# What is the average atomic mass?

Finds the average atomic mass of an element from its isotopes’ masses and abundances, Σ(mass × abundance), or the abundance of each of two isotopes from the average.

- Page: https://www.acalculator.org/chemistry/atomic-mass-calculator
- JSON spec: https://www.acalculator.org/chemistry/atomic-mass-calculator.json
- Version: a41ad0f9ebcb

## Default answer

Example with the default inputs (Find Average atomic mass, Element My own isotopes, Isotopes [Isotope mass (u) 34.969, Abundance 75.78%; Isotope mass (u) 36.966, Abundance 24.22%]): The average atomic mass is 35.4527 u.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| find | Find | The average atomic mass from isotopes, or the abundances of two isotopes from the average. |
| el | Element | An element to fill in its stable isotopes, or your own isotopes. |
| isotopes | Isotopes | Each isotope’s mass in u and its natural abundance in percent. |
| ma | Isotope 1 mass | Isotope 1 mass in unified atomic mass units (u, also Da). |
| mb | Isotope 2 mass | Isotope 2 mass in unified atomic mass units (u, also Da). |
| avg | Average atomic mass | Average atomic mass in unified atomic mass units (u, also Da). |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| mass | Average atomic mass (u) | Σ(isotope mass × abundance) ÷ Σ(abundance). |
| share1 | Isotope 1 abundance | (average − mass 2) ÷ (mass 1 − mass 2) × 100. |
| share2 | Isotope 2 abundance | 100% minus isotope 1’s abundance. |
| total | Abundances add to | The sum of the abundances used; the average divides by it. |
| molar | Molar mass (g/mol) | The same number in grams per mole. |
| working | Working | Each isotope’s part of the average. |
| summary | Answer | The answer in one sentence. |

## Method

Average atomic mass = Σ(mass × abundance) ÷ Σ(abundance). For two isotopes and an average A: abundance 1 = (A − m₂) ÷ (m₁ − m₂) × 100%, abundance 2 = 100% − abundance 1.

## Assumptions

- Abundances are percents of atoms (amount fractions), and must add to 100% within 0.5 points; the average divides by their sum.
- Element presets use NIST’s representative isotopic compositions; natural samples vary a little, which is why IUPAC gives some atomic weights as ranges.
- The molar mass in g/mol has the same number as the average atomic mass in u.

## Worked examples

1. find = average, el = Cl gives mass = 35.452938, total = 100%. Source: NIST, Atomic Weights and Isotopic Compositions for Chlorine (35Cl 34.968852682 u, 0.7576; 37Cl 36.965902602 u, 0.2424), https://physics.nist.gov/cgi-bin/Compositions/stand_alone.pl?ele=Cl (retrieved 2026-10-02); OpenStax, Chemistry 2e, §2.3 Atomic Structure and Symbolism (average atomic mass = Σ(fractional abundance × isotopic mass)), https://openstax.org/books/chemistry-2e/pages/2-3-atomic-structure-and-symbolism (retrieved 2026-10-02).
2. find = average, el = custom, isotopes = {"mass":34.969,"abundance":75.78} or {"mass":36.966,"abundance":24.22} gives mass = 35.452673, summary = The average atomic mass is 35.4527 u. Source: OpenStax, Chemistry 2e, §2.3 Atomic Structure and Symbolism (average atomic mass = Σ(fractional abundance × isotopic mass)), https://openstax.org/books/chemistry-2e/pages/2-3-atomic-structure-and-symbolism (retrieved 2026-10-02).
3. find = average, el = custom, isotopes = {"mass":10.0129,"abundance":19.9} or {"mass":11.0093,"abundance":80.1} gives mass = 10.811016. Source: OpenStax, Chemistry 2e, §2.3 Atomic Structure and Symbolism (average atomic mass = Σ(fractional abundance × isotopic mass)), https://openstax.org/books/chemistry-2e/pages/2-3-atomic-structure-and-symbolism (retrieved 2026-10-02): about 10.81 amu.
4. find = abundance, ma = 34.96885, mb = 36.9659, avg = 35.453 gives share1 = 75.756741%, share2 = 24.243259%. Source: OpenStax, Chemistry 2e, §2.3 Atomic Structure and Symbolism (average atomic mass = Σ(fractional abundance × isotopic mass)), https://openstax.org/books/chemistry-2e/pages/2-3-atomic-structure-and-symbolism (retrieved 2026-10-02): 75.76% 35Cl and 24.24% 37Cl.
5. find = abundance, ma = 62.9296, mb = 64.9278, avg = 63.546 gives share1 = 69.152237%, share2 = 30.847763%. Source: NIST, Atomic Weights and Isotopic Compositions for Copper (63Cu 62.92959772 u, 0.6915; 65Cu 64.92778970 u, 0.3085; standard atomic weight 63.546), https://physics.nist.gov/cgi-bin/Compositions/stand_alone.pl?ele=Cu (retrieved 2026-10-02).
6. find = average, el = Mg gives mass = 24.305052. Source: NIST, Atomic Weights and Isotopic Compositions for Magnesium (standard atomic weight [24.304, 24.307]), https://physics.nist.gov/cgi-bin/Compositions/stand_alone.pl?ele=Mg (retrieved 2026-10-02).

