To recall, we know what percentage is? 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 increased value by the original number and further multiply the answer by 100.
So we get the Percentage Increase Formula as:
Percentage Increase =
\[\frac{Increase}{original value}\] × 100
If you get the answer as a negative number, then this is a percentage decrease.
Percentage Definition
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 % = \[\frac{Actual Value}{Total Value}\] × 100
Some other important percentage formula of percentage change are
Percentage change formula
Percentage error formula
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:
- 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.
- 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
Percent Change = \[\frac{(New Value - Actual Value)}{Actual Value}\] 𝒙 100
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 Increase = \[\frac{Increase}{original value}\] × 100
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 = \[\frac{Decrease}{original value}\] × 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:
So, Increase in Percentage = \[\frac{Increased Value}{Original Value}\] × 100
Thus increased value = 12000 - 10000 = 2000
Original Value = 10000
Percentage increase = \[\frac{2000}{10000}\] × 100
= \[\frac{2}{10}\] × 100
=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%)
= 216 x \[\frac{75}{100}\]
= 162 cm³
The volume of the remaining ice is 162cm³.
Quiz Time
- Soham’s weight decreased from 75 kg to 60kg. Find the percentage decrease in his weight.
- Arpita’s monthly salary increased from rs. 20,000 to 25,000. Calculate salary increment percentage.
