Calculate the relative atomic mass of an element using its isotope masses and relative abundances. Enter your isotope data to get a fast, accurate weighted-average result.
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Calculate Relative Atomic Mass
Enter the isotopic mass and relative abundance for each isotope. The calculator applies the standard relative atomic mass formula and shows your result clearly.
Relative Atomic Mass Formula:
Aᵣ = (m₁ × a₁ + m₂ × a₂ + …) ÷ (a₁ + a₂ + …)
Calculate Relative Atomic Mass
Relative Atomic Mass Calculator
Calculate the relative atomic mass of an element from isotope masses and their relative abundances. See every contribution, step, and assumption as you learn.
Isotope inputs
Enter one row for each naturally occurring isotope.
| Isotope | Isotopic mass | Abundance (%) | Contribution | Actions |
|---|
Relative atomic mass formula
The calculation is a weighted average: each isotope matters in proportion to its abundance.
Step-by-step solution
Intermediate values keep their full precision; only the displayed answer is rounded.
Isotope abundance
The bar height shows each isotope's share of the sample.
Isotope contribution to Ar
Compare how much each isotope adds to the final weighted average.
Try a common example
These are measured isotopic masses and representative natural abundances. Select one to load it into the calculator.
Natural abundance varies slightly by source and sample. Values above are suitable representative educational data, not mass numbers.
Quick calculation
For a fast two-isotope check. The full calculator above remains the source of the detailed solution.
Relative atomic mass vs mass number
These related terms describe different ideas.
Weighted average of an element's isotopic masses. It is usually not a whole number and has no unit.
Total number of protons and neutrons in one isotope. It is always a whole number, such as 35 or 37.
The measured mass of a particular isotope, commonly displayed in unified atomic mass units (u).
The number of protons in an atom. It identifies the element.
What Is Relative Atomic Mass?
Relative atomic mass (Aᵣ) is the weighted average mass of the naturally occurring isotopes of an element, compared with a standard atomic mass scale. Because most elements exist as a mixture of isotopes, their relative atomic mass reflects the masses and abundances of those isotopes.
Why Elements Can Have Multiple Isotopes
Isotopes are atoms of the same element that have the same number of protons but different numbers of neutrons. This gives isotopes different masses while they remain the same element.
Why Isotope Abundance Affects Relative Atomic Mass
Isotopes do not always occur in equal amounts. An isotope with a higher natural abundance has a greater effect on the final relative atomic mass. Less abundant isotopes have a smaller effect.
The result is therefore a weighted average, rather than a simple average of the isotope masses.
How to Calculate Relative Atomic Mass
To calculate relative atomic mass, multiply each isotope’s mass by its relative abundance, then add the contributions together. If abundances are given as percentages, convert them to decimals first.
Relative Atomic Mass Formula
The calculation can be written as:
Aᵣ = (m₁ × f₁) + (m₂ × f₂) + (m₃ × f₃) + …
Where:
m = isotope mass
f = relative abundance expressed as a decimal
Aᵣ = relative atomic mass
For example, an abundance of 75% becomes 0.75, while 25% becomes 0.25.
Step-by-Step Calculation
Identify the isotopes of the element.
Record the mass of each isotope.
Record the relative abundance of each isotope.
Convert percentages to decimals if necessary.
Multiply each isotope mass by its abundance.
Add all the weighted contributions to find the relative atomic mass.
Relative Atomic Mass Calculator Examples
Worked examples can make the weighted-average method easier to understand. The examples below use simple isotope data so you can follow each calculation step by step.
Example With Two Isotopes
Suppose an element has two isotopes:
Isotope 1: mass = 10.0 u, abundance = 60%
Isotope 2: mass = 12.0 u, abundance = 40%
Convert the percentages to decimals:
60% = 0.60
40% = 0.40
Calculate each contribution:
10.0 × 0.60 = 6.00
12.0 × 0.40 = 4.80
Add the contributions:
Aᵣ = 6.00 + 4.80 = 10.80
So, the relative atomic mass is 10.80.
Example With Three Isotopes
Suppose an element has three isotopes:
Isotope 1: mass = 20.0 u, abundance = 50%
Isotope 2: mass = 21.0 u, abundance = 30%
Isotope 3: mass = 22.0 u, abundance = 20%
Convert the abundances to decimals:
50% = 0.50
30% = 0.30
20% = 0.20
Calculate each contribution:
20.0 × 0.50 = 10.00
21.0 × 0.30 = 6.30
22.0 × 0.20 = 4.40
Now add them:
Aᵣ = 10.00 + 6.30 + 4.40 = 20.70
Therefore, the relative atomic mass is 20.70.
