Percentage Calculator

Calculate percentages, percentage changes, increases, and decreases. Essential tool for finance, shopping, and everyday calculations.

Calculate Percentages

Result

25
25% of 100 = 25

How to Use This Calculator

1Choose your calculation type
2Enter your values
3Click calculate to see results

Calculation Types

What is X% of Y: Find a percentage of a number
Percentage Change: Calculate the change between two values
Percentage Increase: Find the increase from one value to another
Percentage Decrease: Find the decrease from one value to another

Understanding Percentages

Percentages are a fundamental concept in mathematics and everyday life. They represent parts per hundred and are used extensively in finance, shopping, statistics, and many other fields. Understanding how to calculate and work with percentages is essential for making informed decisions.

What Are Percentages?

A percentage is a way to express a number as a fraction of 100. The word "percent" comes from the Latin "per centum," meaning "by the hundred." For example, 25% means 25 out of 100, or one-quarter.

Basic Percentage Calculations

The most common percentage calculation is finding what percentage one number is of another:

Formula: What is X% of Y?

Result = (Y × X) ÷ 100

Example: What is 15% of 200? (200 × 15) ÷ 100 = 30

Percentage Change

Percentage change measures how much a value has increased or decreased relative to its original value:

Formula: Percentage Change

Percentage Change = ((New Value - Original Value) ÷ Original Value) × 100

Example: Price increased from $50 to $60. ((60 - 50) ÷ 50) × 100 = 20% increase

Common Percentage Applications

Percentages are used in many real-world scenarios:

  • Finance: Interest rates, discounts, markups, and returns
  • Shopping: Sales, discounts, and tax calculations
  • Statistics: Population changes, survey results, and data analysis
  • Health: Body fat percentages, medication dosages, and test results
  • Business: Profit margins, growth rates, and market share

Percentage Increase vs. Decrease

Understanding the difference between increases and decreases is important:

  • Increase: When a value goes up, the percentage is positive
  • Decrease: When a value goes down, the percentage is negative
  • Relative change: Both use the same formula but interpret results differently

Working with Decimal Percentages

Percentages can be expressed as decimals for calculations:

Converting Between Percentages and Decimals

Percentage to Decimal:
  • 25% = 0.25
  • 150% = 1.50
  • 0.5% = 0.005
Decimal to Percentage:
  • 0.75 = 75%
  • 1.25 = 125%
  • 0.01 = 1%

Compound Percentages

When multiple percentage changes occur, they don't simply add together:

  • Sequential changes: Apply percentages one after another
  • Example: 10% increase followed by 10% decrease ≠ 0% change
  • Final result: 100 × 1.10 × 0.90 = 99 (1% decrease)

Percentage Points vs. Percentages

Don't confuse percentage points with percentages:

  • Percentage: Relative to the base value
  • Percentage points: Absolute difference between percentages
  • Example: An increase from 5% to 6% is a 20% increase but only 1 percentage point

Practical Examples

Here are some common percentage calculations you might encounter:

Real-World Examples

Sales Tax: Item costs $100, tax rate is 8.5%. Tax = $100 × 8.5% = $8.50
Discount: $80 item with 20% off. Savings = $80 × 20% = $16, Final price = $64
Tip: $45 bill with 18% tip. Tip amount = $45 × 18% = $8.10
Investment Return: $1,000 investment grows to $1,150. Return = ((1150 - 1000) ÷ 1000) × 100 = 15%

Common Mistakes to Avoid

Watch out for these percentage calculation errors:

  • Confusing increase/decrease: Always identify which value is the original
  • Forgetting to multiply by 100: Decimal results need to be converted to percentages
  • Adding percentages incorrectly: Sequential changes multiply, not add
  • Base value confusion: Make sure you're using the correct reference point

Ready to Calculate Percentages?

Use our percentage calculator to handle all your percentage-related calculations quickly and accurately.

Conclusion

Percentages are an essential mathematical concept that appears in countless real-world situations. Whether you're calculating discounts, analyzing data, or planning finances, understanding percentages helps you make better decisions. Our calculator provides the tools you need for common percentage calculations, but remember that practice and understanding the underlying concepts will make you more confident in your calculations.