Percentage Calculator
Calculate percentages, percentage change, and percentage difference.
What is X% of Y?
X is what percent of Y?
Percentage Change
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About This Calculator
The Percentage Calculator is your go-to tool for solving any percentage problem quickly and accurately. Whether you're calculating discounts while shopping, figuring out tips at restaurants, determining grade percentages, analyzing investment returns, computing tax amounts, or understanding statistics, this calculator handles it all with precision. Percentages are fundamental to modern life—from sale prices and interest rates to statistics and data analysis—yet many people struggle with the underlying math. Our comprehensive percentage calculator supports every common calculation: finding what percent one number is of another, calculating a specific percentage of any value, determining percentage increase or decrease between two numbers, and computing percentage difference. Simply enter your values and get instant, precise results without any manual calculation errors. With step-by-step explanations and mental math shortcuts, this tool is perfect for students learning about ratios and proportions, shoppers comparing deals, business professionals analyzing financial data, and anyone who needs fast, reliable percentage calculations. Understanding percentages is an essential life skill for managing finances, interpreting data, and making informed decisions.
How to Use the Percentage Calculator
- 1Choose your calculation type from the available options.
- 2"What is X% of Y?" - Enter the percentage and base number to find the result.
- 3"X is what % of Y?" - Enter the part and whole to find the percentage.
- 4"Percentage change" - Enter original and new values to find increase/decrease.
- 5The calculator accepts decimals and negative numbers for all calculations.
- 6View your result instantly with up to 4 decimal places for precision.
- 7Use the clear button to reset and start a new calculation.
- 8Reference the mental math shortcuts below for quick estimates without a calculator.
Essential Percentage Formulas
Understanding the three core percentage formulas will help you solve any percentage problem:
1. Finding a Percentage of a Number
Result = Number × (Percentage ÷ 100)
| Percentage | Of 100 | Of 250 | Of 500 | Of 1,000 |
|---|---|---|---|---|
| 5% | 5 | 12.50 | 25 | 50 |
| 10% | 10 | 25 | 50 | 100 |
| 15% | 15 | 37.50 | 75 | 150 |
| 20% | 20 | 50 | 100 | 200 |
| 25% | 25 | 62.50 | 125 | 250 |
| 50% | 50 | 125 | 250 | 500 |
2. Finding What Percent X is of Y
Percentage = (Part ÷ Whole) × 100
3. Percentage Change (Increase/Decrease)
Change = ((New Value - Original Value) ÷ Original Value) × 100
- Positive result = percentage increase
- Negative result = percentage decrease
Mental Math Percentage Shortcuts
Master these mental math tricks to calculate percentages in your head:
Finding 10% — Move the decimal one place left
- 10% of 85 = 8.5
- 10% of 234 = 23.4
- 10% of 1,500 = 150
Finding 1% — Move the decimal two places left
- 1% of 500 = 5
- 1% of 85 = 0.85
Building Block Method — Combine simple percentages:
| To Find | Calculate | Example (of $80) |
|---|---|---|
| 5% | 10% ÷ 2 | $8 ÷ 2 = $4 |
| 15% | 10% + 5% | $8 + $4 = $12 |
| 20% | 10% × 2 | $8 × 2 = $16 |
| 25% | ÷ 4 | $80 ÷ 4 = $20 |
| 30% | 10% × 3 | $8 × 3 = $24 |
| 50% | ÷ 2 | $80 ÷ 2 = $40 |
| 75% | 50% + 25% | $40 + $20 = $60 |
Quick Tip Calculation (15-20%):
- Calculate 10% (move decimal)
- For 15%: add half of 10%
- For 20%: double the 10%
Real-World Percentage Applications
Shopping & Discounts A $120 jacket is marked 35% off:
- Discount = $120 × 0.35 = $42
- Sale price = $120 - $42 = $78
- Or calculate directly: $120 × 0.65 = $78
Restaurant Tipping Guide
| Service Level | Tip % | On $50 Bill | On $100 Bill |
|---|---|---|---|
| Poor | 10% | $5 | $10 |
| Average | 15% | $7.50 | $15 |
| Good | 18% | $9 | $18 |
| Excellent | 20% | $10 | $20 |
| Outstanding | 25% | $12.50 | $25 |
Sales Tax Calculation Item: $75, Tax rate: 8.25%
- Tax = $75 × 0.0825 = $6.19
- Total = $75 + $6.19 = $81.19
Grade Calculations Test score: 47 out of 55 points
- Percentage = (47 ÷ 55) × 100 = 85.45%
Investment Returns Stock purchased at $45, sold at $63:
- Gain = ((63 - 45) ÷ 45) × 100 = 40% return
Salary Increase Current salary: $52,000, Raise: 4%
- Increase = $52,000 × 0.04 = $2,080
- New salary = $54,080
Common Percentage Mistakes to Avoid
Mistake 1: Confusing Percentage Points vs. Percentages
- Going from 10% to 15% is a 5 percentage point increase
- But it's a 50% relative increase (5 is 50% of 10)
- Example: "Interest rates rose from 4% to 5%" = 1 percentage point increase but 25% relative increase
Mistake 2: Reversing Percentage Changes
- A 50% decrease followed by a 50% increase does NOT return to original
- $100 → 50% decrease → $50 → 50% increase → $75 (not $100!)
