Percentage Calculator helps you in solving your percentage queries in a jiffy, along with an explanation describing the proper method or way to solve it, on your own.
Percentage problems include various formulas, the most common being X/Y = Px100.
This percentage calculator tool is the easiest to use. Select the formula or percentage value you need to find out from the drop down.
Then fill in the values asked. For instance, in the formula for ‘Y is P% of What?’, fill in the values for Y and P%, as required and click Calculate.
Once you click ‘Calculate’, you get the final result with a detailed description of the solution. This helps you understand the complete calculation and correct implication of the formula.
Just like ratios and fractions, percentage is also a way to express the relation of two numbers.
Percentages are widely used as they easily describe situations that include large numbers (like, chances of winning a lottery), average numbers (like, calculating your final grade), and small numbers (like determining the parts per million - PPM of NO2 in the air).
Generally, % sign is used as a percent sign, however, sometimes pct is also used to denote a percentage value. Whenever one wishes to know how much a number is bigger in relation to the other, percentages come into existence. Let’s take an example here.
For instance, if you want to calculate 30% of 20. It simply means to determine the 30 hundredths of 20. Mathematically, 30/100 * 20 = 6. With our percentage calculator tool, you can work with these percentages and decimal fractions with ease.
There are a few different ways to find the percentage of a number, depending on the information you have.
To find the percentage of a number, you can use the formula: (part/whole) * 100
To find the percentage of a number, you can also use the formula: (part/whole) * 100 = percentage
To find the percentage increase or decrease, you can use the formula: ((new value - old value) / old value) * 100
To find the percentage of a number, you can also use the formula: (part/whole) * 100 = percentage
There are various formulas to calculate percent values or related.
Here are some of the important formulas to determine the values and solve your queries.
The formula Y = P% * X
can be used to calculate the percentage of a number X.
P is the percentage expressed as a decimal (e.g. 25% is 0.25) and Y is the result of the calculation.
Example 1:
If X = 100 and P% = 25,
then Y = X * P% = 100 * 0.25 = 25
This means that 25% of 100 is 25.
Example 2:
If X = 500 and P% = 10,
then Y = X * P% = 500 * 0.1 = 50
This means that 10% of 500 is 50.
Example 3:
If X = 1000 and P% = 5, then Y = X * P% = 1000 * 0.05 = 50
This means that 5% of 1000 is 50.
Q1. A store is offering a 20% discount on all items. If a customer wants to buy a dress that costs $100, how much will the customer pay after the discount?
Solution:
Let X = 100 (cost of the dress) and P% = 0.20 (discount percentage)
Using the formula X * P% = Y, we can calculate the amount of discount as
Y = X * P% = 100 * 0.20 = 20
So, the customer will pay 100 - 20 = $80 after the discount.
Q2. A student scored 85% marks in a test. If the test had 20 questions, how many questions did the student answer correctly?
Solution:
Let X = 20 (number of questions in the test) and P% = 0.85 (percentage of marks scored by the student)
Using the formula X * P% = Y, we can calculate the number of questions answered correctly as Y = X * P% = 20 * 0.85 = 17
So, the student answered 17 questions correctly.
Q3. A company's profits increased by 50% from the previous year. If the profits were $500,000 last year, how much did the company make this year?
Solution:
Let X = 500,000 (profits last year) and P% = 0.50 (percentage increase in profits)
Using the formula X * P% = Y, we can calculate the increase in profits as Y = X * P% = 500,000 * 0.50 = 250,000
Therefore, the company's profits this year are 500,000 + 250,000 = $750,000
Q4. A recipe calls for 2 cups of sugar for every 5 cups of flour. How much sugar is needed for 8 cups of flour?
Solution:
Let X=5 (cups of flour) and P% = 2/5 (cups of sugar per cups of flour)
Using the formula X * P% = Y, we can calculate the amount of sugar needed as Y = X * P% = 8 * (2/5) = 3.2 cups
So, 3.2 cups of sugar is needed for 8 cups of flour.
The formula Y/X = P% can be used to calculate the percentage of a number X.
Y is the part of the whole and P% is the percentage expressed as a decimal.
Example 1:
If X = 100 and Y = 25, then
P% = Y/X = 25/100 = 0.25
This means that 25 is 25% of 100 when you convert decimal 0.25 to percent by dividing it by 100
0.25/100 = 25%
Example 2:
If X = 500 and Y = 50, then
P% = Y/X = 50/500 = 0.1
This means that 50 is 10% of 500.
Example 3:
If X = 1000 and Y = 50, then
P% = Y/X = 50/1000 = 0.05
This means that 50 is 5% of 1000.
