# Percentage Increase Formula

View Notes

### What is Percentage?

To recall we know what is percentage? Percentage means any number ‘by the hundred’ or ‘divide by one hundred’. The percentage is used to compare quantities, it means quantity ‘per 100’. So when you say 100% of something, it means you are talking of the whole.  Percentage formula is used to find the share percentage of something in terms of the whole (100%). To calculate the percentage rise formula we have to first work out the difference (increase) between the two numbers you are comparing.

Increase = New Number - Original Number

Then divide the increase value by the original number and further multiply the answer by 100.

So We Get the Percentage Increase Formula as:

Percentage Increase = $\frac{Increase}{\text{Original Value}}$$\times100$

If you get the answer as a negative number, then this is a percentage decrease.

### Percentage

A percentage is a part of the whole.Percent means per hundred. It is represented as  “pct” or “pc”.Percentage is denoted by the symbol ‘%’, the percentage is majorly used to compare and find out ratios.

The Formula for Calculating Percentages

Percentage is equal to the actual value divided by the total value multiplied by 100.

The percentage formula is:

Percentage % = $\frac{\text{(Actual Value)}}{\text{(Total Value)}}$$\times100$

Some other important percentage formula of percentage change are

• Percentage change formula

• Percent Increase

• Percent Decrease

• Percentage error formula

Formula of Percentage Change

Percent Change =  [(New value – actual Value)/ actual value)] x 100

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

• Percentage Increase

• Percentage Decrease

### Percentage Increase Formula

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 Increase = $\frac{Increase}{\text{Original Value}}$$\times100$

### 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.

Percentage Decrease = $\frac{Decrease}{\text{Original Value}}$$\times100$

### Solved Examples

Example 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:

So, Increase in Percentage = $\frac{\text{Increased Value}}{\text{Original Value}}$$\times100$

Thus increased value = 12000 - 10000 = 2000

Original Value = 10000

Percentage increase = 2000/10000 x 100

= 2/10 x 100

=20%

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

Example 2: the volume of an ice cube is 216cm3. Its volume is 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%)

= 216 x 75/100

= 162 cm3

The volume of the remaining ice is 162cm3.

### Quiz Time

1. Soham’s weight decreased from 75 kg to 60kg. Find the percentage decrease in his weight.

2. Arpita’s monthly salary increased from rs. 20,000 to 25,000. Calculate salary increment percentage.

1. How to Convert Ratio to Percentage?

Answer: When you want to turn a ratio into a percentage, you must just take one part to compare against the whole. For example, you could find out the percentage of a student in semester one in the following steps:

The given ratio is 586:600

Step 1: Write a New Fraction

convert the given ratio into fraction.

Because percentages compare one part against the whole, you can write the total marks of a student scored in the examination with the total number of marks.

We have,
586 (total marks scored) / 600  ( total marks)
It could also be written as 586:600

Here you're comparing one part against the whole.
Step 2: Work the Division

Divide the fraction.

586 600

600

= 0.9766666

Rounding up

= 0.98

Step 3: Convert the Decimal to a Percentage

Multiply the result of Step 2 by 100 to convert it into a percentage.
0.98 × 100 = 98%

So the student scored 98% in semester one.

2. How to Calculate the Percentage of a Number?

Answer: Generally, the numbers that are converted into percentage are given in   two formats.

• Decimal Form- If the number is given in decimal form, it is easy to find the percentage. To obtain the percentage, multiply the given decimal number by 100. For example, the given number is 0.85. To convert into a percentage, 0.85 * 100 = 85%

• Fraction Form- If the number is given in fractional format, first convert into decimal value by dividing the numerator by the total value and then multiply with 100.