Relative Atomic Mass Calculator
Enter each isotope's isotopic mass and natural abundance (%). The calculator finds the weighted average.
What is relative atomic mass?
Relative atomic mass (often written as Ar) is the weighted average mass of all naturally occurring isotopes of an element, compared to 1/12 of the mass of a carbon-12 atom. In simpler terms, it is the average atomic mass you see on the periodic table.
Because elements usually exist as a mixture of isotopes, the value is rarely a whole number. For example, chlorine has isotopes near masses 35 and 37, so its relative atomic mass is about 35.45 rather than exactly 35 or 37.
Formula for relative atomic mass
Use the weighted average formula:
Ar = (Σ(isotopic mass × isotopic abundance)) / Σ(abundance)
If abundances are given as percentages that add to 100, this becomes:
Ar = Σ(isotopic mass × abundance %) / 100
Step-by-step method
1) List each isotope
Write down all isotopes for the element and their isotopic masses. Use values from reliable data tables when possible.
2) Record abundance for each isotope
Abundance is typically provided as a percent. Example: 75.77% and 24.23%.
3) Multiply mass by abundance
For each isotope, multiply isotopic mass by its abundance (in % or decimal fraction depending on your formula).
4) Add the products
Sum all the mass × abundance products.
5) Divide by total abundance
Divide by 100 if percentages sum to 100. If your values do not sum exactly to 100 due to rounding, divide by the actual total abundance.
Worked example: chlorine
Chlorine has two main isotopes:
- Chlorine-35: mass = 34.96885, abundance = 75.77%
- Chlorine-37: mass = 36.96590, abundance = 24.23%
Ar = [(34.96885 × 75.77) + (36.96590 × 24.23)] / 100
That gives approximately 35.45, which matches the periodic table value (to standard rounding).
Relative atomic mass vs mass number
- Mass number: whole number for one isotope (protons + neutrons).
- Relative atomic mass: weighted average for all natural isotopes of an element.
This is why mass numbers are integers, while relative atomic masses are usually decimals.
Common mistakes to avoid
- Using mass numbers instead of isotopic masses when high precision is needed.
- Forgetting to divide percentage abundances by 100 (or forgetting denominator correction).
- Not checking whether abundance values actually sum to 100%.
- Rounding too early in multistep calculations.
Quick recap
To calculate relative atomic mass, you compute a weighted average: multiply each isotope's mass by its abundance, add all results, and divide by total abundance. Use the calculator above to do this instantly for any element.