Weighted Average Atomic Mass Calculator With Abundance

This calculator finds the average atomic mass of an element with two isotopes. Enter the mass of each isotope in unified atomic mass units (u) and the percent abundance of the first; the second isotope makes up the rest. You get the weighted average atomic mass and the abundance of the second isotope.

Formula

Average atomic mass = m₁ × (p₁ ÷ 100) + m₂ × (p₂ ÷ 100), with p₂ = 100 − p₁.

• m₁, m₂: masses of the isotopes in u (unified atomic mass units, also written amu or Da)
• p₁, p₂: abundances in percent by number of atoms, not by mass

Worked Example

Chlorine: chlorine-35 (34.96885 u, 75.76%) and chlorine-37 (36.96590 u).

1. Abundance of chlorine-37: 100 − 75.76 = 24.24 %
2. 34.96885 × 0.7576 = 26.49240 u
3. 36.96590 × 0.2424 = 8.96053 u
4. Average: 26.49240 + 8.96053 = 35.4529 u

Assumptions

• The element has exactly two isotopes, or the others are too rare to matter; for three or more, add a term for each.
• Abundances are atom fractions (mole fractions), as tables of natural abundance give them.
• Natural abundances vary slightly between sources of an element, which is why several standard atomic weights are given as ranges or rounded values such as 35.45 for chlorine.

How to read the result

The result lies between the two isotope masses and nearer to the more abundant one. For chlorine it matches the conventional atomic weight of 35.45 used on the periodic table. No single chlorine atom weighs 35.45 u; the value is an average over many atoms. For the mass of a single atom, use the isotope atomic mass calculator.

Limits and common mistakes

• Using mass numbers (35 and 37) instead of the isotope masses gives 35.48 instead of 35.45.
• Entering abundances that do not add up to 100%: here the second is set to the remainder for you.
• Using percent where a fraction is expected: divide by 100 once, not twice.

Frequently Asked Questions

How do you calculate average atomic mass with abundance?

Multiply each isotope mass by its abundance as a fraction and add the products.

What is the average atomic mass of chlorine?

About 35.4529 u from 75.76% chlorine-35 and 24.24% chlorine-37.

Is abundance by mass or by number of atoms?

By number of atoms (mole fraction).

What if an element has three isotopes?

Add a third mass × fraction term; the fractions must add up to 1.

in m1 | Mass of isotope 1 | u | 34.96885 | 0
in a1 | Abundance of isotope 1 | % | 75.76 | 0 | 100
in m2 | Mass of isotope 2 | u | 36.96590 | 0
out avg | Average atomic mass | u | m1 * a1 / 100 + m2 * (100 - a1) / 100 | 4
out a2 | Abundance of isotope 2 | % | 100 - a1 | 2