How To Find The Rate Of Change In A Table

Finding the rate of change in a table may make your head swim, it may even seem pointless to you. But it’s far from pointless. In fact, it has thousands of applications in daily life, across thousands of occupations and hobbies. What’s more, it doesn’t have to melt your brain!

Follow our simple, easy-to-follow tutorial below, and you’ll be the master of finding the rate of change in tables in no time. For any other information, or if you have further questions, please see our FAQ section at the end of this article.

How to find the rate of change in a table


We’ll use this as our example table

  1. When searching for the average rate of change in a table, we calculate it as the change in Y over the change in X (i.e. change in Y divided by the change in X). This equation is written so: YX
  2. To find the first set of figures for our equation, we determine the change between two sets of Y and X numbers. It is useful to start with the top two rows (highlighted here in yellow)
    1. We can see that the change between Y1 and Y2 is +9
    2. We can see that the change between X1 and X2 is +3
  3. We would therefore write our rate of change equation as: 93 = 3. Our rate of change in this table is 3.
  4. However, we have to check this rate of change against other parts of the table, before we can be sure it is correct. To do so, repeat the rate of change equation for a different part of the table – for example, the two rows highlighted here in green: Y3 and Y4, and x3 and X4.
    1. We can see that the change between Y3 and Y4 is +3
    2. We can see that the change between X3 and X4 is +1
  5. We would therefore rewrite our rate of change equation as 31 = 3. Our rate of change is still 3, meaning that our initial calculation was correct
    1. Note: You could repeat this calculation with any two rows of the table, provided the Y and X rows are parallel/side-by-side.
  6. You have successfully found the rate of change in this table, and the rate of change is +3
    1. Note: Some tables may work with negative numbers, and may produce a negative rate of change, which would be written as: -[number]

And that’s how to find the rate of change in a table! If you’re still unsure, then why not test yourself against a few other example tables you can find online, or have from class. And if you’re really stuck, then why not check out our FAQs below.


What is the rate of change in a table?

The rate of change in a table is the average rate at which the numbers in one column change compared to the numbers in another, from top to bottom. It is taught as part of mathematics and/or algebra class to children at around the ages of 10-12 in the USA, and at different stages of schooling elsewhere in the world.

The rate of change is a constant figure which, when solved, will remain the same throughout the table, and can therefore be used to make complex calculations regarding the information contained within the table. 

Whilst it is an algebraic calculation taught to most youngsters in school, it can quite easily fade from our memory over time, especially if we don’t pursue an education in maths, or a career which uses it. And yet, it can come in exceptionally useful in later life, for a whole multitude of reasons.

If you’re here hoping to spruce up on some maths you learned years ago, or on algebra you skipped, you’ve come to the right place.

Why would I need to know the rate of change in a table?

A lot of maths and algebra can seem pretty abstract, even to the point of uselessness. But the thing about mathematics is that we use it every single day of our lives, most of the time without ever really noticing.

Maths comes into play in ways you might find quite surprising, which is exactly the case with finding the rate of change in a table. This calculation is fundamental to a lot of work in the field of science – determining the constant change factor of experimental readings can be crucial to establishing what the experiment is really telling you.

Similarly, in the world of money and finance, finding the constant rate of growth or decay across a table filled with financial figures can help you to detect future trends, and plan for them.

There are a thousand other ways the rate of change in a table can prove useful to you, so don’t dismiss it just yet! 

Can I check my rate of change against any part of the table?

You can indeed. In fact, you should! Once you’ve proven the rate of change in your table against the top two rows, it’s only prudent to then check it against another two rows. These, provided you use the same rows for both columns (i.e. A1, B1) don’t have to be conjoined, either.

Whilst you can check B1-B2/A1-A2, you could just as easily check B3-B7/A3-A7, or B1-B4/A1-A4, the choice is yours. Provided your initial rate of change calculations were correct, you should see the same result every time.