Example Using Percentage Abundance
Suppose an isotope has a mass of 35.0 u and a relative abundance of 75%.
First, convert the percentage to a decimal:
75% ÷ 100 = 0.75
Then multiply the isotope mass by its abundance:
35.0 × 0.75 = 26.25
This 26.25 is the isotope’s contribution to the weighted average. Repeat the same process for the other isotopes, then add all contributions to obtain the relative atomic mass.
Relative Atomic Mass of Isotopes
Isotopes are atoms of the same element with the same number of protons but different numbers of neutrons. Because they have different numbers of neutrons, their masses are different.
When an element has multiple isotopes, each isotope contributes to the element’s relative atomic mass according to its natural abundance. An isotope that occurs more frequently has a greater effect on the final value, while a less abundant isotope has a smaller effect.
How Isotope Abundance Affects the Calculation
To calculate the relative atomic mass of isotopes, multiply each isotope’s mass by its relative abundance and add the results:
Relative atomic mass = Σ (isotope mass × relative abundance)
For example, if one isotope makes up 90% of an element and another makes up 10%, the first isotope has a much larger influence on the final value.
Isotope Mass vs. Relative Atomic Mass
Isotope mass refers to the mass of one particular isotope. Different isotopes of the same element have different masses.
Relative atomic mass is the weighted average of the masses of the element’s naturally occurring isotopes. It considers both isotope masses and their relative abundances.
This is why the relative atomic mass shown for an element is often a decimal rather than a whole number.
For a detailed walkthrough, see our How to Calculate Relative Atomic Mass guide.
When to Use Relative Atomic Mass
Relative atomic mass is useful in many chemistry calculations where the average mass of an element is needed.
Chemistry calculations: Use it when working with the average atomic mass of an element.
Molar mass calculations: Relative atomic masses are used to determine the molar mass of compounds.
Stoichiometry: Use atomic masses when calculating the amounts of substances involved in chemical reactions.
Chemical equations: Relative atomic masses help you calculate the masses and quantities of reactants and products.
Exam and homework problems: You may need to calculate relative atomic mass from isotope masses and abundances.
Checking isotope-abundance calculations: The calculator can help verify a weighted-average calculation and identify possible arithmetic errors.
Common Mistakes When Calculating Relative Atomic Mass
Small errors in the calculation can produce an incorrect result. Watch for these common mistakes.
Forgetting to Convert Percentages to Decimals
If abundance is given as a percentage, divide it by 100 before using it in the formula. For example, 75% = 0.75.
Adding Isotope Masses Without Weighting Them
Do not simply add the isotope masses or calculate an ordinary average. Each isotope must be multiplied by its relative abundance first.
Confusing Mass Number With Isotope Mass
The mass number is the total number of protons and neutrons in an isotope. Isotope mass is a measured mass and can be a decimal value. They are related but are not the same quantity.
Using Abundances That Do Not Add Up Correctly
When using fractional abundances, the values should add up to 1. When using percentage abundances for all isotopes, they should normally add up to 100%.
Rounding Too Early
Keep extra decimal places during the calculation and round the final answer at the end. Early rounding can slightly change the result.
Confusing Relative Atomic Mass With Molar Mass
Relative atomic mass is a dimensionless weighted average based on isotope masses. Molar mass is the mass of one mole of a substance and is typically expressed in g/mol. For an element, their numerical values are often closely related, but they represent different quantities.
Frequently Asked Questions
A relative atomic mass calculator finds the weighted average atomic mass of an element from its isotope masses and relative abundances. It saves time and helps you check your chemistry calculations.
Multiply each isotope mass by its relative abundance, then add the results. If abundances are given as percentages, convert them to decimals before multiplying.
First, list the mass and abundance of each isotope. Multiply each mass by its fractional abundance, then add all the weighted contributions to get the relative atomic mass.
The formula is:
Ar = Σ (isotope mass × relative abundance)When abundance is given as a percentage, divide each percentage by 100 before using it in the calculation.
Most elements contain more than one naturally occurring isotope. Because relative atomic mass is a weighted average of their masses, the result is often a decimal value rather than a whole number.
Mass number is the total number of protons and neutrons in one specific isotope, so it is always a whole number. Relative atomic mass is the weighted average of an element's naturally occurring isotope masses, so it is often a decimal.
Yes. When all naturally occurring isotopes are included and abundance is given as percentages, their abundances should add up to 100%. If using decimal fractions, they should add up to 1.
Yes. Multiply the mass of each isotope by its fractional abundance and add the two results. The same weighted-average method works whether an element has two isotopes or several.