What is a Percentage Calculator?
A percentage calculator is a tool that helps you solve three main types of percentage problems:
- What is X% of Y? - Finds the value that represents a certain percentage of a number
- X is what percent of Y? - Finds what percentage one number is of another
- X is Y% of what? - Finds the original number when you know a percentage of it
Percentage Formulas
1. What is X% of Y?
Formula: Result = (X ÷ 100) × Y
Example: What is 25% of 400?
Solution: (25 ÷ 100) × 400 = 0.25 × 400 = 100
2. X is what percent of Y?
Formula: Percentage = (X ÷ Y) × 100
Example: 75 is what percent of 300?
Solution: (75 ÷ 300) × 100 = 0.25 × 100 = 25%
3. X is Y% of what?
Formula: Original = X ÷ (Y ÷ 100)
Example: 88 is 77% of what?
Solution: 88 ÷ (77 ÷ 100) = 88 ÷ 0.77 = 114.2857
Common Percentage Problems with Solutions
Problem 1: Discount Calculation
Scenario: A $200 item is on sale for 30% off. What's the sale price?
Type: What is X% of Y?
Calculation: What is 30% of 200?
Discount: (30 ÷ 100) × 200 = $60
Sale Price: $200 - $60 = $140
Problem 2: Test Score Percentage
Scenario: You scored 45 out of 60 on a test. What percentage is this?
Type: X is what percent of Y?
Calculation: 45 is what percent of 60?
Solution: (45 ÷ 60) × 100 = 0.75 × 100 = 75%
Problem 3: Original Price Calculation
Scenario: After a 20% discount, you paid $80. What was the original price?
Type: X is Y% of what?
Calculation: $80 is 80% of what? (100% - 20% discount = 80%)
Solution: 80 ÷ (80 ÷ 100) = 80 ÷ 0.80 = $100
How to Use Our Percentage Calculator
- Select the problem type from the tabs above
- Enter the values in the input fields
- Click Calculate to get instant results
- View the quick solution for immediate answer
- Check detailed solution to understand the calculation
- Use quick examples to practice different scenarios
Real-World Applications
🛒 Shopping and Retail
- Calculate discounts and sale prices
- Determine tax amounts on purchases
- Calculate tip percentages at restaurants
- Compare price reductions
💼 Business and Finance
- Calculate profit and loss percentages
- Determine interest rates and returns
- Analyze sales growth percentages
- Calculate commission rates
📊 Education and Academics
- Convert test scores to percentages
- Calculate grade percentages
- Determine attendance percentages
- Analyze survey response rates
Percentage Conversion Table
| Percentage | Fraction | Decimal | Common Use |
|---|---|---|---|
| 10% | 1/10 | 0.10 | Common discount |
| 25% | 1/4 | 0.25 | Quarter discount |
| 50% | 1/2 | 0.50 | Half price |
| 75% | 3/4 | 0.75 | Three-quarters |
| 100% | 1/1 | 1.00 | Full price |
Frequently Asked Questions (FAQ)
Q1: How do I calculate percentage quickly?
A: For quick calculations: 10% = move decimal left one place, 1% = move decimal left two places, 50% = divide by 2, 25% = divide by 4.
Q2: What is the formula for percentage?
A: Basic percentage formula: (Part/Whole) × 100 = Percentage
Q3: How do I find the original number if I know the percentage?
A: Use: Original = Part ÷ (Percentage ÷ 100). Example: If 60 is 75% of a number, original = 60 ÷ 0.75 = 80.
Q4: Can percentage be more than 100%?
A: Yes, when the part is greater than the whole. Example: 150 is 150% of 100.
Q5: How do I add a percentage to a number?
A: Multiply the number by (1 + percentage/100). Example: Add 20% to 100 = 100 × 1.20 = 120.
Q6: How do I subtract a percentage from a number?
A: Multiply the number by (1 - percentage/100). Example: Subtract 15% from 200 = 200 × 0.85 = 170.
Conclusion
Understanding percentages is essential for everyday calculations in shopping, finance, education, and business. Our percentage calculator makes it easy to solve all types of percentage problems instantly, with detailed step-by-step solutions to help you learn the concepts.
💡 Pro Tip:
Remember the basic percentage triangle: Part = Percentage × Whole ÷ 100. Knowing any two values lets you find the third!