Average Atomic Mass Calculator

How to use the average atomic mass calculator

What this calculator does

This calculator finds the weighted mean mass of an element's isotopes. It multiplies each isotope's mass by its fractional abundance and adds the products. The result is expressed in unified atomic mass units, symbol u (often written amu in classroom materials). It is an exact weighted-average identity for the numbers entered, but it does not identify an unknown element, measure a sample, or guarantee that a laboratory specimen has the same isotope distribution as a published natural-abundance table.

When to use it

Use it to check general-chemistry homework, reproduce a periodic-table atomic weight from isotope data, compare a sample's measured isotope mix with a natural reference, or explore how enrichment changes the weighted mean. For reference data, consult the NIST chlorine isotope composition table, which lists isotope masses and representative compositions.

How to calculate

1. The calculator opens with a complete chlorine demonstration and an immediately available validated XLSX workbook.
2. Choose Number of isotopes from 2 through 10. Only the selected rows participate.
3. Choose Abundance format. Percent entries must total 100; fractional entries must total 1. Switching formats converts the values already entered.
4. Replace each Abundance and Isotopic mass (u) value. Results and the contribution table update live.
5. Read Average atomic mass, verify Total abundance, and inspect each row's Contribution (u).
6. Select Download Excel to export the current validated model. Reset clears the demonstration values and disables export until a complete valid set is entered again.

Input guide

Number of isotopes is a required integer selector from 2 to 10. A value of 2 is suitable for chlorine. Increasing it reveals more required isotope rows; hidden rows are excluded. Abundance format is a required mode selector. Choose Percent (%) for values such as 75.76, or Fraction (0 – 1) for 0.7576. Do not mix the two formats, use scientific notation, or type a percent sign into the field. Each visible Abundance 1 – 10 is a required nonnegative decimal. A higher abundance gives that isotope more influence. Each visible Isotopic mass 1 – 10 (u) is a required positive decimal, such as 34.968852682. A higher mass raises the average in proportion to its abundance. Commas are accepted only as thousands separators in unambiguous U.S. notation; decimal-comma input such as 1,5 is rejected rather than interpreted as 15.

Output guide

Average atomic mass is the weighted mean in u. Total abundance is a validation check and must equal 100.0000% within a very small numerical tolerance. Weighted sum repeats the unrounded weighted total so the calculation is auditable. The header pills show the active isotope count, normalized abundance total, and readiness state. In the table, Abundance shows the normalized percent, Isotopic mass (u) is the entered mass, Contribution (u) is abundance fraction times mass, and Share of weighted sum shows how much of the final weighted total comes from that row. A zero abundance is allowed and produces a zero contribution; a zero or negative mass is invalid.

Worked example

The startup example uses chlorine-35 at 34.968852682 u with 75.76% abundance and chlorine-37 at 36.965902602 u with 24.24% abundance. The calculation is:

(0.7576 × 34.968852682) + (0.2424 × 36.965902602) = 35.4529375826 u

This value lies inside the current chlorine standard atomic-weight interval published by the Commission on Isotopic Abundances and Atomic Weights. Small differences from a textbook's rounded answer usually come from using rounded isotope masses or abundances.