Percentage Increase Formula

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Percentage Increase Formula

Percentage increase formula is the ratio of value increased to the original value and multiplied by 100. It is expressed in percentage. If there is an increase in the value of anything, then there is an increase in percentage.

The Percentage Increase Formula is given as,

Solved Example

Question:

What is the percentage change in the rent of the house if on the month of January it was Rs. 10,000 and in the month of March it is Rs. 15,000?

Solution:

We can clearly see that there is an increase in the amount of rent.

Here, Increased value = 15000 – 10000 = 5000

Original Value = 10000

Percentage Increase = (Increased Value ⁄ Original Value) × 100

= (5000 ⁄ 10000) × 100

= 50%

Hence, there is a 50% increase in the amount of rent.

Percentage Increase Formula

The percentage increase formula is used to compare the growth in a quantity from the initial value to its final value, over a period of time. Mathematically, this formula is represented as the difference between the final value and the initial value which is divided by the initial value and then multiplied by 100. Let us learn more about the percentage increase formula in this article.

What is Percentage Increase Formula?

Before learning more about the percentage increase formula, let us understand what percentage increase means. Percentage increase is the difference between the final value and the initial value, expressed in the form of a percentage. To calculate the percentage we need to have the initial value and the increased (new) value. Following this concept, the percentage increase formula is derived and expressed as: Percentage Increase = [(Final Value – Initial Value)/Initial Value] × 100. It should be noted that since the percentage has to be a positive quantity, we take the absolute value of the initial value.

How to Calculate Percentage Increase?

We know that percentage increase is expressed as the difference between the final value and the initial value which is divided by the initial value and then multiplied by 100. Let us understand how to calculate percentage increase with the help of an example.

Example 1: The production of sugar in a firm increases from 400 tons to 700 tons after a year. Find the percentage increase in the production of sugar.

Solution: Initial value = 400 tons; Final value = 700 tons

Percentage Increase = [Final Value – Initial Value)/Initial Value] × 100

= [(700 – 400)/400] × 100 = 75%

Therefore, the sugar production increased by 75%. In other words, the percentage increase in the production of sugar was 75%.

Example 2: The height of a tree increased from 10 ft to 15 ft after a year. Find the percentage increase in its height.

Solution:

The initial height of the tree = 10 ft.; the final height of the tree = 15 ft.

Using the percentage increase formula,

Percentage Increase = [(Final Value – Initial Value)/Initial Value] × 100.

= [(15 – 10)/10)] × 100 = (5 /10) × 100

= 50%

Therefore, the percentage increase in the height of the tree = 50%.

Use of the Percentage Increase Formula

The percentage increase formula helps in comparing how much a value has increased over time. This formula has many real-life applications like comparing the profit of a business after every year, or the percentage increase in the salary of a person, or the percentage increase in the production of goods, and many more. It gives us an idea about how much a quantity has increased compared to the initial value because it allows us to determine the relative scale of the increase. It shows that the percent increase between two given values is the difference between the final value and the initial value, which is expressed as a percentage of the initial value. Let us understand this with an example. Consider the profit earned by two businessmen for 2 years.

BusinessmenProfit in 2020Profit in 2021
Mark$10,000$15,000
Robert$30,000$35,000

We can see that the profit of both businessmen increased by $5,000 in the second year. Increase in profit for Mark’s business = 15000 – 10000 = $5000; Increase in profit for Robert’s business = 35000 – 30000 = $5000

Does this mean that they are growing at the same rate? No, because the growth has to be compared with the initial value. We use the percentage increase formula for this. Let us calculate the percentage increase for both of them separately using the percentage increase formula: Percentage Increase = [(Final Value – Initial Value)/Initial Value] × 100.

Percentage increase of profit in Mark’s business = [(15000 – 10000) / 10000] × 100 = (5000/10000) × 100 = 50%

Percentage increase of profit in Robert’s business = [(35000 – 30000 / 30000) × 100 = (5000/30000) × 100 = 16.67%

It means that Mark earned more profit than Robert.

Examples Using Percentage Increase Formula

Example 1: The price of Ken’s toy car increased from $15 to $20. Find the percentage increase in the price using the percentage increase formula.

