Average Atomic Mass Calculator

Last updated: June 2026

Use this average atomic mass calculator to calculate the relative atomic mass of an element from its isotopic masses and isotopic abundances. The page also includes an isotope abundance calculator for two-isotope questions in which the average atomic mass is known but the percentage abundance is unknown.

Key takeaway: Average atomic mass is a weighted average. An isotope with a higher abundance contributes more strongly to the final average than an isotope with a lower abundance.
How to use this calculator
  1. Choose Average mass when the isotopic masses and their abundances are known.
  2. Select whether the abundances are entered as percentages or fractions.
  3. Enter the isotopic mass and abundance for each isotope, adding more rows when needed.
  4. Choose Missing abundance when the average mass and the masses of two isotopes are known.
  5. Select Calculate to see the weighted-average equation, substitution and final answer.

What is average atomic mass?

Average atomic mass is the weighted average mass of the naturally occurring isotopes of an element. At school level, this value is usually discussed as the relative atomic mass, Ar.

It is a weighted average because isotopes do not normally occur in equal amounts. The mass of a more abundant isotope has a greater effect on the final value.

Chlorine contains mainly chlorine-35 and chlorine-37. Because chlorine-35 is more abundant, the relative atomic mass of chlorine lies closer to 35 than to 37.

Average atomic mass equation

When the abundances are given as percentages:

average mass = Σ(isotopic mass × percentage abundance) ÷ 100

When the abundances are given as fractions:

average mass = Σ(isotopic mass × fractional abundance)

Percentage abundances should add up to 100%, while fractional abundances should add up to 1.

Why a weighted average is needed

Simply adding the isotope masses and dividing by the number of isotopes assumes that every isotope occurs in equal abundance. That assumption is usually incorrect.

A weighted average gives each isotope a contribution that depends on both its mass and its abundance.

contribution from one isotope = isotopic mass × fractional abundance

The separate contributions are then added to obtain the average atomic mass.

Isotope Abundance Calculator

Some questions provide the average atomic mass and the masses of two isotopes, then ask for the abundance of each isotope.

Let the fractional abundance of isotope 1 be x. The fractional abundance of isotope 2 must then be 1 − x.

average mass = x(mass 1) + (1 − x)(mass 2)

Rearranging gives:

x = (average mass − mass 2) ÷ (mass 1 − mass 2)

This gives the fractional abundance of isotope 1. Multiplying by 100 converts it into a percentage abundance.

Worked example: chlorine

Suppose chlorine-35 has an abundance of 75.8% and chlorine-37 has an abundance of 24.2%.

average mass = [(35 × 75.8) + (37 × 24.2)] ÷ 100
average mass = (2653.0 + 895.4) ÷ 100 = 35.484

The value is commonly rounded to 35.5. It lies closer to 35 because chlorine-35 has the greater abundance.

Worked example: missing isotope abundance

Boron has two main isotopes, boron-10 and boron-11. Suppose the average atomic mass is 10.81. Let the fractional abundance of boron-10 be x.

10.81 = 10x + 11(1 − x)
10.81 = 10x + 11 − 11x
x = 0.19

Boron-10 therefore has an abundance of approximately 19%, while boron-11 has an abundance of approximately 81%.

Using mass spectrometry data

In a mass spectrum, the position of an isotopic peak gives the isotopic mass or mass-to-charge ratio, while the relative peak height gives the relative abundance.

Relative peak heights do not have to add directly to 100. They can first be converted into fractions by dividing each peak height by the total height.

fractional abundance = individual peak height ÷ total peak height

Common exam traps

Trap 1: Do not calculate a simple mean unless the isotopes have equal abundance.
Trap 2: When abundances are percentages, divide the weighted total by 100.
Trap 3: Fractional abundances must add up to 1, while percentage abundances must add up to 100%.
Trap 4: The average atomic mass must lie between the lightest and heaviest isotope masses entered.
Trap 5: The average atomic mass should lie closer to the isotope with the greater abundance.

Frequently Asked Questions

What does an average atomic mass calculator calculate?

It calculates the weighted average mass of an element from the masses and abundances of its isotopes.

Why is relative atomic mass usually not a whole number?

Most elements exist naturally as mixtures of isotopes. Their relative atomic mass is therefore an average of different isotope masses.

What is the difference between mass number and relative atomic mass?

Mass number is the total number of protons and neutrons in one particular isotope. Relative atomic mass is the weighted average for the naturally occurring isotopic mixture.

Why is the isotope abundance calculator on this page?

Missing-abundance questions use the same weighted-average relationship, so they are naturally connected to average atomic mass calculations.

Should isotope abundances add up to 100%?

Yes. Percentage abundances should total 100%. When abundances are entered as fractions, they should total 1.

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