You can also express P% in percentage form by multiplying with 100, P% = Y/X * 100
Q1. A student scored 75 out of 100 in a test. What percentage did the student score?
Solution:
Let X = 100 (total marks in the test) and Y = 75 (marks scored by the student)
Using the formula Y/X = P%, we can calculate the percentage as P% = Y/X = 75/100 = 0.75
Therefore, the student scored 75% in the test.
Q2. A car traveled 150 miles on 5 gallons of gasoline. What is the mileage of the car?
Solution:
Let X = 5 (gallons of gasoline) and Y = 150 (miles traveled)
Using the formula Y/X = P%, we can calculate the mileage as P% = Y/X = 150/5 = 30
Therefore, the car has a mileage of 30 miles per gallon.
Q3. A box contains 24 chocolates out of which 12 are dark chocolates. What percentage of chocolates are dark chocolates?
Solution:
Let X = 24 (total number of chocolates) and Y = 12 (number of dark chocolates)
Using the formula Y/X = P%, we can calculate the percentage as P% = Y/X = 12/24 = 0.5
Therefore, 50% of the chocolates in the box are dark chocolates.
Q4. A company's profits increased by $500,000 from the previous year. If the profits were $1,000,000 last year, what percentage increase in profits was there?
Solution:
Let X = 1000000 (profits last year) and Y = 500000 (increase in profits)
Using the formula Y/X = P%, we can calculate the percentage as P% = Y/X = 500000/1000000 = 0.5
Therefore, the company's profits increased by 50%.
The formula Y/P% = X can be used to calculate the whole number X based on the percentage P% and the part of the whole Y. P% is the percentage expressed as a decimal (e.g. 25% is 0.25).
Example 1:
If Y = 25 and P% = 0.25, then X = Y/P% = 25/0.25 = 100
This means that 25 is 25% of 100.
Example 2:
If Y = 50 and P% = 0.1, then X = Y/P% = 50/0.1 = 500
This means that 50 is 10% of 500.
Example 3:
If Y = 50 and P% = 0.05, then X = Y/P% = 50/0.05 = 1000
This means that 50 is 5% of 1000.
It is important to notice that this formula is similar to Y/X = P% where X is being calculated. This formula is useful when you know the part of the whole and the percentage but not the whole.
Also please note that if you want to express P% in percentage form, you need to multiply with 100.
Q1. A student scored 75 out of 100 in a test. What is the total marks of the test?
Solution:
Let Y = 75 (marks scored by the student) and P% = 0.75 (percentage scored by the student)
Using the formula Y/P% = X, we can calculate the total marks as X = Y/P% = 75/0.75 = 100
Therefore, the total marks in the test are 100.
Q2. A car traveled 150 miles on 5 gallons of gasoline. What is the total distance the car can travel with 20 gallons of gasoline?
Solution:
Let Y = 150 (miles traveled on 5 gallons) and P% = 5/150 = 1/30 (mileage of the car)
Using the formula Y/P% = X, we can calculate the total distance as X = Y/P% = 20 * (1/30) = 20/30 = 20/3 = 666.67 miles
Therefore, the car can travel 666.67 miles on 20 gallons of gasoline.
Q3. A box contains 24 chocolates out of which 12 are dark chocolates. How many chocolates are there in the box if 25% of them are dark chocolates?
Solution:
Let Y = 12 (number of dark chocolates) and P% = 0.25 (percentage of dark chocolates)
Using the formula Y/P% = X, we can calculate the total number of chocolates as X = Y/P% = 12/0.25 = 48
Therefore, there are 48 chocolates in the box.
Q4. A company's profits increased by $500,000 from the previous year. If the profits increased by 20%, what were the profits last year?
Solution:
Let Y = 500000 (increase in profits) and P% = 0.2 (percentage increase in profits)
Using the formula Y/P% = X, we can calculate the profits last year as X = Y/P% = 500000/0.2 = 2,500,000
Therefore, the company's profits last year were $2,500,000.
Please note that in the last example, you can express P% in percentage form by multiplying with 100, P% = Y/X * 100 = 0.2 * 100 = 20%.
The formula X * (1 + P%) = Y can be used to calculate the final value Y after an increase or decrease of a certain percentage P% on a starting value X. P% is the percentage expressed as a decimal (e.g. 25% is 0.25). The term (1 + P%) is known as the growth factor.
Example 1:
If X = 100 and P% = 0.25, then Y = X * (1 + P%) = 100 * (1 + 0.25) = 100 * 1.25 = 125
This means that an increase of 25% on 100 results in 125.
Example 2:
If X = 500 and P% = -0.1, then Y = X * (1 + P%) = 500 * (1 - 0.1) = 500 * 0.9 = 450
This means that a decrease of 10% on 500 results in 450.
