The MathBlog Percentage Calculator allows you to easily and quickly perform a variety of percentage calculations to meet all your needs. Whether you’re figuring out discounts, tips, or changes in values, use the calculators below to help you find the answers in just a few clicks.

## What is percentage of \( x \)?

## \( x \) is what percentage of \( y \)?

## \( x \) is \( p \)% of what?

## Percentage change calculator

Percent change formula

\( \frac {(P2 - P1) \times 100}{|P1|} \)

## What Is a Percentage?

A percentage is a way to express a number as a fraction of 100. This method of representation helps us understand proportions and compare different quantities easily. The symbol “%” is used to denote percentages. For instance, 25% can be written as 0.25 in decimal form or \( \frac{25}{100} \) as a fraction.

Percentages are a crucial tool in various real-life applications. Here are a few examples of how they work:

Imagine you are a teacher grading a test. If a student scores 18 out of 20, you can calculate their percentage score to understand their performance better. The calculation would be:

\( ( \frac{18}{20} ) \times 100 = 90% \)

This means the student scored 90% on the test.

Percentages also come in handy when analyzing data, such as understanding population growth. Suppose a small town had 1,000 residents last year and now has 1,200 residents. To find the percentage increase in population, you would do the following calculation:

\( ( \frac{1200 – 1000}{1000} ) \times 100 = 20% \)

Thus, the town’s population increased by 20%.

Another common use of percentages is in financial contexts, such as calculating interest rates. If you invest $500 in a savings account that offers a 5% annual interest rate, the interest earned in one year would be:

\( ( \frac{5}{100} ) \times 500 = 25 \)

So, you would earn $25 in interest after one year.

Percentages make it simpler to understand and communicate changes, comparisons, and proportions. They are especially useful in everyday scenarios like shopping. For example, if a pair of shoes costs $80 and is on sale for 15% off, you can find the discount amount as follows:

\( ( \frac{15}{100} ) \times 80 = 12 \)

This means you save $12, and the sale price of the shoes is:

\( 80 – 12 = 68 \)

Therefore, the shoes will cost $68 after the discount.

## How to Calculate Percentages

Calculating percentages involves using simple formulas. Here’s a quick overview of what you can do with our calculators:

**Find \( P \text{%} \) of \( X \)**: Determine what percentage of a number you need.**\( X \) is what percent of \( Y \)**: Figure out the percentage relationship between two numbers.**\( X \) is \( P \text{%} \) of what**: Identify the base number when you know the percentage and the part.**Change Calculator**: Calculate how much a value has increased or decreased in percentage terms.

### Basic Percentage Formulas

Understanding the basic formulas can help you manually verify the results:

**Percentage of a number (formula):**\( P \text{%} \times X = Y \)**What percent of \( X \) is \( Y \) (formula):**\( \frac{Y}{X} \times 100 = P \text{%} \)**\( X \) is \( P \text{%} \) of what (formula):**\( \frac{X \times 100}{P} = Y \)**Percentage change (formula):**\( \frac{\text{New Value} – \text{Old Value}}{\text{Old Value}} \times 100 = \text{% Change} \)

### Practical Applications

Percentages are everywhere! From calculating sales tax to determining body fat percentages, understanding how to work with percentages is crucial in many aspects of life. Here are some common uses:

**Shopping**: Calculate discounts to know how much you’re saving.**Finance**: Understand interest rates, investment returns, and loan calculations.**Health**: Track fitness progress, such as body fat or caloric intake.**Education**: Calculate grades and test scores.