## FAQ

### How do I calculate average atomic mass?

Multiply each isotope's mass by its abundance as a fraction, and add the results. For boron, 19.9% is ¹⁰B (10.0129 u) and 80.1% is ¹¹B (11.0093 u): 10.0129 × 0.199 + 11.0093 × 0.801 = 10.81 u.

### Why is the atomic mass on the periodic table not a whole number?

It is an average over the element's isotopes, weighted by how common each one is. Chlorine is about three quarters ³⁵Cl and one quarter ³⁷Cl, so its average is about 35.45, not 35 or 37.

### How do I find the abundance of two isotopes from the average?

Call the share of isotope 1 x, so isotope 2 is 1 − x. Then x × m₁ + (1 − x) × m₂ = average, so x = (average − m₂) ÷ (m₁ − m₂). For chlorine, (35.453 − 36.96590) ÷ (34.96885 − 36.96590) = 0.7576, or 75.76% ³⁵Cl.

### What if my abundances do not add to 100%?

Rounded abundances often add to 99.99% or 100.01%. The page divides by their sum, so small gaps do not matter, but it asks you to check them when the sum is more than half a point away from 100%.

### Is atomic mass the same as molar mass?

They have the same number. An average atomic mass of 35.45 u means one mole of the element's atoms has a mass of 35.45 g, so its molar mass is 35.45 g/mol.

### Why do some atomic weights have a range?

The isotope mix of some elements, such as chlorine, boron and carbon, varies a little between natural samples. IUPAC gives their standard atomic weights as intervals, such as [35.446, 35.457] for chlorine. The presets use NIST's representative compositions.

## Sources

- OpenStax, Chemistry 2e, §2.3 Atomic Structure and Symbolism (average mass = Σ(fractional abundance × isotopic mass); boron, magnesium and neon examples; chlorine abundances 75.76% and 24.24% from the average 35.453 amu). https://openstax.org/books/chemistry-2e/pages/2-3-atomic-structure-and-symbolism (retrieved 2026-10-02)
- NIST Physical Measurement Laboratory, Atomic Weights and Isotopic Compositions for All Elements (relative atomic masses and representative isotopic compositions of B, C, Mg, Cl, Cu, Br and Ag, from IUPAC/CIAAW). https://physics.nist.gov/cgi-bin/Compositions/stand_alone.pl (retrieved 2026-10-02)
- IUPAC Commission on Isotopic Abundances and Atomic Weights (CIAAW), Chlorine (standard atomic weight [35.446, 35.457]; isotope amount fractions ³⁵Cl [0.755, 0.761], ³⁷Cl [0.239, 0.245]). https://www.ciaaw.org/chlorine.htm (retrieved 2026-10-02)