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Walk-through

How to Use This Calculator

3 steps

1

List each isotope's mass and abundance

On the Average Mass tab, enter the isotopic mass (in atomic mass units, u) and the natural abundance (%) for every stable isotope of the element. Add a row for each isotope — most elements have two or three.

2

Check that abundances sum to 100%

The calculator tracks the running total of your abundance percentages and warns you if they don't add up to 100%. Natural abundances always sum to 100% for a complete isotope list.

3

Read the weighted average

The result card shows the average atomic mass — the value you'd find on the periodic table — along with a breakdown of each isotope's contribution (mass × abundance ÷ 100).

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Reference

Formula & Methodology

2 formulas

Average atomic mass (weighted mean)

average = Σ (mass_i × abundance_i ÷ 100)

Multiply each isotope's mass by its fractional natural abundance, then sum across all isotopes. Abundance is entered as a percentage (e.g. 75.76) and divided by 100 to convert it to a fraction before weighting.

Solve for an unknown abundance (two isotopes)

x₁ = (average − mass₂) ÷ (mass₁ − mass₂)

For an element with exactly two isotopes, if you know the average atomic mass and both isotope masses, you can solve algebraically for the fractional abundance of isotope 1 (x₁); the abundance of isotope 2 is 1 − x₁.

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Glossary

Key Terms Explained

6 terms

Average atomic mass The weighted mean mass of all naturally occurring isotopes of an element, weighted by each isotope's natural abundance. This is the number shown on the periodic table for each element, measured in atomic mass units (u).

Isotope An atom of the same element (same number of protons) that has a different number of neutrons, giving it a different mass. Chlorine, for example, occurs naturally as Cl-35 and Cl-37.

Natural abundance The percentage of atoms of an element, as found in nature, that are a particular isotope. Natural abundances for a given element's isotopes always sum to 100%.

Atomic mass unit (u) Also called the dalton (Da), one atomic mass unit is defined as 1/12 the mass of a carbon-12 atom. Isotopic and average atomic masses are both expressed in this unit.

Weighted mean An average where each value is multiplied by a weight reflecting its relative importance before summing, rather than treating every value equally. Average atomic mass weights each isotope's mass by how common it is in nature.

Relative atomic mass Another name for average atomic mass — a dimensionless ratio comparing an element's average isotopic mass to 1/12 the mass of carbon-12. In practice it carries the same numeric value as average atomic mass in u.

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Scenarios

Real-World Examples

3 worked examples

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Chemistry student

Chlorine's two stable isotopes

Cl-35 mass / abundance 34.9689 u / 75.76% Cl-37 mass / abundance 36.9659 u / 24.24%

34.9689 × 0.7576 + 36.9659 × 0.2424 ≈ 35.45 u — this matches chlorine's standard atomic weight on the periodic table. Because Cl-35 is roughly three times more abundant than Cl-37, the average sits much closer to 35 than to the midpoint of the two isotope masses.

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Lab technician

Solving for an unknown abundance

Average atomic mass 63.546 u Cu-63 mass / Cu-65 mass 62.9296 u / 64.9278 u

Using x₁ = (63.546 − 64.9278) ÷ (62.9296 − 64.9278), copper's Cu-63 abundance solves to about 69.15%, leaving Cu-65 at about 30.85% — matching the accepted natural abundances for copper.

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Data-entry check

Abundances that don't sum to 100%

Isotope A mass / abundance 10.0 u / 60% Isotope B mass / abundance 11.0 u / 30%

The calculator still computes a weighted average (10.3 u) but flags that the entered abundances only total 90%, not 100% — a signal that an isotope is missing or a percentage was mistyped before trusting the result.

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Deep Dive

Understanding the Average Atomic Mass Calculator

3 chapters · 4 min read

Every atomic mass on the periodic table is an average, not the mass of any single atom. This calculator computes that weighted average from isotope masses and natural abundances, and can also work backward to solve for an unknown abundance.

How the Average Atomic Mass Calculator works

Elements exist in nature as a mixture of isotopes — atoms with the same number of protons but different numbers of neutrons, and therefore different masses. The average atomic mass reported on the periodic table is a weighted mean: each isotope's mass is multiplied by its fractional natural abundance, and the results are summed. That is, average = Σ (mass_i × abundance_i ÷ 100). A more abundant isotope pulls the average closer to its own mass, which is why chlorine's average atomic mass (35.45 u) sits much closer to Cl-35's mass (34.9689 u) than to Cl-37's (36.9659 u) — Cl-35 makes up roughly three-quarters of naturally occurring chlorine.

