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Isotope-Weighted Mean Atomic Mass

Average two through ten isotope masses using entered percentage abundances.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

Equal 50% abundances with masses 10 and 12 give mean mass 11.

Mean atomic mass = sum(abundance percent × isotope mass)/100

Worked example

Enter these known values and leave the other values blank.

How many isotopes do you have?
2
Percentage of 1st isotope
50 %
Mass of 1st isotope
10 amu
Percentage of 2nd isotope
50 %
Mass of 2nd isotope
12 amu
Average atomic mass
11 amu

Assumptions and limitations

  • Abundances must sum to 100% for the selected complete isotope set. The calculation uses supplied masses and abundances; it does not select natural-isotope data or standard atomic weights.
  • Masses must share a unit, such as unified atomic mass units. A weighted mean is usually not the mass of any single isotope. The source form supports two to ten positively abundant isotopes.

Common questions

What does this model assume?

Abundances must sum to 100% for the selected complete isotope set. The calculation uses supplied masses and abundances; it does not select natural-isotope data or standard atomic weights.

Can I solve backward?

Clear the unknown value and enter compatible known values. Choices, one-way outputs and singular boundary cases cannot always be inverted.

References

Explicit physical and mathematical model domains: finite positive denominators, dilute limiting-law applicability, integral ionic charge numbers, nonnegative concentrations and normalized isotope abundances.

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