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How to Calculate Percentage Change – Video & Lesson Transcript

Maria Airth, Yuanxin (Amy) Yang Alcocer

Learn the percentage increase and decrease formula and how to calculate percentage change. Look at examples of percentage growth and percentage reduction. Updated: 06/22/2021

• Percentage Increase and Decrease
• How to Calculate Percentage Change
• Examples of Percentage Increase and Decrease
• How to Reverse Percentage Increase and Decrease
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## Percentage Increase and Decrease

The degree to which a value increases expressed in percent form is known as percentage increase. Alternatively, percentage decrease is the percentage degree to which the measure of an item decreases. These two measures are known, collectively, as percentage change.

For example, a scientist may want to monitor a population of endangered frogs in a certain pond. Rather than just record the number of frogs present at various times to see if the number is higher or lower, it would be more useful to know by how much the total population is increasing or decreasing.

If the scientist notices that the total population has increased since the last count, he could calculate the percentage increase, or percentage growth, to find the exact amount of increase. If the population has decreased since the last count, the scientist could calculate the percentage decrease, or percentage reduction, to know exactly how much the number has declined. Knowing the percentage change will give the scientist a better idea of whether the frogs are thriving or struggling in that environment.

Whether the comparison involves the value of stocks, the cost of goods, or the number of endangered animals in a particular ecosystem, percentage change formulas allow the user to calculate both percentage increase and decrease quickly.

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## Percentage Changes

Changes happen every day. Like, one day the temperature outside can be nice and warm, and you wear a shirt and shorts to go play outside. But, then the next day can be cold, and you end up wearing your grandma’s sweater with pants. In business, important changes, such as less sales one year compared to the previous year, need to be analyzed. To help businesses analyze these changes, we calculate the percentage increase or decrease, the amount of increase or decrease expressed as a percentage.

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## How to Calculate Percentage Change

It is important to know how to calculate percentage change. Percentage change information is much stronger for comparisons than simple calculations of numbers.

To understand this concept, consider an investment decision to be made between Company A and Company B. The current values of the companies are very different, so it is hard to compare them directly (an apples and oranges scenario). However, using percentage change formulas, it is easy to turn the data into something directly comparable.

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### Finding the Increase and Decrease

Continuing to consider Company A and Company B, Company A stock has increased from \$125 to \$150 in the last twelve months while Company B stock has increased from \$1250 to \$1350.

Since both values have risen over the time period in question, the percentage change calculation will be a percentage increase or percentage growth calculation.

The steps to calculate percentage change are:

1. Find the difference between the original and new values.
2. Divide the difference by the original value.
3. Multiply the resulting quotient by 100.
4. If the result is positive, format the result as a percentage increase. If it is negative, format it as a positive percentage and identify it as a percentage decrease.

Here is how to calculate percentage increase for both Company A and Company B:

• Company A: find the difference between the current stock value and the past stock find then divide by the original value. Finally, multiply by 100 to format the answer as a percent. So, we have eqdfrac150-125125 times 100 = 20text% /eq
• Company B: find the percentage growth in the same manner to get, eqdfrac1350-12501250 times 100 = 8text% /eq

Notice that Company A had a percentage growth of 20%, while Company B, which had a larger absolute difference between values, actually had a much smaller percentage growth of only 8%. Company A would be seen as the stronger investment because its percentage growth is higher than that of Company B.

Finding percentage decrease entails finding the difference between the original price and the new price, then dividing by the original price and multiplying the result by 100.

### Percentage Increase and Decrease Formula

Essentially, the formulas for percentage increase and percentage decrease are the same. The general formula is:

If the percent change value is positive, the answer represents a percentage increase. If the value is negative, it can be written as a positive and identified as a percentage reduction.

For example, if the value of a single share in a company dropped from \$2.00 to \$1.90, this would represent a -5% percentage change or a 5% percentage reduction.

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The direct percentage decrease formula is:

Notice that this formula is basically the same formula with the only change being that the difference is calculated in such a way as to end with a positive number; it is still the difference divided by the original value with that quotient multiplied by 100.

## Examples of Percentage Increase and Decrease

The best way to learn a new mathematical concept is to practice. Percentage change problems are best approached using real-world examples. Here are some examples to help you practice how to do percentage change problems.

### Example 1

The housing market has seen a drastic decline in recent years. Five years ago, houses in Neighborhood C averaged \$1,350,000. Today, the average property value in the same neighborhood is \$1,150,000. What is the percentage reduction in property value for this neighborhood?

This is a percentage reduction problem so the formula can be formatted like this:

eqbeginalign textPercentage reduction &= dfrac1,350,000-1,150,0001,350,000 times 100 \ &\ &= dfrac200,0001,350,000 times 100 \ &\ &= 0.1481 times 100 \ &\ &approx 14.8text% endalign /eq

The percentage reduction for the area is approximately 14.8%

### Example 2

Scientists are concerned about the population growth rate of an invasive species of mushrooms in Forest M. If the population growth rate is higher than 55% the scientists must start an eradication program in the area. The original sample found 1125 mushrooms and the most recent sample found 1800 mushrooms. Will an eradication program be needed?