Inputs and what they mean

Each isotope row needs two numbers: the isotopic mass in atomic mass units (u), and the natural abundance as a percentage. Isotopic masses are typically just above the isotope's mass number (Cl-35 has a mass of 34.9689 u, not exactly 35, because protons, neutrons, and binding energy don't add up to whole numbers). Natural abundances for all of an element's stable isotopes must sum to 100% — the calculator checks this for you and flags entries that are off. The Solve Abundance tab instead takes the average mass and both isotope masses as inputs, useful when a textbook problem gives you the answer and asks you to find the missing abundance split.

Limits and edge cases

This calculator handles stable, naturally occurring isotopes — it isn't meant for radioactive isotopes with vanishingly small or time-varying abundances. The Solve Abundance tab only works for elements with exactly two stable isotopes (like chlorine or copper); elements with three or more isotopes (like magnesium or oxygen) need at least two known abundances to solve for the rest, which this tool doesn't attempt. If your abundances don't sum to 100%, the reported average atomic mass is still mathematically computed from what you entered, but it won't match the standard periodic-table value until the entries are corrected.

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Questions

Frequently Asked Questions

6 questions

What is the formula for average atomic mass?+

Average atomic mass = Σ (isotope mass × natural abundance ÷ 100), summed across every stable isotope of the element. Each isotope's mass is weighted by how common it is in nature, so more abundant isotopes pull the average closer to their own mass.

Why do natural abundances need to sum to 100%?+

Natural abundance is the percentage of naturally occurring atoms of an element that are a given isotope. If you've listed every stable isotope, those percentages must account for the whole sample — 100% of the atoms. If your entries sum to something else, either an isotope is missing or a percentage was entered incorrectly, and the calculator flags this.

How does the chlorine example work?+

Chlorine has two stable isotopes: Cl-35 (mass 34.9689 u, 75.76% abundant) and Cl-37 (mass 36.9659 u, 24.24% abundant). Weighting each mass by its abundance and summing gives 34.9689 × 0.7576 + 36.9659 × 0.2424 ≈ 35.45 u, matching chlorine's standard atomic weight on the periodic table.

How do I solve for an unknown isotope abundance?+

On the Solve Abundance tab, enter the element's known average atomic mass and both isotope masses. The calculator solves x₁ = (average − mass₂) ÷ (mass₁ − mass₂) for the fractional abundance of isotope 1, then reports isotope 2's abundance as the remainder up to 100%. This only works cleanly for two-isotope elements.

What units does this calculator use?+

Isotopic and average atomic masses are entered and reported in atomic mass units (u), also called daltons (Da) — defined as 1/12 the mass of a carbon-12 atom. Abundances are entered and displayed as percentages that should sum to 100% across an element's isotopes.

Why isn't an element's atomic mass a whole number?+

Two reasons. First, an individual isotope's mass isn't exactly its mass number because protons, neutrons, and nuclear binding energy don't sum to a round value (Cl-35 is 34.9689 u, not 35). Second, the periodic-table value is a weighted average across multiple isotopes with different masses, which almost never lands on a whole number.

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Average Atomic Mass Calculator

Result

How to Use This Calculator

List each isotope's mass and abundance

Check that abundances sum to 100%

Read the weighted average

Formula & Methodology

Key Terms Explained

Real-World Examples

Chemistry student

Lab technician

Data-entry check

Understanding the Average Atomic Mass Calculator

How the Average Atomic Mass Calculator works

Inputs and what they mean

Limits and edge cases

Frequently Asked Questions

Get a branded PDF of your results

Average Atomic Mass Calculator

Result

Related Calculators

How to Use This Calculator

List each isotope's mass and abundance

Check that abundances sum to 100%

Read the weighted average

Formula & Methodology

Key Terms Explained

Real-World Examples

Understanding the Average Atomic Mass Calculator

How the Average Atomic Mass Calculator works

Inputs and what they mean

Limits and edge cases

Frequently Asked Questions

Get a branded PDF of your results

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