Example 3:
If X = 1000 and P% = 0.05, then Y = X * (1 + P%) = 1000 * (1 + 0.05) = 1000 * 1.05 = 1050
This means that an increase of 5% on 1000 results in 1050.
This formula is useful when you want to calculate the final value after a percentage increase or decrease. It is also known as the percentage change formula.
Q1. A store is offering a 20% increase on the price of a product. If the original price of the product is $100, what is the new price after the increase?
Solution:
Let X = 100 (original price) and P% = 0.20 (percentage increase)
Using the formula X * (1 + P%) = Y, we can calculate the new price as Y = X * (1 + P%) = 100 * (1 + 0.20) = 100 * 1.20 = $120
Therefore, the new price of the product is $120.
Q2. An investor invested $1000 in a stock that decreased by 10%. How much did the investment decrease in value?
Solution:
Let X = 1000 (original investment) and P% = -0.10 (percentage decrease)
Using the formula X * (1 + P%) = Y, we can calculate the decrease in value as Y = X * (1 + P%) = 1000 * (1 - 0.10) = 1000 * 0.90 = $900
Therefore, the investment decreased in value by $100.
Q3. A company is offering a 5% raise to its employees. If an employee's salary is $50,000, what will be the employee's new salary after the raise?
Solution:
Let X = 50000 (original salary) and P% = 0.05 (percentage raise)
Using the formula X * (1 + P%) = Y, we can calculate the new salary as Y = X * (1 + P%) = 50000 * (1 + 0.05) = 50000 * 1.05 = $52,500
Therefore, the employee's new salary after the raise is $52,500.
Q4. A stock decreased by 15%. If it was worth $5000, what is its worth now?
Solution:
Let X = 5000 (original stock value) and P% = -0.15 (percentage decrease)
Using the formula X * (1 + P%) = Y, we can calculate the new value as Y = X * (1 + P%) = 5000 * (1 - 0.15) = 5000 * 0.85 = $4250
Therefore, the stock worth now is $4250
Please note that in the last example, P% is negative because the stock decreased in value.
It's important to understand that the value P% can be positive or negative depending on the scenario, representing an increase or decrease respectively.
The formula Y/1+P% = X can be used to calculate the original value X before a percentage increase or decrease, based on the final value Y and the percentage change P%. P% is the percentage change expressed as a decimal (e.g. 25% increase is 0.25, 10% decrease is -0.1) and (1+P%) is known as the percentage change factor.
Example 1:
If Y = 125 and P% = 0.25, then X = Y/(1+P%) = 125/(1+0.25) = 125/1.25 = 100
This means that an increase of 25% on 100 results in 125.
Example 2:
If Y = 450 and P% = -0.1, then X = Y/(1+P%) = 450/(1-0.1) = 450/0.9 = 500
This means that a decrease of 10% on 500 results in 450.
Example 3:
If Y = 1050 and P% = 0.05, then X = Y/(1+P%) = 1050/(1+0.05) = 1050/1.05 = 1000
This means that an increase of 5% on 1000 results in 1050.
This formula is useful when you want to calculate the original value before a percentage increase or decrease, It is also known as the inverse percentage change formula.
Q1. The price of a product was increased by 25%. If the new price is $125, what was the original price?
Solution:
Let Y = 125 (new price) and P% = 0.25 (percentage increase)
Using the formula Y/1+P% = X, we can calculate the original price as X = Y/(1+P%) = 125/(1+0.25) = 125/1.25 = $100
Therefore, the original price of the product was $100.
Q2. An investment decreased by 10%. If its current value is $900, what was its original value?
Solution:
Let Y = 900 (current value) and P% = -0.10 (percentage decrease)
Using the formula Y/1+P% = X, we can calculate the original value as X = Y/(1+P%) = 900/(1-0.10) = 900/0.9 = $1000
Therefore, the original value of the investment was $1000.
Q3. An employee's salary was increased by 5%. If the new salary is $52,500, what was the original salary?
Solution:
Let Y = 52500 (new salary) and P% = 0.05 (percentage increase)
Using the formula Y/1+P% = X, we can calculate the original
When you wish to calculate the percentage change from one number to the other, the Percent Change Calculator comes into action. This change is usually expressed as percentage increase or percentage decrease. For instance, first you had 10 cookies and now you have 20. Then you had a 100% increase in your cookies count.
This percentage change calculator only works if there is an initial and final value. Without any one, it is of no use. When the change is positive, it denotes the increase in percentage value and if the change is negative, it denotes the decrease in the value.
If the numbers’ order matters to you, then the percentage change calculator is used with the initial and final value.