Solution:

The initial value of the car = $15; the final value of the car = $20.

Using the percentage increase formula, Percentage increase = [(Final Value – Initial Value)/Initial Value] × 100.

= [(20 – 15) /15] × 100 = (5 /15) × 100

= (5 / 15) × 100

= 33.33%

Therefore, the percentage increase in the price of the toy car = 33.33%.

Example 2: What is the percentage increase in the rent of a house if in the month of November it was $200 and in the month of March it was $250?

Solution:

The initial rent = $200; the increased rent = $250

Using the percentage increase formula, Percentage Increase = [(Final Value – Initial Value)/Initial Value] × 100.

= [(250 – 200)/200] × 100 = (50/200) × 100

= (50/200) × 100

= 25%

Therefore, the percentage increase in the rent is 25%.

FAQs on Percentage Increase Formula

What is the Percentage Increase Formula?

The percentage increase formula is used to compare the growth in a quantity from the initial value to its final value, over a period of time. We know that percentage increase is the difference between the final value and the initial value, expressed in the form of a percentage. Mathematically, the formula is expressed as: Percentage Increase = [(Final Value – Initial Value)/Initial Value] × 100.

What is Percentage Increase in Math?

Percentage increase is the difference between the final value and the initial value, expressed in the form of a percentage. In other words, it is the difference between the final value and the initial value which is divided by the initial value and then multiplied by 100.

How to Calculate Percentage Increase between two numbers?

To calculate the percentage increase between two numbers, we use the formula, Percentage Increase = [(Final Value – Initial Value)/Initial Value] × 100. For example, the height of an apple tree increases from 15 ft to 18 ft in a year. In order to find the percentage increase in the height of the tree, we can use the given formula and substitute the values as: Final value = 18, initial value = 15. After substituting the values in the formula, we get, [(18 – 15)/15] × 100 = (3/15) × 100 = 20%. Therefore, the percentage increase in the height of the apple tree is 20%.

How to Calculate Percentage Increase in Salary?

In order to calculate the percentage increase in the salary of a person, we use the percentage increase formula, Percentage Increase = [(Final Value – Initial Value)/Initial Value] × 100. For example, the salary of a person increases from $700 to $1050 after a year. Here, the initial value = 700, the final value = 1050. Substituting the values in the formula, Percentage Increase = [(1050 – 700)/700] × 100 = (350/700) × 100 = 50%. Therefore, the percentage increase in the salary of the person is 50%.

What is the Percentage Increase from 20 to 25?

In the given question, the percentage increase can be calculated with the help of the percentage increase formula, Percentage Increase = [(Final Value – Initial Value)/Initial Value] × 100. Here, the initial value is 20 and the final value is 25. Substituting the values in the formula, Percentage Increase = [(25 – 20)/20] × 100 = (5/20) × 100 = 25%.

Example Problem: Percentage Increase

Last year your favorite jeans cost $36 per pair. This year they cost $45 per pair. What is the percentage increase in the price of these jeans from last year to this year?

Percentage Increase = [ (Final Value – Starting Value) / |Starting Value| ] × 100

45 – 36 = 9
9 / 36 = 0.25
0.25 × 100 = 25%

So the price of your favorite jeans increased by 25% from last year to this year.

What is the percent increase formula?

The percent increase formula is:

New number (value) – original number (value) = increase

Increase / original number (value) x 100 = percent increase

A percent increase refers to how much a percentage has gone up over time. In order to reach this number, you would need to find the difference between the original value and the final value, subtracting to find the exact total of the decrease. When you find that number, you need to calculate the percentage of change, as simply knowing the amount of the decrease may not provide you with the information you need to determine the scale of the change between the two numbers.

You might apply the percent increase formula to determine how a price of a particular product or item has changed in the last year or during another period of time.

Why is the percent increase formula important for business?

Calculating the increase in the form of a percentage is often used in a business setting when looking at the financial changes year over year. The result represents a degree of change over a period of time. You can use the percent increase formula for any quantity that relies on a measurement over time, although one of its most common uses is in investing. You can use this formula to track the changes of a security price or market value.

