# Percentage Calculator

Use this versatile percentage calculator to easily calculate the percentage difference between two numbers, to calculate percent change (percentage increase, percentage decrease), and to find out what % is a given number from any other given number.

## What is a percentage?

A **percentage** is a dimensionless number, represented as **a fraction of 100**, e.g. 50 out of 100 can be written as 50%, and 1 out of 10 can be written as 10%. A percentage is by definition a ratio. The sign for percent is "%", but the abbreviation "pct" is sometimes used in its place, while in older literature and documents one can encounter "per cent", where "cent" is an abbreviation of the Latin "centum" which literally means "one hundred", so the phrase means "per one hundred" - the literal definition of percentage.

Percentages have a wide array of application in many disciplines and everyday usage which is why having a percentage calculator can be very handy. They are common in statistics, social sciences, economics, finance, accounting. In everyday usage we often encounter percent off coupons. Promotions, sales, and various discounts are often expressed as percentage from a previous reference price of an item or service. Percentages can be used when measuring productivity or load of a person or machine, e.g. "he is working at 100%" (at maximum capacity).

Percentage increase or decrease are used to describe the relative **growth or decline** of something, e.g. a population, capital, personal wealth, etc. Differences between any two objects can be expressed as ratios or as percentage difference. The measurement error of a tool or process can be described in terms of percent error.

## How to calculate percent change?

**Percent change** calculations are common when comparing quantities, business metrics, or other measurements from **two time periods**, or when comparing a new state of things to an old state of things. Our percentage calculator is of great assistance for calculating **percent increase / decrease**, but you can also calculate percentage change on your own.

For example, say you are reviewing the performance of your business on a monthly basis and you see that the past month you had 80 customers while the month before you were able to acquire only 64. To find out the growth rate of your business you need to calculate percent change using the formula:

**Percent change = new / old * 100 - 100**

where **new** is the newer quantity or measure, and **old** is the older quantity or measure. In the above example this would be 80 / 64 * 100 - 100 = 1.25 * 100 - 100 = 125 - 100 = 25%. Your monthly percentage change (percent growth, percent increase) was thus 25 percent.

In another situation, you might be examining a proposition to increase your salary from $100,000 a year to $120,000 a year to keep you on the payroll and want to know what percent is the new salary versus your old one. You divide 120,000 by 100,000 to get 1.2, then multiply by 100 to get 120. Minus 100 leaves 20%. Therefore, you were offered a 20% increase of your salary and as the new salary is 120% of your current salary.

## How to calculate X is what percent of Y?

Let's say you are a car salesman and you have a car originally priced at $50,000, but you have done some calculation and determine that you can take $5,000 off the price of the car and still be ahead after the sale. How can you determine what percentage is $5,000 from $50,000? The formula to use is:

x is **x / y * 100** % of y

so in this case that would be 5,000 / 50,000 * 100 = 0.1 * 100 = 10%. If you were to offer a $5,000 discount on a $50,000 car, that would be a 10% discount.

In another example you might want to calculate what percentage of your total yearly income you have to pay in taxes. If your yearly income is $80,000 and you have calculated that your total tax amount is $36,000, then your tax rate is 36,000 / 80,000 / 100 = 0.45 * 100 = 45%, since $36,000 is 45 percent of $80,000. You can do all these calculations easily using our online percentage calculator.

## How to calculate percent difference?

**Percentage difference** of two numbers (quantities): **a** and **b** is calculated using the formula:

**Percent Difference = |a - b| / ((a + b) / 2) * 100** percent

For example, if one item costs $5 and another costs $6 the percent difference between them is: |5 - 6| / ((5 + 6) / 2) * 100 = 1 / (11 / 2) * 100 = 1 / 5.5 * 100 = 18.18%. Please, note that this doesn't mean that 5 is 18.18% smaller than 6, or that 6 is 18.18% larger than 5. The correct percentages if you are asking the question of "what percent is a from b" would be 16.66% and 20%, respectively, as explained above.

Percentage difference is useful in few situations, so it should be used with care. For example, one should not use it when comparing time periods, as the first metric is another state of the second metric, so percent change is the appropriate calculation. Similarly, calculating a price change should not be done using percentage difference.

## Compounding and averaging percentages

Percentages should not be added up (compounded) or averaged like simple numbers, as this will result in an incorrect end result. **Compounding** is often encountered in finance, e.g. when calculating compound interest or multi-year return of a financial portfolio. Averaging percentages is often encountered in business calculations, for example to determine the average growth of a company, but also in finance and banking where average growth of an asset or asset portfolio may be calculated.

Here is an example of **adding percentages**: say you have a $100,000 bank deposit at a 2% interest rate, applied yearly at the end of the year. If you keep it for 5 years, you might think that the way to calculate your deposit's value at the end of the 5-year period is to simply multiply 2% x 5 = 10% (or, equivalently, 2% + 2% + 2% + 2% + 2% = 10%). By this calculation you would expect to have $110,000 at the end of the period (10% of 100,000 is $10,000). However, you will have $110,408, since at the end of each year you will get your interest and then in the following years you will also accrue interest over the interest from the first year. And so on for the second, third...

To **average percentage growth** a year, it would be incorrect to just sum up the growth % in each year and then divide by the number years. Let us say you have an asset that grew 5% the first year, 6% the second year, 10% the third year, and then lost 10% the fourth year. The growth is not 5% + 6% + 10% - 10% = 11%, but it is instead the geometric mean: 2.4549% times the number of years = 2.4549 x 4 = 9.82%.

The above peculiarities are also the reason why if you lose 25% of some asset, you need to grow it 33.33% to recoup the loss. A quick calculation that you can also do using our percent calculator, shows that $10,000 * 25% = $7,500, while $10,000 of $7,500 = 133.33% (or $10,000 - $7,500 = $2,500 to return to zero, and $2.500 is 33.33% of $7,500).

#### Cite this calculator & page

If you'd like to cite this online calculator resource and information as provided on the page, you can use the following citation:

Georgiev G.Z., *"Percentage Calculator"*, [online] Available at: https://www.gigacalculator.com/calculators/percentage-calculator.php URL [Accessed Date: 26 May, 2018].