Average Atomic Mass Calculator

Created by Komal Rafay
Reviewed by Purnima Singh, PhD and Steven Wooding
Last updated: Jul 28, 2022

Welcome to the average atomic mass calculator! This tool will be helpful to all chemistry enthusiasts as well as the students who might not be too excited about chemistry but still have to do their assignments.

Here you will learn the definition of average atomic mass, but that is not all. We will also discuss the difference and relationship between atomic mass and average atomic mass.

Average atomic mass definition

The average atomic mass of an element is the average mass of all the isotopes of an element.

As we know, the atomic mass of an element is approximately the sum of protons and neutrons present in the nucleus. In an atom, each proton and neutron contribute around one amu, and the electronic mass, being so small, is negligible, so the atomic mass is approximately equal to the mass number.

Some atoms of the same element have varying numbers of neutrons, which does not make them a new element. These atoms of an element with the same number of protons and electrons but different numbers of neutrons are called isotopes. And that is where average atomic mass comes to the rescue.

Average atomic mass calculator

Our average atomic mass calculator is a tool for your convenience and knowledge. It is straightforward to use and determines the average atomic mass of elements efficiently.

Let's take a look at the steps involved.

1. Input the percentage abundance of the first element, making sure you select the correct unit, % for percentage abundance and decimal for fractional abundance.
2. Input the mass of the first isotope;
3. Input the percentage abundance of the second isotope;
4. Input the mass of the second isotope; and
5. The result is the average atomic mass expressed as atomic mass units (amu).

🔎 You can calculate the average atomic mass of up to 10 elements as the highest number of stable isotopes of one of the elements is 10. Can you guess which element it is?

Average atomic mass equation

The average atomic mass formula is easy to handle once you understand the basis of the calculations.

It uses the isotopic abundance of the element in percentage and the atomic mass of the isotope in atomic mass unit (amu).

The equation of average atomic mass is:

$\small\text {AM} = \text{f}_1\text{m}_1 + \text{f}_2\text{m}_2 + ... + \text{f}_n\text{m}_n$

where:

• $\text{AM}$ – Average atomic mass;
• $\text{fₙ }$ – Natural abundance of nth isotope; and
• $\text{mₙ}$ – Atomic mass of nth isotope.

🔎 And you guessed right, the element with ten and the highest number of stable isotopes is tin.

How to calculate the average atomic mass

The average atomic mass makes use of the isotopic abundance and the mass of the isotope. So the calculation involves both variables. Questions, calculations, answers, you want it all, and hence we have it all.

• How to calculate the average atomic mass of isotopes?
• How to find average atomic mass with percent abundance? and
• What is the average atomic mass formula?

No matter which of these you a curious about, we will satisfy you.

So, the equation of average atomic mass, as mentioned before, is:

$\small\text {AM} = \text{f}_1\text{m}_1 + \text{f}_2\text{m}_2 + ... + \text{f}_n\text{m}_n$

It may look like a complex equation but don't worry; it is not. It's a piece of cake. Now let's see what this piece of cake is made of and understand how to find the average atomic mass with percent abundance.

The percent abundance of an isotope is the abundance or amount of isotope that naturally exists on the planet. It is a fancy way of saying, how much quantity of the isotope exists?

1. The first step is multiplying the isotopic abundance by the isotope's mass. Do this for each isotope of the element available.

2. Next, sum together the products of abundance and masses you obtained in step one.

3. The result is the average atomic mass.

Simple yet engaging, isn't it? And if you want to use similar tools, check out our molecular weight calculator.

Isotope abundance and average atomic mass

We have been familiar with the atomic mass of an element since we started learning about elements and their atoms. It is the mass of a single atom of that element.

Experimentally it is calculated by mass spectrometry (an analytical technique used to measure the mass-to-charge ratio of ions). But we can figure it out by adding up the number of protons and neutrons in the nucleus of an atom. This calculation gives us the mass of a single atom of an element. The unit of atomic mass is non-SI, amu (atomic mass unit).

Then came isotopes, the atoms that differ slightly in atomic masses due to the varying number of neutrons in their nucleus. Isotopes became the reason for calculating the average atomic masses, as we must consider an element's isotopes. The average atomic mass expresses the atomic mass of elements with isotopes. Its unit is also amu.

But the average atomic mass depends on one more critical aspect, the isotopic abundance. It is the abundance of isotopes of an element found naturally, expressed in percentages.

So technically, both atomic mass and average atomic mass are atomic masses, but one represents a single atom, and the other represents the average of the isotopes.

💡 If you are interested in isotopes, you might also want to know about ions, then don't forget to check out our ionic strength calculator, which swiftly calculates the ionic strength of a solution.

FAQ

How do I calculate the average atomic mass of isotopes?

To calculate the average atomic mass, you may use the simple formula.

AM = f₁ × m₁ + f₂ × m₂ + ... + fₙ × mₙ

where:

• AM – Average atomic mass;
• fₙ – Natural abundance of nth isotope; and
• mₙ – Atomic mass of nth isotope.

All you have to do is:

1. Multiply the natural abundance by the atomic mass of each isotope.
2. Sum all the products obtained in step one.
3. The resultant value is the average atomic mass of the element.

What is the average atomic mass of chlorine?

The two stable isotopes of chlorine are ³⁵Cl and ³⁷Cl.

Their atomic masses are 34.96885 amu and 36.96590 amu. And their natural abundances are 75.78% and 24.22%, respectively.

AM = (Mass of ³⁵C × Isotopic abundance of ³⁵C) + (Mass of ³⁷Cl × Isotopic abundance of ³⁷Cl)

Substitute the values:

AM = [(34.96885 × 75.78) + (36.96590 × 24.22)]/100

AM = 35.452536 amu

Is average mass the same as atomic mass?

Sometimes taken for each other, they are slightly different.

Atomic mass is the approximate sum of protons and neutrons present in the nucleus of an element.

Atoms of some elements have a different number of neutrons, thus resulting in isotopes. It means each isotope has its atomic mass. So, we calculate an average for the atomic masses of isotopes based on their masses (amu) and natural abundance(%), known as average atomic mass.

Why is average atomic mass used?

Average atomic mass accounts for the presence of isotopes for elements. It gives us the average atomic masses of all the isotopes of the element.

It is beneficial because its value equals the molar mass of an element. And knowing the molar mass is significant in analyzing the results of experiments, especially in a chemical reaction.

Komal Rafay
You may enter values for up to 10 isotopes:
Percentage of 1st isotope
%
Mass of 1st isotope
amu
Percentage of 2nd isotope
%
Mass of 2nd isotope
amu
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