The result of the percent increase formula will tell you whether the value of something is going up or going down over time. A negative value indicates a decrease in the percentage, while a positive value shows an upward trend. If you are considering investing in a company, using the percent increase formula can help you determine how the value has changed over a set period of time. You can use the formula to calculate the percent increase in value over five years or even since the company first began.

Applying this formula will determine how the value of a company has changed, often based on its stock prices. A business balance sheet will often include comparative financial statements that indicate the prices of certain assets at various points in time, as well as the percent of increase or decrease of each asset over that period of time.

How to calculate percent increase formula

Calculating the percent increase formula involves applying the numbers into the basic formula outlined above. Follow these steps and plug in your own numbers to calculate the percent increase.

  1. To apply the formula, you must first determine the difference between the two values. For example, if you were calculating the percent increase of a security that cost $5 per share in 2010 and $50 per share in 2015, you would begin by deducting five from 50 to get the difference of 45. You would then take that number and divide it by the original value, or five, and multiple the total by 100.
  2. The formula to calculate the percent increase is:
    New number (value) – original number (value) = increase
    Increase / original number (value) x 100 = percent increase
  3. Inputting the numbers from the previous example produces a percent increase of each share of 900%, which indicates that the value of a single share of that stock increased by 900% in value between 2010 and 2015.
  4. If you want to calculate the percent decrease of a value, you can apply the same formula. If the example situation were reversed and the security cost per share was $50 in 2010 and $5 in 2015, you could use the same formula to calculate the percentage of decrease.
  5. Inputting the numbers from the previous example (5-50 = -45 [decrease], -45 / 50 x 100 = -90) shows a 90% decrease in the value.
  6. You may also utilize the percent increase formula when calculating changes between multiple values. For example, if you wanted to calculate the year-over-year change in rainfall in a particular area, you would use the data from two consecutive years at a time and plug in the numbers.
    2018: 35 inches of rainfall
    2019: 39 inches of rainfall
    2020: 34 inches of rainfall
    2018-2019 percent increase: 39-35 = 4 (difference)
    4 / 35 x 100 = 11.4% increase
    2019-2020 percent decrease: 34-39 = -5 (difference)
    -5 / 39 x 100 = -12.8% decrease

Examples of percent increase formula

Many industries rely on the percent increase formula to determine the change in a value over time. These examples indicate its usage in various applications.

Example 1

Robert worked 95 hours at his part-time job during the month of January. In February, demand increased and he worked 110 hours. To calculate the percent increase in his working hours between January and February, you would begin by deducting the original value from the new value, or 95 from 110, to get the increase of 15.

15 / 95 x 100 = 15.8% increase in working hours from January to February

The company Robert works for slowed down in March, resulting in a cutback in his hours. He worked 75 hours in March and is looking at the percent decrease in hours worked between February and March. To calculate this number, you would deduct the original value of 110 from 75, to get the decrease of

-35 / 110 x 100 = -31.8% decrease in hours worked from February to March

Example 2

A box of candy contains 144 pieces of candy, and a store sold 44 of those pieces of candy in one day. The percent decrease of the box of candy is 30.5%.

-100 (difference) / 144 (original value) x 100 = -30.5%

Example 3

The value of a share of Apple stock was $110 in 2017 and $240 in 2020. In order to calculate the percent increase of a single stock share, you would begin by calculating the difference between the original value and the new value, or 130.

130 (difference) / 110 (original value) x 100 = 2000% increase in stock share price

Percentage Increase Calculator

The percentage increase calculator is a useful tool if you need to calculate the increase from one value to another in terms of a percentage of the original amount. Before using this calculator, it may be beneficial for you to understand how to calculate percent increase by using the percent increase formula. The upcoming sections will explain these concepts in further detail.

How to calculate percent increase

The concept of percent increase is basically the amount of increase from the original number to the final number in terms of 100 parts of the original. An increase of 5 percent would indicate that, if you split the original value into 100 parts, that value has increased by an additional 5 parts. So if the original value increased by 14 percent, the value would increase by 14 for every 100 units, 28 by every 200 units and so on. To make this even more clear, we will get into an example using the percent increase formula in the next section.

🙋 While the percentage increase calculator is important in mathematics, it is also useful in science, such as calculating the percent increase in mass of a chemical element in a compound.

