to four isotope masses and their percent abundances to compute the standard atomic-weight idea directly. For compound work, this value feeds tools such as the molar mass calculator and grams to moles calculator. Authoritative isotope data can be checked with NIST and CIAAW.
Why periodic-table atomic masses are decimals
A periodic-table atomic mass represents a natural population of atoms, not one isolated atom. If an element has multiple stable isotopes, each isotope contributes according to how often it occurs in nature. The weighted average can therefore be a decimal, and it usually sits closer to the most abundant isotope. The atomic mass calculator is closely related, while this page focuses specifically on the weighted-average reason behind standard atomic weights.
A single isotope has an exact isotope mass.
A natural element sample has isotope fractions.
The periodic-table value combines those fractions into one usable average.
The result is reported in unified atomic mass units, u.
Average atomic mass formula
Use Ar = Σ(fᵢ × mᵢ), where *mᵢ* is isotope mass and *fᵢ* is fractional abundance. Because lab tables usually list abundance as a percent, convert with fᵢ = aᵢ/100. For chlorine, the calculation is 34.969 × 0.7577 + 36.966 × 0.2423 = 35.453 u, which rounds to 35.45 u. This agrees with the IUPAC Gold Book definition of relative atomic mass.
The simple arithmetic mean of 34.969 and 36.966 would be about 35.97 u, which is wrong for natural chlorine because the isotope abundances are not 50:50.
How to calculate it by hand
First list every isotope you want to include, then write the exact isotope mass and natural abundance beside it. Divide each abundance by 100, multiply that fraction by its isotope mass, and sum the products. Finally, check that total abundance is close to 100%. If your chemistry problem later asks for atom counts, moles, or grams, continue with the mole calculator.
Use exact isotope masses rather than mass numbers.
Convert 75.77% to 0.7577, not 75.77.
Add contributions in u.
Round the final answer to the precision justified by your input data.
Benchmark isotope calculations
These standard classroom examples are useful for checking the weighted-average setup before solving unfamiliar elements.
| Element | Isotopes entered | Weighted average |
|---|---|---|
| Chlorine | ³⁵Cl 34.969 u @ 75.77%; ³⁷Cl 36.966 u @ 24.23% | 35.45 u |
| Boron | ¹⁰B 10.013 u @ 19.9%; ¹¹B 11.009 u @ 80.1% | 10.81 u |
| Copper | ⁶³Cu 62.930 u @ 69.15%; ⁶⁵Cu 64.928 u @ 30.85% | 63.55 u |
| Carbon | ¹²C 12.000 u @ 98.93%; ¹³C 13.003 u @ 1.07% | 12.011 u |
| Silver | ¹⁰⁷Ag 106.905 u @ 51.84%; ¹⁰⁹Ag 108.905 u @ 48.16% | 107.87 u |
Interpreting the abundance total
The calculator also reports total abundance. A complete natural-isotope set should total about 100%, allowing for rounding in source tables. If the total is below 99.5%, the average is probably missing one or more isotopes. If it is above 100.5%, a percentage was likely copied incorrectly or duplicate isotope data were included.
When total abundance is not close to 100%, use the status as a data-quality warning rather than as a new chemistry law.
Where this weighted average is used
Average atomic mass is the bridge from isotope-scale measurements to everyday chemical calculations. Standard atomic weights are used in molecular formulas, reagent preparation, percent composition, and stoichiometry. They also help explain isotope patterns in mass spectrometry and why high-precision isotope-ratio work must state the sample origin. For background atomic structure, the electron configuration calculator and atom calculator are useful companions.
Quick Reference Card
Average Atomic Mass — Quick Reference
Quick reference • Average Atomic Mass Calculator
Ar = Σ(mᵢ × abundanceᵢ/100)Valid range: Use exact isotope masses greater than 0 u and natural abundances that sum to about 100%.
Common Values
⚠ Watch Out
- •Do not average isotope masses equally unless their abundances are equal.
- •Do not use mass numbers such as 35 and 37 when exact isotope masses are required.
- •If abundances total far below 100%, missing isotopes will pull the calculated mass too low.
- •If abundances total above 100%, at least one percentage or isotope entry is inconsistent.
Pro Tips
- →Check that the final average lies between the lightest and heaviest isotope masses.
- →Carry extra decimal places through the products and round only the reported final mass.
- →Use NIST or CIAAW data when comparing against periodic-table standard atomic weights.
- →For monoisotopic elements, enter one isotope with 100% abundance to get its exact isotope mass.
FAQs
Why is average atomic mass not usually a whole number?
Most elements are mixtures of isotopes. The periodic-table value is a weighted average of exact isotope masses, so it reflects both isotope mass and natural abundance rather than a whole-number mass number.
What is the difference between isotope mass and mass number?
Mass number counts protons plus neutrons and is an integer. Exact isotope mass is measured in u and differs slightly because nuclear binding energy changes the actual mass.
Do abundances have to add to 100%?
For a complete natural element composition, yes. Small deviations are common from rounded source values, but totals far from 100% indicate missing or inconsistent isotope data.
Can I use more than two isotopes?
Yes. This calculator supports up to four isotope mass-abundance pairs and ignores zero-filled unused pairs.
Why does carbon have average atomic mass 12.011 u?
Natural carbon is mostly ¹²C but includes about 1% ¹³C. That small heavier-isotope contribution raises the natural average above exactly 12 u.
Is average atomic mass the same as molar mass?
The concepts differ, but the numerical value in u per atom equals the molar mass in g/mol for one mole of atoms of that element.