Percentage Calculator – Calculate Percentages, Increases, and Decreases
Use our comprehensive percentage calculator to solve various percentage problems including calculating percentages, percentage increases, decreases, and percentage differences. Perfect for business, finance, academics, and everyday calculations.
What is X% of Y?
Calculate what percentage of a number equals another number.
X is what % of Y?
Find what percentage one number is of another number.
Percentage Increase
Calculate the percentage increase from one value to another.
Percentage Decrease
Calculate the percentage decrease from one value to another.
Add X% to a Number
Calculate a number after adding a specific percentage to it.
Subtract X% from a Number
Calculate a number after subtracting a specific percentage from it.
Understanding Percentages
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 extensively in finance, statistics, science, and everyday life to compare values and express ratios.
Basic Percentage Formulas
Types of Percentage Calculations
1. Basic Percentage Calculation
Finding what percentage one number is of another. This is useful for calculating grades, completion rates, or market share.
Example:
Question: 75 is what percentage of 300?
Calculation: (75 ÷ 300) × 100 = 25%
Answer: 75 is 25% of 300
2. Percentage of a Number
Calculating what a specific percentage of a number equals. Common in discounts, tips, and tax calculations.
Example:
Question: What is 15% of $240?
Calculation: (15 ÷ 100) × 240 = $36
Answer: 15% of $240 is $36
3. Percentage Increase
Measuring how much a value has grown compared to its original amount. Used in finance, population studies, and performance metrics.
Example:
Question: Sales increased from $1,000 to $1,200. What’s the percentage increase?
Calculation: ((1,200 – 1,000) ÷ 1,000) × 100 = 20%
Answer: Sales increased by 20%
4. Percentage Decrease
Measuring how much a value has decreased compared to its original amount. Important for analyzing losses, discounts, and reductions.
Example:
Question: Price dropped from $500 to $400. What’s the percentage decrease?
Calculation: ((500 – 400) ÷ 500) × 100 = 20%
Answer: Price decreased by 20%
Common Percentage Applications
| Application | Use Case | Example |
|---|---|---|
| Discounts & Sales | Calculate savings on purchases | 30% off $100 = $30 discount, pay $70 |
| Tips & Service Charges | Calculate gratuity amounts | 18% tip on $50 bill = $9 tip |
| Tax Calculations | Determine tax amounts | 8.25% sales tax on $200 = $16.50 |
| Interest Rates | Calculate loan interest or investment returns | 5% annual interest on $1,000 = $50 |
| Grade Calculations | Convert test scores to percentages | 18 out of 20 questions = 90% |
| Statistics & Analytics | Express data relationships | 60% of survey respondents agreed |
| Business Metrics | Measure performance and growth | 15% increase in monthly revenue |
Percentage Calculation Tips
💡 Quick Mental Math Tips
- 10%: Move decimal point one place left (10% of 250 = 25)
- 1%: Move decimal point two places left (1% of 250 = 2.5)
- 5%: Calculate 10% and divide by 2 (5% of 200 = 20 ÷ 2 = 10)
- 25%: Divide by 4 (25% of 200 = 200 ÷ 4 = 50)
- 50%: Divide by 2 (50% of 200 = 200 ÷ 2 = 100)
- 75%: Calculate 25% and multiply by 3, or subtract 25% from 100%
Business and Finance Applications
Profit Margins
Calculate profit margins to understand business profitability:
Return on Investment (ROI)
Measure investment performance:
Market Share
Calculate company’s market position:
Common Percentage Mistakes to Avoid
⚠️ Avoid These Common Errors
- Percentage Point vs. Percentage: A change from 20% to 25% is a 5 percentage point increase, but a 25% relative increase
- Base Value Confusion: Always identify what the percentage is “of” – the base value matters
- Double Percentage Applications: 50% off, then 20% off is not 70% off total
- Rounding Errors: Be consistent with decimal places in calculations
- Negative Percentages: Understand when negative percentages represent decreases
Advanced Percentage Concepts
Compound Percentages
When percentages are applied multiple times or to changing base values. Common in compound interest calculations.
Percentage Differences vs. Percentage Change
Percentage Change: Compares new value to original value
Percentage Difference: Compares difference to average of two values
Weighted Percentages
When different components contribute different amounts to the total percentage, such as in weighted grade calculations.
Frequently Asked Questions
How do you calculate percentage increase?
Subtract the original value from the new value, divide by the original value, then multiply by 100. Formula: ((New – Original) ÷ Original) × 100
What’s the difference between 50% more and 50% as much?
“50% more” means 150% of the original (original + 50%). “50% as much” means exactly 50% of the original amount.
Can percentages be greater than 100%?
Yes, percentages can exceed 100%. For example, if something doubles, it increases by 100%, making the new amount 200% of the original.
How do you convert decimals to percentages?
Multiply the decimal by 100 and add the % symbol. For example: 0.75 × 100 = 75%
How do you add and subtract percentages?
You cannot directly add percentages unless they have the same base. Convert to actual values first, perform the operation, then convert back to percentage if needed.