Percent increase formula

The percent increase formula is as follows:

Percent increase = [(new value - original value)/original value] * 100

An example using the formula is as follows. Suppose a $1,250 investment increased in value to $1,445 dollars in one year. What is the percent increase of the investment? To answer this, us the following steps:

  1. Identify the original value and the new value.
  2. Input the values into the formula.
  3. Subtract the original value from the new value, then divide the result by the original value.
  4. Multiply the result by 100. The answer is the percent increase.
  5. Check your answer using the percentage increase calculator.

Working out the problem by hand we get:

  1. [(1,445 - 1,250)/1,250] * 100
  2. (195/1,250) * 100
  3. 0.156 * 100
  4. 15.6 percent increase.

The percentage growth calculator is a great tool to check simple problems. It can even be used to solve more complex problems that involve percent increase. You may also find the percentage calculator is also useful in this type of problem.

Calculating percent decrease

If you want to know how to calculate percent decrease, we follow a very similar process as percent increase. Notice the slight modification of the formula:

Percent decrease = [(original value - new value)/original value] * 100

Suppose we have the same investment value after one year of $1,445. A year later the value decreased to $1,300. The percent decrease would be calculated as follows:

  1. [(1,445 - 1,300)/1,445] * 100
  2. (145/1,445) * 100
  3. 0.10 * 100 = 10 percent decrease

FAQ

Where is percentage increase useful?

Percentage increase is useful when you want to analyse how a value has changed with time. Although percentage increase is very similar to absolute increase, the former is more useful when comparing multiple data sets. For example, a change from 1 to 51 and from 50 to 100 both have an absolute change of 50, but the percentage increase for the first is 5000%, while for the second it is 100%, so the first change grew a lot more. This is why percentage increase is the most common way of measuring growth.

How do I calculate percentage increase over time?

  1. Divide the larger number by the original number. If you have already calculated the percentage change, go to step 4.
  2. Subtract one from the result of the division.
  3. Multiply this new number by 100. You now have the percentage change.
  4. Divide the percentage change by the period of time between the two numbers.
  5. You now have the percentage increase over time. Remember that the units will be % / [time], where time is the units you divided by, e.g. s for seconds, min for minutes etc. Please note that this does not take into account compounding.
  6. For linear plots, multiply this number by any time difference to get the percentage change between the two times.
  7. For non-linear plots, just replace the larger number with your equation and solve algebraically. This will only find the percentage change between a number you input and the original number.

How do I add a percentage increase to a number?

If you want to increase a number by a certain percentage, follow these steps:

  1. Divide the number you wish to increase by 100 to find 1% of it.
  2. Multiply 1% by your chosen percentage.
  3. Add this number to your original number.
  4. There you go, you have just added a percentage increase to a number!

How do I add 5% to a number?

  1. Divide the number you wish to add 5% to by 100.
  2. Multiply this new number by 5.
  3. Add the product of the multiplication to your original number.
  4. Enjoy working at 105%!

How do I add two percentages?

To add two percentages together follow these steps:

  1. Calculate the first percentage by dividing the number you wish to find the percentage of by 100.
  2. Multiply the result by the percentage in its percentage form (e.g. 50 for 50%) to get the percentage of the original number.
  3. Repeat steps 1 & 2 for the other number.
  4. Add these two numbers together to get the addition of two percentages.
  5. If the number you wish to find the percentage of is the same for both percentages, you can just add the two percentages together and use this new percentage to get the result of the addition.

How do I calculate a 10% increase?

  1. Divide the number you are adding the increase to by 10.
  2. Alternatively multiply the value by 0.1.
  3. Add the product of the previous step to your original number.
  4. Be proud of your mathematical ability!

What is a 50% increase?

A 50% increase is where you increase your current value by an additional half. You can find this value by finding half of your current value and adding this onto the value. For example, if you wanted to find what a 50% increase to 80 was, you’d divide by 2 to get 40, and add the two values together to get 120. A 50% increase is different to a 100% increase, which is double the original value.

How do I calculate percentage increase in Excel?