This is a percentage increase problem since the new number is higher than the original number. Set up the problem like this:

eqbeginalign textPercentage increase &= dfrac1800-11251125 times 100 \ &\ &= dfrac6751125 times 100 \ &\ &= 0.6 times 100 \ &\ & = 60text% endalign /eq

The percentage growth amount is 60%, which is higher than the maximum allowed 55% growth; thus, an eradication program must begin.

## How to Reverse Percentage Increase and Decrease

Sometimes it is necessary to work backward to find the original value from the new value and the percentage increase or decrease. This might happen when trying to calculate the original cost of a car prior to a discount deducted from the price. For instance, assume a car is being sold for \$15,000 and the salesman states this represents a 25% discount (percentage decrease) on the original price.

It is tempting to just reverse the previous steps, but that will not work.

To find the original price follow these steps:

1. Subtract the percentage from 100 (since it is a decrease in price. An increase in price would need to be added to 100).
2. Convert the resulting percentage into a decimal (by dividing by 100).
3. Divide the given price (new value) by the percentage in decimal form to arrive at the original price.

For the car example:

1. 25% discount means 100-25 = 75%
2. 75% = 0.75
3. 15,000/0.75= \$20,000.

The car originally cost \$20,000 before the discount.

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## Lesson Summary

Percentage change is a measure of the degree to which a value has changed, either increased or decreased, over time presented in percent form. In the case of percentage increase the change represents an increase in the overall value of the measured item and can be said to represent its percentage growth. Alternatively, percentage decrease represents percentage reduction, or the amount a measured item decreases in overall value over time.

To find percentage change, follow these steps:

1. Find the difference between the original and new values.
2. Divide the difference by the original value.
3. Convert the resulting decimal into percent form.

Reversing percentages requires altering 100% either up or down depending on the direction of the reversal, converting the new percentage into a decimal, and then dividing the given value by the decimal version of the percent.

## How to Calculate

How do we calculate this percentage increase or decrease? We begin by first calculating the first total and then comparing it to the second total. For example, if we are analyzing the change in sales from one year to the next, our first total will be the sales of the one year, and our second total will be the sales of the next year. We then determine if there is an increase or decrease happening. For example, we have an increase if the second total is greater than the first and we have a decrease if the second total is lower than the first.

Once we have determined whether the change is an increase or decrease, we then calculate how much the change is by subtracting the lesser from the greater. We then divide it by the first total. To find the percentage, we then multiply by 100.

We can write a simple formula for the percentage increase or decrease. We can say that the percentage increase or decrease is (the increase or decrease) / (first total) * 100.

No matter what problem we are given, as long as we are able to find the first total and the amount of increase or decrease, then we can calculate the percentage increase or decrease. Let’s take a look at a couple of examples.

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## Example 1

A pet store owner is analyzing his sales for this month. He wants to compare it to his sales last month. He doesn’t know if his sales increased or decreased. He also wants to find out by how much his sales increased or decreased. The numbers he has available to work with are the following:

Month 1 Sales Month 2 Sales
Puppies: \$400 Puppies: \$300
Kittens: \$700 Kittens: \$900
Fish: \$100 Fish: \$50
Small Animals: \$200 Small Animals: \$250

Looking at his numbers, we see that we first have to find the total for each month. So, for each month, we add up all the sales.

• For month one, we have 400 + 700 + 100 + 200 = 1400. So, month one gave the owner a total of \$1,400.
• For month two, we have 300 + 900 + 50 + 250 = 1500. So, month two has a total sales of \$1,500.

Comparing these two totals with each other, we see that month two has a total greater than month one. So, we have an increase going on. How much is our increase? \$1,500 is \$100 greater than \$1,400. So, our increase is \$100.

To find our percentage increase then, we divide our 100 by our month one total. We get 100/1400 = 0.0714. Multiply this by 100, we get a percentage of 7.1%. So our sales increased by 7.1%. And we are done!

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## Example 2

This time, we have a teacher looking at her attendance charts. She wants to know if the attendance this week is better than the attendance last week. She wants to know because this week, she changed her teaching approach to a more humorous one. The previous week, she was very serious and didn’t allow any fooling around. Looking at her records, she sees that the previous week, she had an attendance record of 95%. This week, her attendance record is 90%. Do we have an increase or decrease?

We have a decrease since the second total is lower. How much is our decrease? We have 95 – 90 = 5. We decreased by five percent. How much of a percentage decrease is this? We divide our 5 / 95 * 100. We get approximately 5.3%. So, we have a percentage decrease of 5.3%. And we are done.

Notice here that in this problem we are already dealing with percentages. But our process is still the same. So, as long as we have the same format of our totals, then we use the same process regardless if the numbers are already percentages or not.

## Lesson Summary

Let’s review what we’ve learned. A percentage increase or decrease is the amount of increase or decrease expressed as a percentage. To calculate it, we first calculate the first total and then the second total. If we are comparing two consecutive years, the first year gives us the first total, and the second year gives us the second total. Then we determine if there is an increase or decrease happening. Then we calculate the amount of this increase or decrease. To find the percentage, we divide the amount of increase or decrease by the first total and multiply by 100.

