Rates of Change


How do you find the rate of change?

2 years ago


171 Replies




Vickie Shanahan

171 Answers


The rate of change is how something is changing. Imagine you have a toy car that moves on a track. The rate of change tells you how fast the car is moving or if it's going faster or slower.

To find the rate of change, you can look at two things: how much something changes and how much time it takes. For example, if the car moves 10 centimeters in 2 seconds, the rate of change is 5 centimeters per second because it moves 5 centimeters each second.

You can also think of the rate of change as a slope on a hill. If the hill is steep, it means things are changing quickly. If it's not very steep, things are changing slowly.

So, the rate of change is like a measurement that tells you how fast something is changing or how steep the change is. It can help you understand how things are moving or growing.

Dewain Sewell

Distance traveled divided by time it takes. On a graph that would be calculating the difference in the change in y and the change in x

Zeid Al-Arqan

(Change in y) divided by (change in x) for the rate of change in a graph but for a problem solving question its the the change divided by the original

Haseeb Ullah Khan

Consider the following equation


The changing quantity is represented by the letter "y" called the independent variable. It is dependent upon a variable called the dependent variable denoted by 'x'. Find the value of "y" at two values of x. let Y1 be the output of X1 and Y2 be the output of X2. The rate of change of y will be calculated as follows:

dy/dx= (Y2-Y1)/(X2-X1)

Michael Welch

Rate of change is found through differentiation, this in its simplest form can be found by reducing the power of the function by one and timesing through by the power you have reduced, if it is a constant function you could simply find the gradient.


The rate of change (ROC) is the speed at which a variable changes over a specific period of time


Finn Mortimore

If we have a graph, the rate of change at a particular point is the gradient of the tangent at that point - this is known as the derivative. Given some values, we could approximate the rate of change by calculating the gradient of the graph of those values at that point i.e. rise over run

Donovan Maddock

This is an easy thing to find out. If you have a straight line on a X-Y graph, the formula you would use is y=mx+c. The rate of change is m in this formula is is how steep the line is . To calculate m for this formula you choose two separate points on the line (taking note of their X-Y coordinates). Then you take the difference between the y coordinates then take the difference between the x coordinates. Then you take these two numbers and divide the difference between the y coordinates by the difference between the x coordinates. This will give you the steepness of the line which is m in the formula of a straight line.

Loubna Profile Picture
Loubna Verified Sherpa Tutor ✓

Your bridge to Maths & Physics success. Let's ace it together!

2 reviews

The rate of change can be found by calculating the difference in the values of a quantity over a certain period of time or another variable. It is often calculated using the formula:

Rate of change = (Change in quantity) / (Change in time or another variable)

For example, to find the rate of change of distance with respect to time, you would divide the change in distance by the change in time. This gives you the speed or velocity.

I'm available for 1:1 private online tuition!

Click here to view my profile and arrange a free introduction.
Abdul Askar

The rate of change refers to what degree a variable relates to another.

Considering two points connected by a line on an XY graph. The rate of change of the variable Y in relation to X can be calculated by finding the gradient. The gradient = the change in Y, divided by, the change in X.

For example, given a line graph of distance travelled against time, the average gradient between two points along the graph can be found by: gradient = distance1-distance2/time1-time2. This also represents the speed between time1 and time2, as speed is defined as the rate of change of distance.

Stuart W Profile Picture
Stuart W Verified Sherpa Tutor ✓

Experienced Physics and Mathematics tutor from beginner to degree

The Rate of change (ROC) is the increase or decrease of one value related to another value.

The speed of a car for instance is the distance covered divided by the time taken.

In mathematics this can be the gradient of a graph in general terms.

I'm available for 1:1 private online tuition!

Click here to view my profile and arrange a free introduction.
Sam Morris

To find the average rate of change of a function over an interval, you can use the formula:

Average Rate of Change = (Change in Y) / (Change in X) = (ΔY) / (ΔX)

Mohamed E Profile Picture
Mohamed E Verified Sherpa Tutor ✓

Teaching Math, Physics and Chemistry for over 10 years!

12 reviews

Hi Vickie,

The rate of change is usually obtained if you divide by time.

I'm available for 1:1 private online tuition!

Click here to view my profile and arrange a free introduction.
Rojan Santhakrishnan

Derivative with respect to another variable

Jennifer A Profile Picture
Jennifer A Verified Sherpa Tutor ✓

7+ years teaching KS3, GCSE, 11+ Math & English and A-Level Economics

4 reviews

We can find the rate of change by calculating the gradient of the curve or line. We identify two points on the line. Next we find the difference in the y-axis points and divide by the difference in the x-axis points. E.g. (Y2 - Y1)/(X2 - X1)

I'm available for 1:1 private online tuition!

Click here to view my profile and arrange a free introduction.

Think you can help?

More Maths GCSE Questions
Sherpa Badge

Need a GCSE Maths tutor?

Get started with a free online introductions with an experienced and qualified online tutor on Sherpa.

Find a GCSE Maths Tutor