Above you will find the most used percentage calculators. Further on this page you will also find more specific online calculators which show the calculation of discounts and percentage deviations and show the conversion from percentages to decimals or fractions.
Percentage formula and examples
In the following percentage formulas, the letter P always shows the percent and the letter V indicates the value from which we calculate the percentage. If there are two values, we make the distinction between V1 and V2.
1. Normal percentage calculation
This calculation answers the question: what is P percent of V?
The formula for this is: (P/100)*V
For example, what is 15% of 160? According to the formula we calculate (15/100)*160 = 0.15*160 = 24
2. Adding or subtracting a percentage
This calculation answers the question: add P percent to V or subtract P percent of V.
First we deal with how we can add percentages. Add P percent to the value V.
To add percentages the formula is: V + (P/100*V)
For example: add 25 percent to 280. According to the formula we can deduce: 280 + (25/100*280) = 280 + (0.25*280) = 350
The procedure to subtract a percentage is more or less similar. How can we deduct P percent of V?
To remove percentages the formula is: V - (P/100*V)
For example: subtract 20% of 240. After applying the above formula we get: 240 - (20/100*240) = 240 - (0.2*240) = 192
3. Calculating the percentage difference between two values
Our percentage calculator uses the following formula to calculate the percent difference between two values V1 and V2. V1 is the initial value and V2 is the end value.
percent change = ((V2-V1)/V1) * 100
With a positive result, we have a percentage increase.
With a negative result, we have a percentage decrease.
For example: what is the percentage increase between 45 and 79?
Subject to the application of the formula, we get: ((79-45)/45)*100 = 75.55%. So there is a percentage increase of 75.55%.
Other percentage calculators
Here are some less common questions regarding percentages:
The number V1 is what percentage of the number V2?
The number V1 is the percentage of P% of what?
Percentage formula and examples for these extra percentage calculators
1. The formula in case you want to know the answer to the question: V1 is what percentage of V2 is as follows:
P = (100/V2)*V1
For example: 16 is what percentage of 88? If we fill in the formula, we get: P = (100/88)*16 = 1.14*16 = 18.18
So the solution is: 16 is 18.18 percent of 88.
2. The formula for the answer to the second question: V1 is P% of what is just as easy:
X = (V1/P)*100
For example: 24 is 9% of what? The formula gives us the following result: X = (24/9) * 100 = 2.66 * 100 = 266
So the solution to this question is: 24 is 9% of 266.
Deviation in percentage
We may need the deviation in percentages (=percent error) when we compare a theoretical value with a measured value.
We can use the following as a formula for this percentage deviation:
Deviation in percent = 100* | measured value - theoretical value |/ | theoretical value |
We take the absolute value both in the numerator and in the denominator.
Converting percentages into decimal places or fractions
Converting percentages into decimal numbers is easy if you keep in mind that 100% is represented as the number 1.
Consequently, 50% corresponds to the number 0.5. The percentage of 16% corresponds to 0.16, and so on.
We can use the following formula: decimal = percent / 100
Proposing percentages as fractions follows the same formula or method.
For example 35% corresponds to the fraction of 35/100.
We can then simplify the fraction by dividing the numerator and denominator by the same number. If we divide the numerator and denominator of 35/100 by 5, we get the decimal form: 7 / 20. This is the simplest representation of this fraction since we can no longer divide the numerator and denominator by the same number.
To list the above clearly, we have created a useful table:
Discount calculation / Percent off
To calculate what amount corresponds to a certain percentage discount, you must perform a normal percentage calculation. You can do this with our percentage calculator.
The percentage formula for this is: discount = (P/100)*V
Where P is the percent of the discount and V is the price.
For example: if you get a discount of 13% on a price of 65 dollar, what is the amount of this discount? Discount = (13/100) * 65 = 8.45 dollar. The final price will therefore be: 59.51 dollar.
However, if you receive a discount from a certain amount on a total price, what is the discount percentage applied?
You can use this formula: P = (100/V2)*V1
For example: you get a discount of 12 dollars on a total price of 88 dollars. The discount percentage is then equal to (100 / 88 ) * 12 = 13.64 %
How to use our percentage calculator in the daily life: examples
1. Turnover tax
When purchasing a certain product, the turnover tax is 8 percent. Suppose that this 8 percent corresponds to the amount of 16 dollars.
What is the original price on which the sales tax was levied?
Eight percent equals the fraction of 8/100. If we simplify the fraction 8/100 by dividing the numerator and denominator by 4, we get 2/25.
We can find the solution to the problem through the following equation: 8/100 * X = 2/25 * X = 16
This means that X = 200.
2. Discount voucher for a certain amount
Suppose you want to buy a product for 35 dollars . However, you have a discount voucher of 5 dollars.
What percentage will you save by using the discount coupon?
We can solve this through the comparison: P / 100 * 35 = 5
By working out this comparison we find: P = 500 / 35 = 14.29%
3. Discount coupon of a certain percentage
Suppose you want to buy a new refrigerator and this refrigerator costs 360 dollars. However, through a publicity campaign you could seize a discount coupon of 12 percent. How much money can you save by actually using this voucher?
We can find the solution through the following comparison: 12/100 * 360 dollar = 43.2 dollar
4. Calculation of a tip
After a nice meal in a local restaurant, you want to leave a tip for the friendly service. A tip of 9 percent of the bill seems like a good idea. Suppose the bill for the meal is 89 dollar, what should be the amount of your tip?
This comparison gives us the solution: 9/100 * 89 = 8.01 dollar
5. Interest on a bond
You still have an old bond of 5000 dollars which yields 4 percent per year. What amount can you dispose of after 1 year?
After 1 year we receive an interest of 4 percent on top of the invested amount of 5000 dollars.
We can make the following calculation: 5000 + 4/100 * 5000 = 5000 + 200 = 5200 dollar.
6. Increase of percentage on a savings account
Suppose you have an amount of 450 dollar in your savings account at the bank. After 1 year this amount has risen to 465 dollar.
What is the percentage difference after 1 year?
percentage increase = ((V2-V1)/V1)*100 = ((465-450)/450)*100 = 3.33 %
7. Decrease of percentage after a price reduction
At the local furniture store an oak cupboard costs 420 dollar. However, the price drops to 360 dollar due to a closing sale.
What is the percent change between these two prices?
percentage decrease = ((V2-V1)/V1)*100 = ((360-420)/420)*100 = - 14.28 %
8. Difference between measured and actual values
Assume the measured value from a test is equal to 12.86 while the actual value is equal to 14.
What is the deviation in percentage (=percent error)?
We use the formula: 100*| measured value - theoretical value|/ |theoretical value| = 100*| 12.86 - 14 | / |14| = 8.14%
9. Deviation after rounding
Suppose a value of 5.2 is rounded down to 5. What is the percentage deviation due to rounding?
We apply this percentage formula: 100*| measured value - theoretical value|/ |theoretical value| = 100 * | 5 – 5.2|/ |5.2| = 3.85 %
For questions about this percentage calculator, you can contact us at this email address: firstname.lastname@example.org.