Calculate Percentages
What is X% of Y?
X is what percent of Y?
Percentage Increase/Decrease
Understanding Percentage Calculations
What is a Percentage?
A percentage is a way of expressing a number as a fraction of 100. The word "percent" comes from the Latin "per centum," meaning "by the hundred." Percentages are used in many aspects of daily life, from calculating discounts and taxes to understanding statistics and financial reports.
Common Percentage Formulas
1. Finding X% of Y
Formula: (X / 100) × Y
Example: What is 25% of 200?
Solution: (25 / 100) × 200 = 50
2. Finding What Percent X is of Y
Formula: (X / Y) × 100
Example: 50 is what percent of 200?
Solution: (50 / 200) × 100 = 25%
3. Calculating Percentage Change
Formula: ((New Value - Original Value) / Original Value) × 100
Example: A price increased from 100 to 150. What is the percentage increase?
Solution: ((150 - 100) / 100) × 100 = 50% increase
Real-World Applications
- Shopping & Discounts: Calculate sale prices and savings (e.g., "30% off original price")
- Finance: Interest rates, investment returns, loan calculations, and profit margins
- Taxes: Sales tax, income tax, and VAT calculations
- Statistics: Survey results, demographic data, and probability
- Academic Grading: Test scores and grade calculations
- Health & Fitness: Body fat percentage, nutrient composition, weight loss tracking
- Business: Market share, growth rates, commission calculations
Tips for Percentage Calculations
- Remember that percentages are always out of 100
- To convert a decimal to a percentage, multiply by 100 (0.25 = 25%)
- To convert a percentage to a decimal, divide by 100 (25% = 0.25)
- A percentage increase of 100% means the value doubled
- You can't have a percentage decrease greater than 100%
- Use our calculator above for quick and accurate results
Frequently Asked Questions
Q: What's the difference between percentage increase and percentage point increase?
A: A percentage increase is relative to the original value, while a percentage point increase is an absolute difference. For example, if interest rates go from 5% to 8%, that's a 3 percentage point increase but a 60% increase ((8-5)/5 × 100).
Q: Can percentages be greater than 100%?
A: Yes! For example, if something increased from 50 to 150, that's a 200% increase. However, percentage decreases cannot exceed 100% (you can't lose more than everything).
Q: How do I calculate a discount price?
A: If an item is 30% off, you can either calculate 30% of the price and subtract it, or multiply the price by 0.70 (100% - 30% = 70%). For example, a $100 item at 30% off: $100 × 0.70 = $70.