Before understanding how to calculate the percent, let us know what a percent is.
What’s The Percentage Of A Number?
The term “percentage or percent” was adapted from the Latin word “per centum”, which implies “by the hundred”. A number or a ratio expressed in terms of fractions of 100 is known as a percentage.
The abbreviation used to represent the percentage is “pct” or “pc”.
It is represented by the symbol “%”. In other words, the percentage is defined as how much of one quantity is made by the different quantity, and it is evaluated at about 100. Or we can say that it is the relation between part and whole where the value of the whole is always taken as 100.
Example:- If Sameer scored 40% marks in his math test, it means that he scored 40 marks out of 100. It is written as 40:100 in terms of ratio and 40/100 in the fraction form.
How to Calculate Percentages Using Formula
We can use the formula to calculate the percentage quickly and easily. The formula of percentage is equal to the ratio of the actual value to the total value multiplied by 100. The formula of percentage is:
Percentage, % = (Actual Value / Total Value) × 100
Example: What is 25 of 200?
Solution: As we know that, Percentage, % = (Value / Total Value) × 100
% = (25/200) × 100
Divide the numerator by denominator;
= (1/8) × 100
= 100/8
= 25/2
= 12 .5 %
Hence, the answer is 12.5%
How to Calculate Percentage of Marks
How to calculate the percentage of marks obtained in exams is a question that arises in the minds of most of the students
Steps to find the percentage of marks :
Step 1: To divide the marks obtained in the examination by the maximum marks of the test.
Step 2: Multiply the result by 100.
Let us understand this concept with the help of an example in a better way.
If a student named Vijay scored 1156 marks in the examination out of 1500 marks. Calculate the marks % secured by Vijay.
No of marks scored = 1156
Maximum marks = 1500
% of marks =(1156/1500) × 100
% = 0.77 × 100
Therefore, the % of marks obtained by Vijay is 77%.
How to Calculate Percentage of a Number
There are many online calculators to find percentages, but percentages can be calculated manually by following these simple steps:
Determine the original format of the number to be converted to a percentage
Identify the original form of the number, i.e. decimal or fraction. The original form will define the following mathematical operation on the number. An example of a decimal number is 0.25, which may be the calculated ratio of the values we are comparing, while an example of a fraction is 4/15.
Carry out a mathematical process on the number to be convert a number into a percentage by carrying out a mathematical process
Perform the mathematical operation on the number. That means, if the given number is a decimal number, then leave it as it is but if the number is a fraction form convert it into decimal number i.e.
4/15 = 0.267
Multiply the answer of the mathematical procedure by 100
Multiply the result by 100 and the resulted value should be expressed in a percentage format.
0.267 × 100 = 26.7%.
Alternative Method:
Changing the number into a fraction with the denominator 100 is also a way to calculate the percentage of a number.
Example: Convert 4/20 to a percentage.
Solution: The given fraction is 4/20.
Let us convert the denominator to 100.
(4/20) × (5/5) = 20/100
Now, multiply the result by 100.
(20/100) × 100 = 20
Hence, 4/20 = 20%
Note: We can only use this method of calculating the percentage when the denominator is a factor of 100. Otherwise, we can use the basic method to calculate the percentage.
How to Calculate Percentage Change
Percentage change is frequently used for many purposes in finance to determine the change in the price of a security over time. Hereinafter laid down is the formula for solving a percentage change –
Percentage increase:
Firstly find out the difference (increase) between the two numbers you are comparing.
Increase = New Number – Original Number
To divide the increase by the original number and then multiply it by 100.
% increase or Percentage increase = (Increase ÷ Original No) × 100.
Percentage decrease:
Firstly find out the difference (decrease) between the two numbers you are comparing.
Decrease = Original Number – New Number
Then divide the decrease by the original number and multiply it by 100.
% Decrease or Percentage Decrease = (Decrease ÷ Original No) × 100
Example: Let us consider Ira, who bought shares of a stock at $45 per share on Jan. 2. On Feb. 2, the stock was worth $55.50 per share. By what percentage did Ira’s share value increase?
Solution: Firstly calculate the difference in price between the new and old numbers
$55.50 – $45 = $10.50
Then, divide the increase by the original (January) number
10.5 / 45 = 0.23
Multiply it by 100 and finally we get the percentage.
0.23 × 100 = 23
Hence, Ira’s stock increased 23%.
Difference Between Percentile and Percentage
In most cases, many individuals might get confused with percentile and percentage.
The following schedules determine the difference between percentile and percentage in detail.
- Percentiles cannot be written as ratios or proportions but Percentages can be written as ratios or proportions.
- Percentile is written in the form of xth but the percentage is written in the form of x%.
- Percentile is not a number out of 100 while the percentage represents the number out of 100.
- A percentile is a percentage of values that can be found below a specific value while a percentage is obtained by multiplying the ratio of two numbers by 100.
- Percentile is based on ranking numbers but the percentage is not based on ranking numbers.
- Percentile is based on the Comparison of one case with another but the percentage is based on only one case.
- Percentile relies on the normal distribution but the percentage does not rely on it.
