Percentage Calculator

Solve various percentage problems with ease.

Select the type of percentage problem you want to solve and enter the required values. Our calculator handles three common types of percentage calculations.

Examples

Click on an example to load it into the calculator.

Calculate a Discount

findPercentageOf

Find 25% of a $150 item.

Percentage: 25

Total Value: 150

Find Exam Score Percentage

isWhatPercentOf

You scored 45 out of 50. What is the percentage?

Value: 45

Total Value: 50

Calculate Original Price

isPercentOfWhat

A sale item is $60, which is 80% of the original price. What was the original price?

Value: 60

Percentage: 80

Calculate a Tip

findPercentageOf

Calculate an 18% tip on a $78.50 bill.

Percentage: 18

Total Value: 78.50

Other Titles
Understanding Percentages: A Comprehensive Guide
Master the concept of percentages and their applications in daily life, finance, and mathematics.

What is a Percentage?

  • Understanding the core concept of 'per cent'
  • Converting between percentages, fractions, and decimals
  • The importance of percentages in everyday contexts
A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, '%'. The word 'percent' is derived from the Latin 'per centum', meaning 'by the hundred'. Essentially, it's a way to express how large or small one quantity is relative to another quantity.
Core Idea
If we say '50 percent' (or 50%), we mean 50 parts out of every 100 parts. This can be written as the fraction 50/100, which simplifies to 1/2, or as the decimal 0.50. This flexibility makes percentages a universal tool for comparisons.

Conversion Examples

  • 75% = 75/100 = 3/4 = 0.75
  • 20% = 20/100 = 1/5 = 0.20
  • 150% = 150/100 = 3/2 = 1.5

Step-by-Step Guide to Using the Percentage Calculator

  • Selecting the correct calculation type for your problem
  • Entering values accurately into the input fields
  • Interpreting the calculated result correctly
Our calculator simplifies percentage problems by breaking them into three main types. Here's how to use it:
1. 'What is X% of Y?'
Use this to find a specific percentage of a number. Select this option, enter the percentage in the first box and the total number in the second box. For example, to find 20% of 300, enter 20 and 300.
2. 'X is what percent of Y?'
Use this when you want to find out what percentage one number represents of another. For example, to find what percentage 25 is of 125, enter 25 in the first box and 125 in the second.
3. 'X is Y% of what?'
Use this when you know a part of a total and the percentage it represents. For example, if you know that 50 is 25% of a number, enter 50 in the first box and 25 in the second to find the total.

Practical Scenarios

  • What is 15% of 250? → 37.5
  • 18 is what percent of 60? → 30%
  • 45 is 90% of what? → 50

Real-World Applications of Percentages

  • Finance: Interest rates, discounts, and returns
  • Shopping: Calculating sales tax and tips
  • Statistics: Representing data and changes
Percentages are one of the most common mathematical concepts we encounter daily.
In Finance and Shopping
When you shop, discounts are almost always shown as percentages (e.g., '30% off'). Sales tax is a percentage added to your bill. When you eat out, you calculate a tip as a percentage of the bill. Banks advertise loan interest rates and investment returns using percentages.
In Health and Science
Nutritional labels show the percentage of daily recommended intake for various nutrients. Scientists use percentages to express the concentration of a substance in a mixture or the error margin in an experiment.

Everyday Examples

  • A $50 shirt with a 20% discount costs $40.
  • A 6% sales tax on a $100 purchase is $6.
  • A student who answers 40 out of 50 questions correctly has a score of 80%.

Common Misconceptions and Correct Methods

  • Confusing percentage points with percentage change
  • Incorrectly adding or subtracting percentages
  • The importance of the base value in calculations
While percentages seem simple, they can be tricky. Understanding common pitfalls is key to using them correctly.
Percentage Points vs. Percentage Change
If an interest rate increases from 5% to 6%, it has increased by one 'percentage point'. The 'percentage change', however, is (6-5)/5 * 100 = 20%. These are not the same.
Adding and Subtracting Percentages
You cannot simply add percentages of different bases. A 20% discount followed by a 10% discount is not a 30% discount. On a $100 item, the first discount makes it $80. The 10% discount is then on $80 (which is $8), making the final price $72. The total discount is 28%.

Pitfall Examples

  • A stock price rises 10% and then falls 10%. It does not return to the original price.
  • If your salary of $50,000 increases by 5%, your new salary is $52,500. The increase is $2,500.

Mathematical Formulas and Derivations

  • The three fundamental percentage formulas
  • Algebraic rearrangement for each calculation type
  • Worked examples for each formula
All percentage calculations are based on one simple equation that can be rearranged to solve different problems. The base formula is: (Part / Whole) = (Percentage / 100).
Formula 1: Finding the Part
To answer 'What is X% of Y?', we solve for the 'Part'. The formula is: Part = (Percentage / 100) Whole. Example: What is 15% of 200? Part = (15 / 100) 200 = 30.
Formula 2: Finding the Percentage
To answer 'X is what percent of Y?', we solve for 'Percentage'. The formula is: Percentage = (Part / Whole) 100. Example: 45 is what percent of 150? Percentage = (45 / 150) 100 = 30%.
Formula 3: Finding the Whole
To answer 'X is Y% of what?', we solve for the 'Whole'. The formula is: Whole = Part / (Percentage / 100). Example: 60 is 40% of what? Whole = 60 / (40 / 100) = 60 / 0.4 = 150.

Formula Applications

  • What is 5% of 1,200? → (5/100) * 1200 = 60
  • 7 is what percent of 35? → (7/35) * 100 = 20%
  • 12 is 25% of what? → 12 / (25/100) = 48