When comparing two figures against each other, it’s often useful to do so in terms of percentage change. This means expressing, as a percentage, the difference between an original value and a new value.

Percentage change can be either an increase or a decrease. As a mathematical concept, it is often used to quantify changes over time, with its most common applications in the world of finance.

When we talk about percentage decrease in this context, we usually refer to a financial loss, or depreciation in value. For example, if an asset is worth £30,000 in year x, and £24,000 in year y, we can work out the percentage decrease to express the depreciation in percentage terms.

Percentage decrease has many other applications in areas such as science and data analysis. It can also be useful in everyday life.

As an example, you may want to work out your reduction of energy consumption expressed as a percentage. Here, you would take your consumption in month x, compared to month y, and apply a simple formula to determine the percentage decrease.

## A step-by-step guide to calculating percentage decrease

Whatever the purpose, the method of calculating percentage decrease is the same. It’s a relatively straightforward process that takes just four steps to complete.

Each of these steps is explained below, followed by some practice exercises.

## Step 1: Calculate the difference

The first step is to work out the difference, or decrease, between the two figures you’re dealing with. Take the original number, and subtract the new number from it.

As a basic example, say we want to calculate the percentage decrease between 16 and 12. So 16 is our original number, and 12 our new number:

16 - 12 = 4

4 is the numerical value we need to move onto the next step.

## Step 2: Divide the decrease by the original number

Next, take the numerical decrease, and divide it by the total value of your original number.

In our basic example, this means dividing 4 by 16:

4 ÷ 16 = 0.25

## Step 3: Convert this into a percentage

Now take the output of the last equation, and multiply it by 100 to express it as a percentage:

0.25 x 100 = 25

We can now say the percentage decrease between 16 and 12 is 25%.

## Step 4: Confirm it's a percentage decrease

If, after performing the steps above, you’re left with a negative figure, you’re actually dealing with a percentage increase, not a decrease.

In most cases this will be obvious from the start, as with a percentage decrease your original figure will be of greater value than the new figure.

It’s always worth checking though before finalising your answer.

To recap:

Original number - new number = x

x ÷ original number = y

y x 100 = percentage change

A positive result indicates a percentage decrease, a negative result indicates a percentage increase.

## Example questions

Below you’ll find two example questions presented as word problems. The figures are not necessarily mentioned in the right order, so be sure to read the question carefully before applying the formula.

### Example question 1

In 2020, a town had a total population of 17,560. Three years prior, the town’s population was 20,410. What was the percentage decrease of the town’s population over the three-year time frame?

First, determine the order of the values. The original number here is the one given second: 20,410. And 17,560 is our new figure, so:

20,410 - 17,560 = 2,850

2,850 is the decrease of the town’s population. Now divide this by the original population:

2,850 ÷ 20,410 = 0.1396 (to four decimal places)

Multiply this by 100 to determine the percentage decrease:

0.1396 x 100 = 13.96 (to two decimal places)

**Answer:** The town’s population had decreased by 13.96%

### Example question 2

A company’s sales figures indicate that in its first year of trading, it made a gross profit of £28,120. In its second year, gross profit had fallen to £21,950. What was the company’s drop in profit, expressed as a percentage decrease?

This time, our values are given in the correct order, so we subtract the second figure from the first:

28,120 - 21,950 = 6,170

Now take the difference in profit, and divide it by the profit made in year one:

6,170 ÷ 28,120 = 0.219 (to three decimal places)

Multiply this by 100 to express it as a percentage decrease:

0.219 x 100 = 21.94 (to two decimal places)

**Answer:** The company’s gross profit had fallen by 21.94%