## Learning Outcomes

By the end of this lesson you should be able to:

• State the formula for determining percent increase or decrease
• Calculate the percentage of increase of decrease

To unlock this lesson you must be a Study.com Member.

Video Transcript

## Percentage Changes

Changes happen every day. Like, one day the temperature outside can be nice and warm, and you wear a shirt and shorts to go play outside. But, then the next day can be cold, and you end up wearing your grandma’s sweater with pants. In business, important changes, such as less sales one year compared to the previous year, need to be analyzed. To help businesses analyze these changes, we calculate the percentage increase or decrease, the amount of increase or decrease expressed as a percentage.

## How to Calculate

How do we calculate this percentage increase or decrease? We begin by first calculating the first total and then comparing it to the second total. For example, if we are analyzing the change in sales from one year to the next, our first total will be the sales of the one year, and our second total will be the sales of the next year. We then determine if there is an increase or decrease happening. For example, we have an increase if the second total is greater than the first and we have a decrease if the second total is lower than the first.

Once we have determined whether the change is an increase or decrease, we then calculate how much the change is by subtracting the lesser from the greater. We then divide it by the first total. To find the percentage, we then multiply by 100.

We can write a simple formula for the percentage increase or decrease. We can say that the percentage increase or decrease is (the increase or decrease) / (first total) * 100.

No matter what problem we are given, as long as we are able to find the first total and the amount of increase or decrease, then we can calculate the percentage increase or decrease. Let’s take a look at a couple of examples.

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## Example 1

A pet store owner is analyzing his sales for this month. He wants to compare it to his sales last month. He doesn’t know if his sales increased or decreased. He also wants to find out by how much his sales increased or decreased. The numbers he has available to work with are the following:

Month 1 Sales Month 2 Sales
Puppies: \$400 Puppies: \$300
Kittens: \$700 Kittens: \$900
Fish: \$100 Fish: \$50
Small Animals: \$200 Small Animals: \$250

Looking at his numbers, we see that we first have to find the total for each month. So, for each month, we add up all the sales.

• For month one, we have 400 + 700 + 100 + 200 = 1400. So, month one gave the owner a total of \$1,400.
• For month two, we have 300 + 900 + 50 + 250 = 1500. So, month two has a total sales of \$1,500.

Comparing these two totals with each other, we see that month two has a total greater than month one. So, we have an increase going on. How much is our increase? \$1,500 is \$100 greater than \$1,400. So, our increase is \$100.

To find our percentage increase then, we divide our 100 by our month one total. We get 100/1400 = 0.0714. Multiply this by 100, we get a percentage of 7.1%. So our sales increased by 7.1%. And we are done!

## Example 2

This time, we have a teacher looking at her attendance charts. She wants to know if the attendance this week is better than the attendance last week. She wants to know because this week, she changed her teaching approach to a more humorous one. The previous week, she was very serious and didn’t allow any fooling around. Looking at her records, she sees that the previous week, she had an attendance record of 95%. This week, her attendance record is 90%. Do we have an increase or decrease?

We have a decrease since the second total is lower. How much is our decrease? We have 95 – 90 = 5. We decreased by five percent. How much of a percentage decrease is this? We divide our 5 / 95 * 100. We get approximately 5.3%. So, we have a percentage decrease of 5.3%. And we are done.

Notice here that in this problem we are already dealing with percentages. But our process is still the same. So, as long as we have the same format of our totals, then we use the same process regardless if the numbers are already percentages or not.

## Lesson Summary

Let’s review what we’ve learned. A percentage increase or decrease is the amount of increase or decrease expressed as a percentage. To calculate it, we first calculate the first total and then the second total. If we are comparing two consecutive years, the first year gives us the first total, and the second year gives us the second total. Then we determine if there is an increase or decrease happening. Then we calculate the amount of this increase or decrease. To find the percentage, we divide the amount of increase or decrease by the first total and multiply by 100.

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## Learning Outcomes

By the end of this lesson you should be able to:

• State the formula for determining percent increase or decrease
• Calculate the percentage of increase of decrease

To unlock this lesson you must be a Study.com Member.

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#### How do you calculate percentage increase?

First, find the difference between the new value and the original value. Then divide the difference by the original value. Finally, convert the resulting decimal into percentage form.

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#### How do you calculate percentage decrease?

1. Original value – new value = difference

2. Difference / original value = decimal change rate

3. Decimal change rate x 100 = percentage decrease

#### What is the percent change from 50 to 35?

To find the percentage change follow these steps:

1. Percentage change = (50 – 35)/50 x 100.

2. 15/50 x 100.

3. 0.3 x 100 = 30% percentage decrease.

#### What is the percent change from 5 to 6?

The percentage change will be a percentage increase since the number is rising from 5 to 6.

Step 1: 6-5 = 1

Step 2: 1/5 = 0.2

Step 3: 0.2 x 100 = 20% percentage increase.

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