The Percentage change is derived by dividing the change in value by the absolute value of the initial value and then multiplying it by 100. Let’s explain this in detail with an example.
Using the formula: (New value - Old value) / Old value * 100 = percent change
If the price of a product was $100 and it increased to $125, you can use the formula: (125 - 100) / 100 * 100 = 25%. This means that the price of the product increased by 25%.
For example, if a company's profits were $1 million last year and $1.2 million this year, you can use the formula: (1.2 - 1) / 1 * 100 = 20%. This means that the company's profits have increased by 20% this year.
if you have the current value and the original value and you want to find the percent change, you can use the formula: (New value - Old value) / Old value * 100
For example, if an employee's salary was $50,000 and now it's $52,500. you can use the formula: (52,500-50,000)/50,000 * 100 = 5%.
This means that the employee's salary increased by 5%
More Examples
Q1. If a product's original price was $100 and it's now $120, the percentage difference can be calculated as:
Solution - (|120 - 100| / (120 + 100) * 2) * 100 = (20 / 220) * 100 = 9.09%.
This means that the product's price has increased by 9.09%
Q2 - If a company's profit was $1,000,000 and it's now $900,000, the percentage difference can be calculated as:
Solution -(|900,000 - 1,000,000| / (900,000 + 1,000,000) * 2) * 100 = (100,000 / 2,000,000) * 100 = 5%.
This means that the company's profit has decreased by 5%.
Q3. If a stock was trading at $50 and it's now trading at $60, the percentage difference can be calculated as:
Solution - (|60-50| / (60+50) * 2) * 100 = (10 / 110) * 100 = 9.09%. This means that the stock has increased by 9.09%
The formula calculates the absolute difference between the two values. Therefore, the result is always positive.
With the Fraction to Percent Calculator, you can convert any proper and improper fractions to percentage.
Formula - Fraction * 100 = Percentage
This can be done in two easy steps:
2. Multiply the decimal value by 100 to get the percentage value.
This goes as it says. Multiply the decimal value, i.e. 0.75 by 100 to get the percent value, 75%.
0.75 x 100 = 75%
You can also reduce the fraction to the minimum value, before converting it to a decimal, to make the division easier. The final answer will be the same.
Examples
You can also convert a decimal to a percentage by multiplying it by 100 and adding the percentage sign(%). For example, 0.5 as a decimal is 50% as a percentage.
It's important to notice that if you are converting a fraction to a percentage, the fraction must be simplified first, otherwise, you will get an incorrect result.
The Percent to Fraction Calculator also helps in converting a percent to a fraction. When the percent value is more than 100%, it is first converted to a mixed fraction.
Formula - Percentage / 100 = Fraction
To convert the percent value to fraction, it is first converted into a decimal value and then into a fraction. The percent value can also be in decimal, for eg; 6.25% or 0.56%.
Converting a Percent to Fraction
Examples -
You can also convert a decimal to a fraction by dividing the decimal by 1 and expressing the result in the form of a fraction. For example, 0.5 as a decimal is 1/2 as a fraction.
It's important to note that when you convert a percentage to a fraction, the resulting fraction will be in its simplest form.
The Percent to Decimal calculator divides the percent value by 100 to convert it to the decimal value. You just input the percent value and it shows the result, which is a decimal value.
Formula - Percentage / 100 = Decimal
To convert a percent value to a decimal, you just divide the percent by 100 and remove the percentage sign. For instance, to convert 20% to a decimal, 20% becomes 20/100 = 0.20. An easier way to convert a percent to a decimal is that the percent sign be removed and the decimal point is moved 2 places to the left.
Examples -
If you have 25% and you want to know what decimal it is, you can use the formula: 25 / 100 = 0.25. This means that 25% is 0.25 as a decimal.
It's important to note that when you convert a percentage to a decimal, you always divide the percentage by 100.
It's also important to note that a decimal is a way of expressing a number in base 10, while a percentage is a way of expressing a proportion as a fraction of 100.
With the Decimal to Percent calculator, you can easily convert the whole number and even the decimal part of a number to a percent value.
Formula - Decimal x 100 = Percentage
To convert a decimal to percent, you just multiply the number by 100 and add the percent sign at the end. For instance, to convert 0.20 into percent, 0.20 becomes 0.20 x 100 = 20%. Similarly, 0.275 becomes 0.275 x 100 = 27.5%.
Another easier way to convert decimal to percent is to move the decimal point 2 places to the right and then add %.
Examples -
It's important to note that when you convert a decimal to a percentage, you always multiply the decimal by 100.
It's also important to note that a decimal is a way of expressing a number in base 10, while a percentage is a way of expressing a proportion as a fraction of 100.