While it’s easier to use the Omni Percentage Increase Calculator, here are the steps to calculate discount rate in Excel:

  1. Input the original number (for example into cell A1).
  2. Input the increased number (for example into cell B1).
  3. Subtract the original number from the increased number (In C1, input =B1-A1) and label it ‘difference’.
  4. Divide the difference by the original price and multiply it by 100 (In D1, input =(C1/A1)*100) and label it ‘percentage increase’.
  5. Right click on the final cell and select Format Cells.
  6. In the Format Cells box, under Number, select Percentage and specify your desired number of decimal places.

How do I add 20% to a number?

  1. Divide the original number by 100 to get 1% of it.
  2. Multiply 1% by your desired percentage, in this case 20.
  3. Add the product of the previous step to your original number.
  4. Congratulate yourself on adding 20% to your number!

About Percentage Increase

When you compare how much any value has increased over the time, you will first need to find out the difference between the initial values and the final values for finding the exact amount of this increase by subtracting them. By taking the hypothetical example, let’s understand this better. During the winters of 2010 – 2011, the Paris city received around 26 inches of snowfall in total while in the winters of 2011 – 2012, 54 inches of snow in total. Thus the amount of snow which increased from one winter to the next is 27.9 inches. However, when we only know the value of this increment, it is not going to tell that much as the relative scale of this increase isn’t well known. However, the percent increase which was done between any two values is the difference between any final value and an initial value which is being expressed as a percentage of the initial value. 

How to Calculate Percentage Increase?

For finding the percentage increase, firstly we have to subtract the initial value from the final value. Then you have to take this difference and divide this difference by the initial value. Then at last, you have to multiply this answered number by 100% for converting this number to a percentage. The final result will represent the percentage increase between these two values.

It is very important to keep in mind that you can find the percentage increase between the both of the two numbers and the two percentages as the calculation is being done in the same way as it is done with the percentages. In other words, you can still be able to follow the same steps for calculating the percentage increase between the two numbers, if the initial value and the final values are percentages.

The Formula for Percentage Increase

The formula which is used in calculating the percentages with the fraction value is as follows – for converting the fraction to a value in percentage, we need to divide the concerned value by the total value and multiply the whole by 100.

The formula of percentage increase is the ratio of the ratio of the value which is increased to the original value, and which is further multiplied by 100. It is being expressed in the terms of percentage. If we find any increase in the value of any value, then there will definitely be an increase in the percentage.  

For calculating the percentage increase, we have to follow the following steps:

  1. In the first step, we need to work out the difference which is the increase between the two numbers which we are comparing with each other. It means that the increase is equal to the new number subtracted by the original number.
  2. In the second step, we have to divide the increase by the original number and need to multiply the answer by 100. It means that the percentage increase is equal to the increase divided by the original number and the whole is multiplied by 100.

Formula of Percentage Change

There are two different types of the percentage change. They are

  • Percentage Increase
  • Percentage Decrease

The percentage increase formula is the increased value divided by the original value and further multiplied by 100. It is expressed in terms of percentage. If value is  increased, then there is an increase in percentage.

Thus to calculate the percentage increase we will follow two steps:

Step-1: Calculate the difference i.e. increase between the two numbers.

i.e. Increase = New Number – Original Number

Step-2:  Divide the increased value by the original number and further multiply the answer by 100.

Formula to calculate percentage increase

Percentage Decrease Formula

The percentage decrease formula is the decreased value divided by the original value and further multiplied by 100. It is expressed in terms of percentage. If there is a decrease in the value, then there is a decrease in percentage.

Thus to calculate the percentage decrease we will follow two steps:

Step-1: Calculate the difference i.e. decrease between the two numbers.

i.e. Decrease = New Number – Original Number

Step-2:  Divide the decrease value by the original number and multiply the answer by 100.

Solved Examples

1. What is the percentage change in the rent of the house if in the month of January it was Rs. 10,000 and in the month of March it is Rs. 12,000?

Solution: We can see here that there is an increase in the value of rent.  Therefore the percentage increase will be given as:

=20%

Hence, there is a 20%  net increase in the value of rent.

2. The volume of an ice cube is 216cm³. Its volume decreased by 25% after an hour. Find the volume of the remaining ice.

Solution: New volume = original volume x (100% – percentage decrease)

= 216 x (100% – 25%)

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