Average atomic mass calculator
Enter each isotope's mass in atomic mass units and its natural abundance in percent to get the element's average atomic mass. The second mode works backwards, which is the classic homework question; from the average mass and the masses of two isotopes, it finds how much of each is present.
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How to use it
Average mass
- Enter the mass (u) and abundance (%) of each isotope. Leave unused isotopes at 0.
- Read the average atomic mass and the sum of the abundances.
Abundances
- Switch to “Abundances of two isotopes”.
- Enter the element’s average atomic mass and the masses of the two isotopes.
- Average: M = Σ (mᵢ × aᵢ) ÷ Σ aᵢ.
- Two isotopes: x₁ = (M − m₂) ÷ (m₁ − m₂), x₂ = 1 − x₁.
Worked example
Magnesium has three stable isotopes: Mg-24 at 23.98504 u (78.99 %), Mg-25 at 24.98584 u (10.00 %) and Mg-26 at 25.98259 u (11.01 %).
M = (23.98504 × 78.99 + 24.98584 × 10 + 25.98259 × 11.01) ÷ 100 = (1894.5783 + 249.8584 + 286.0683) ÷ 100 = 24.30505 u.
Boron backwards: M = 10.81 u from B-10 (10.01294 u) and B-11 (11.00931 u). x = (10.81 − 11.00931) ÷ (10.01294 − 11.00931) = 0.200036, so boron is about 20 % B-10 and 80 % B-11.
Common mistakes
- Mass number instead of mass. Use 34.96885, not 35, or the answer drifts in the second decimal.
- Percent vs fraction. Enter abundances in percent; 75.76, not 0.7576.
- Average outside the range. An average mass must lie between the lightest and heaviest isotope; if not, a value was mistyped.
Frequently asked questions
How is average atomic mass calculated?
It is a weighted average of the isotope masses, with the natural abundances as weights, M = Σ mᵢ × aᵢ ÷ 100. For chlorine, 34.96885 u at 75.76 % and 36.9659 u at 24.24 % give 35.45293 u.
What if my abundances do not add up to exactly 100 %?
Published values are rounded and may add up to 99.99 % or 100.01 %. The calculator divides by the actual sum, Σ mᵢaᵢ ÷ Σ aᵢ, and shows the sum so you can spot a typo.
How do I find the abundance of two isotopes from the atomic mass?
Call the share of the first isotope x and of the second 1 − x. Then M = m₁x + m₂(1 − x), so x = (M − m₂) ÷ (m₁ − m₂). For copper, 63.546 u with Cu-63 at 62.9296 u and Cu-65 at 64.92779 u gives 69.1521 % Cu-63.
Is the average atomic mass the same as the molar mass?
Numerically, yes. An average atomic mass of 35.45293 u means one mole of the element weighs 35.45293 g, so the molar mass is 35.45293 g/mol.