Average Atomic Mass: How to Calculate It

This calculator works out the average atomic mass of an element from its naturally occurring isotopes. You enter each isotope’s mass (in atomic mass units, u) and its natural abundance (as a percentage), and the calculator returns the weighted average—the number you see on the periodic table. The equation is simple: multiply each isotope’s mass by its fractional abundance, then add those products together.

Formula

The average atomic mass is the weighted mean of the masses of an element’s isotopes. The formula is:

Average atomic mass = (massâ‚� × abundanceâ‚�) + (massâ‚‚ × abundanceâ‚‚) + …

Where:

• massâ‚�, massâ‚‚, … are the atomic masses of each isotope, measured in atomic mass units (u). One u is approximately 1.6605 × 10â�»Â²â�· kg.
• abundanceâ‚�, abundanceâ‚‚, … are the fractional abundances of each isotope, expressed as a decimal (e.g., 19.9% becomes 0.199). The sum of all fractional abundances must equal 1 (or 100% if using percentages).

If you have three isotopes, the formula expands to:

Average atomic mass = (mass� × abundance�) + (mass₂ × abundance₂) + (mass₃ × abundance₃)

This is a weighted average, not a simple arithmetic mean. Isotopes that are more abundant contribute more to the final value.

Worked Example

Using the default values from the calculator above (which correspond to boron):

• Isotope 1 (boron-10): mass = 10.013 u, abundance = 19.9%
• Isotope 2 (boron-11): mass = 11.009 u, abundance = 80.1%

First, convert the percentages to fractions:

19.9% = 0.199, 80.1% = 0.801

Now multiply each mass by its fraction:

10.013 × 0.199 = 1.9926

11.009 × 0.801 = 8.8182

Add the products:

1.9926 + 8.8182 = 10.8108

The average atomic mass of boron is approximately 10.811 u, which matches the periodic table value. The calculator rounds to three decimal places, giving 10.811.

When to Use This Calculation

This calculation is used in chemistry and physics whenever you need the average mass of an element’s atoms for stoichiometry, molar mass calculations, or understanding isotopic distributions. It is also used in mass spectrometry to interpret the average mass of an element from its isotopic peaks. The result is what you see as the atomic weight on the periodic table for most elements.

Note that the average atomic mass is not the mass of any individual atom—it is the weighted mean. A sample of boron contains some atoms of mass 10.013 u and some of 11.009 u, but none with a mass of exactly 10.811 u.

Common Mistakes

• Using percentages instead of fractions: The most common error is plugging in 19.9 and 80.1 directly without dividing by 100. Always convert to decimals first.
• Forgetting to check that abundances sum to 100%: If your abundances don’t add up to 100%, your result will be wrong. For example, 19.9% + 80.1% = 100%, but if you accidentally use 19.9% and 79.1%, the sum is 99%, and the average will be off.
• Using the mass number instead of the isotopic mass: The mass number (e.g., 10 for boron-10) is close to the actual mass but not exact. Use the precise isotopic mass (10.013 u) for accurate results.
• Ignoring significant figures: The result should have no more significant figures than the least precise input. If your abundances have three significant figures, the average should have three.
• Mixing up units: Isotopic masses are in atomic mass units (u). If you use grams or kilograms, the result will be off by many orders of magnitude.

Tips

• Always verify that your abundance percentages sum to exactly 100% (or 1 as fractions) before calculating.
• When using a periodic table, the atomic weight listed is already the average atomic mass—you don’t need to calculate it unless you have specific isotope data.
• For elements with only one naturally occurring isotope (e.g., fluorine-19, phosphorus-31), the average atomic mass equals that isotope’s mass exactly.
• If you have more than three isotopes, extend the formula: add another (mass × abundance) term for each additional isotope.
• Use a calculator with enough precision. The differences between isotopes are small, so rounding early can change the result.

Troubleshooting

My result doesn’t match the periodic table. Check your abundances: they must sum to 100%. Also verify that you are using the correct isotopic masses—look them up in a reliable source, as they vary slightly by element. If you have more than two isotopes, make sure you included all of them.

I get a negative number. That’s impossible if all masses and abundances are positive. Check that you didn’t accidentally enter a negative abundance or mass.

The calculator shows an error. Make sure you entered numbers in all required fields. If you have only two isotopes, leave the third mass and abundance as 0. If you have three, ensure the abundance of the third is not 0 unless it truly has zero abundance.

My abundances don’t sum to 100%. This happens when you have a third isotope that you didn’t include, or when the data you have is approximate. Re-check your source. If the sum is slightly off (e.g., 99.9% or 100.1%), you can normalize by dividing each abundance by the sum of all abundances.

Frequently Asked Questions

Why is the average atomic mass not a whole number? Because it’s a weighted average of isotopes with different masses. For example, chlorine has isotopes of mass 34.969 u (75.78%) and 36.966 u (24.22%), giving an average of 35.45 u—not a whole number.

What is the difference between atomic mass and mass number? Atomic mass is the actual mass of an atom in atomic mass units, which includes the mass of electrons and the binding energy. Mass number is simply the total number of protons and neutrons in the nucleus, a whole number. For a specific isotope, the mass number is close to but not exactly equal to the atomic mass.

Can I use this equation for molecules? No, this equation is for individual atoms of an element. For molecules, you would calculate the molecular mass by summing the average atomic masses of all atoms in the molecule.

Why do some elements have only one isotope? Some elements, like beryllium-9 and sodium-23, have only one stable isotope. In that case, the average atomic mass is simply the mass of that isotope, and the abundance is 100%.

How do I find the isotopic masses? You can find them in a table of isotopes from a chemistry reference book or a reliable online database. They are not the same as the mass numbers—for example, carbon-12 has a mass of exactly 12 u by definition, but carbon-13 has a mass of 13.003 u.

What if I have more than three isotopes? The calculator above supports up to three. For more, you can extend the formula manually: add (mass × abundance) for each additional isotope and divide by the sum of all fractional abundances (which should be 1).

Related

• Bond Order: Formula and How to Calculate It
• Change in H Chemistry: Calculate ΔH Step by Step
• Bond Order: How to Calculate It Step by Step

in t | Isotope 1 mass (u) | u | 10.013 | 0
in d | Isotope 1 abundance (%) | % | 19.9 | 0
in a | Isotope 2 mass (u) | u | 11.009 | 0
in b | Isotope 2 abundance (%) | % | 80.1 | 0
in c | Isotope 3 mass (u) | u | 0 | 0
in e | Isotope 3 abundance (%) | % | 0 | 0
out avg | Average atomic mass | u | (t * d/100 + a * b/100 + c * e/100) / ((d/100) + (b/100) + (e/100)) | 3