Percentage Problems
These are variations related to percentage problems.
X is what percent of Y?
Written as an equation :
X = P% ? Y
Here, we want to solve the ‘what’ i.e. P%
By dividing both sides by Y to get P% on one side of the equation
X ÷ Y = (P% ? Y) ÷ Y
X ÷ Y = P%
Or, P% = X ÷ Y
Solve for P% using the percentage formula
P% = X ÷ Y
Example: 10 is what percent of 250?
Written using the formula P% = X ÷ Y
Here, X = 10, Y = 250
P% = 10 ÷ 250 = 0.04
Convert the decimal to percent
P% = 0.04 × 100 = 4%
Hence, 10 is 4% of 120
Y is what percent of X?
Written as an equation :
Y = P% ? X
Here, we want to solve the ‘what’ i.e. P%
By dividing both sides by X to get P% on one side of the equation
Y ÷ X = (P% ? X) ÷ X
Y ÷ X = P%
Or, P% = Y ÷ X
Solve for P% using the percentage formula
P% = Y ÷ X
Example: 36 is what percent of 720?
Written using the formula P% = Y ÷ X
Here, Y = 36, X = 720
P% = 36 ÷ 720 = 0.05
Convert the decimal to percent
P% = 0.05 × 100 = 5%
Hence, 36 is 5% of 720
What is X percent of Y ?
Written as an equation:
P = X% * Y
Here, we want to solve the ‘what’ i.e. X
Remember to 1st change % to decimal, dividing by hundred
Substitute the value into the formula and solve it
Example: What is 10% of 150?
Convert the question to an eq. using the % formula
P = X% * Y
Let Y = 150, X = 10%
So, the equation is
P = 10% * 150
Firstly convert percentage to a decimal 10/100 = 0.1
Substitute 0.1 for 10% in the equation and it becomes
P = 0.1 * 150
P = 15
Hence, 10% of 150 is 15
What percent of X is Y?
Written as a formula: P% * X = Y
The ‘what’ is P% that we want to find the result for
You are required to divide both the sides by X to get P % on 1 side of the formula
(P% * X) ÷ X = Y ÷ X gets transformed to P% = Y ÷ X
Solution: Solve for P% using the % equation
P% = Y ÷ X
Example: What percent of 25 is 20?
Written using the formula: P% = 20 ÷ 25
20 ÷ 25 = 0.8
Convert decimal to percent
P% = 0.8 × 100
P% = 80%
So 80% of 25 is 20
Example: What percent of 832 is 26?
Written using the formula: P% = 26 ÷ 832
26 ÷ 832 = 0.03125
Convert decimal to percent
P% = 0.03125 × 100
P% = 3.125%
So 3.125% of 832 is 26
Example: What percent of 109 is 23?
Written using the formula: P% = 23 ÷ 109
23 ÷ 109 = 0.2110091743
Convert decimal to percent
P% = 0.2110091743 × 100
P% = 21.10091743%
So 21.10091743% of 109 is 23
X out of X is what percent?
Written as an equation: X / X = P%
The ‘what’ is P% that we want to find the result for
Answer: Solve for P% using the % equation
P% = X/ X
Example: 13 of 13 is what percent?
Written using the formula: P% = Y / X
13 ÷ 13 = P%
13 ÷ 13 = 1
Convert decimal to % by multiplying by hundred
1 * 100 = 100%
13 ÷ 13 = 100%
So 13 of 13 is 100%
How to calculate 10 percentage of a no
Deploy the % equation: P% * X = Y
Example of the above percentage problem type: What is 10% of 150?
Convert the problem to an equation using the % equation : P% * X = Y
P is 10%, X is 150, so the formula is 10% * 150 = Y
Convert ten percent to a decimal by removing the % sign and dividing by hundred: 10/100 = 0.10
Substitute 0.10 for 10% in the formula: 10% * 150 = Y gets transformed to 0.10 * 150 = Y
Do the mathematics: 0.10 * 150 = 15
Y = 15
So 10% of 150 is 15
Double check your result with the original problem: What is 10% of 150? Multiply 0.10 * 150 = 15
What Percent/Percentage Is X Of Y
Here, is the formula to find the output for What Percent/Percentage Is X Of Y:
What Percent/Percentage Is X Of Y = (X/Y) * 100 %
Where X is the part and Y is the base, respectively.
Steps To Calculate What % Is X Of Y
To determine What % Is X Of Y, divide X by Y, and multiply the result by 100 to get the %. Remember that these no must be positive real numbers.
The complete step-by-step calculation for finding What % Is X Of Y is given below:
Step-1: First and foremost, take the formula for What % Is X of Y = (X/Y) * 100.
Step-2: Now apply the given input data i.e., X and Y in the percent equation.
Step-3: After performing all the mathematics calculations, you will get the final percent output.
Step-4: Finally, you have P% Is X Of Y.
What Percentage Of X Is Y?
You can find the X is what percentage of Y by using the direct formula X is what percentage of Y = (X/Y) * 100. Substitute the provided input values and obtain the corresponding result within a fraction of seconds.