# Average Atomic Mass Calculator

Calculate average atomic mass from isotope masses and abundances. Weighted average formula with step-by-step solution for up to three isotopes.

## What this calculates

Find the weighted average atomic mass of an element using its isotope masses and natural abundances. This is the number you see on the periodic table for each element.

## Inputs

- **Isotope 1 Mass** (amu) — min 0 — Atomic mass of the first isotope in atomic mass units.
- **Isotope 1 Abundance** (%) — min 0, max 100 — Natural abundance of isotope 1 as a percentage.
- **Isotope 2 Mass** (amu) — min 0 — Atomic mass of the second isotope.
- **Isotope 2 Abundance** (%) — min 0, max 100 — Natural abundance of isotope 2 as a percentage.
- **Isotope 3 Mass (optional)** (amu) — min 0 — Atomic mass of a third isotope. Leave 0 if there are only two.
- **Isotope 3 Abundance (optional)** (%) — min 0, max 100 — Natural abundance of isotope 3. Leave 0 if unused.

## Outputs

- **Average Atomic Mass** (amu) — Weighted average atomic mass.
- **Total Abundance** (%) — Sum of all abundances (should be 100%).
- **Calculation Steps** — formatted as text — Step-by-step weighted average calculation.

## Details

Every element on the periodic table has an atomic mass that is not a whole number. That is because most elements exist as a mixture of isotopes, each with a slightly different mass. The value on the periodic table is the weighted average of all naturally occurring isotopes.

**The Formula**

Average atomic mass = (mass1 x fraction1) + (mass2 x fraction2) + ...

Fractions are the decimal form of the percent abundance. So 80.1% becomes 0.801.

**Boron Example**

Boron has two stable isotopes:
- Boron-10: mass = 10.0129 amu, abundance = 19.9%
- Boron-11: mass = 11.0093 amu, abundance = 80.1%

Average = (10.0129 x 0.199) + (11.0093 x 0.801) = 1.9926 + 8.8184 = 10.811 amu

That matches the periodic table value for boron.

**Common Mistakes**

- Using percentages instead of fractions (divide by 100 first)
- Forgetting that abundances must add up to 100%
- Confusing mass number (integer) with exact isotope mass (decimal)

## Frequently Asked Questions

**Q: Why is average atomic mass not a whole number?**

A: Because it is a weighted average of multiple isotopes. Each isotope has a slightly different mass, and they occur in different proportions in nature. The weighted average almost never lands on a round number.

**Q: What if my abundances do not add up to 100%?**

A: They should add up to 100% (or very close to it). If they do not, double-check your data. Small rounding differences of 0.1-0.2% are common in textbooks, but a large gap means a missing isotope or a typo.

**Q: What is an atomic mass unit (amu)?**

A: One amu is defined as 1/12 the mass of a carbon-12 atom. It is also called a dalton (Da). Protons and neutrons each have a mass very close to 1 amu, so the mass number of an isotope is close to its mass in amu.

**Q: Can I use this for more than three isotopes?**

A: This calculator supports up to three isotopes, which covers most common elements. For elements like tin (10 stable isotopes), you would apply the same weighted-average formula with more terms.

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Source: https://vastcalc.com/calculators/chemistry/average-atomic-mass
Category: Chemistry
Last updated: 2026-04-08