- To return to original after X% decrease: need (X/(100-X))×100% increase
Mistake 3: Adding/Subtracting Percentages Incorrectly
- Wrong: 20% off + extra 10% off = 30% off
- Correct: $100 × 0.80 × 0.90 = $72 (28% total discount)
- Percentages multiply, not add!
Mistake 4: Percentage of vs. Percentage Off
- 25% OF $80 = $20 (what you save)
- 25% OFF $80 means you pay $60 (what you spend)
Mistake 5: Comparing Different Bases
- Company A grew 100% (from $1M to $2M)
- Company B grew 10% (from $100M to $110M)
- Company B grew $10M more in absolute terms!
Percentage in Finance and Business
Interest Rate Calculations:
Simple Interest:
Interest = Principal × Rate × Time
$10,000 at 5% for 3 years = $10,000 × 0.05 × 3 = $1,500
Compound Interest:
A = P(1 + r/n)^(nt)
$10,000 at 5% compounded annually for 3 years: Year 1: $10,500 Year 2: $11,025 Year 3: $11,576.25
Profit Margin vs. Markup:
| Term | Formula | Example |
|---|---|---|
| Profit Margin | (Profit/Revenue) × 100 | $20 profit on $100 sale = 20% margin |
| Markup | (Profit/Cost) × 100 | $20 profit on $80 cost = 25% markup |
Return on Investment (ROI):
ROI = ((Gain - Cost) / Cost) × 100
Investment: $5,000, Returns: $6,500 ROI = ((6,500 - 5,000) / 5,000) × 100 = 30%
Annual Percentage Rate (APR) vs. APY:
- APR: Simple annual interest rate
- APY: Includes compound interest effects
- A 12% APR compounded monthly = 12.68% APY
Percentage Conversions
Percent, Decimal, and Fraction Equivalents:
| Percent | Decimal | Fraction |
|---|---|---|
| 1% | 0.01 | 1/100 |
| 5% | 0.05 | 1/20 |
| 10% | 0.10 | 1/10 |
| 12.5% | 0.125 | 1/8 |
| 20% | 0.20 | 1/5 |
| 25% | 0.25 | 1/4 |
| 33.33% | 0.333... | 1/3 |
| 50% | 0.50 | 1/2 |
| 66.67% | 0.666... | 2/3 |
| 75% | 0.75 | 3/4 |
| 100% | 1.00 | 1/1 |
| 150% | 1.50 | 3/2 |
| 200% | 2.00 | 2/1 |
Conversion Rules:
- Percent to Decimal: Divide by 100 (move decimal 2 places left)
- Decimal to Percent: Multiply by 100 (move decimal 2 places right)
- Fraction to Percent: Divide, then multiply by 100
- Percent to Fraction: Put over 100, then simplify
Examples:
- 45% → 0.45 → 45/100 = 9/20
- 3/8 → 0.375 → 37.5%
- 0.0625 → 6.25% → 1/16
Percentage in Statistics and Data
Percentage Distribution: Survey of 500 people:
- Yes: 215 people = 43%
- No: 185 people = 37%
- Undecided: 100 people = 20%
- Total: 500 people = 100%
Percentile vs. Percentage:
- Percentage: A portion of 100 (85% correct on test)
- Percentile: Ranking among a group (85th percentile = scored higher than 85% of test-takers)
Percentage Change in Data: Month 1: 1,000 visitors Month 2: 1,350 visitors
- Change = ((1,350 - 1,000) / 1,000) × 100 = 35% increase
Month 3: 1,100 visitors
- Change = ((1,100 - 1,350) / 1,350) × 100 = -18.5% decrease
Year-Over-Year (YoY) Comparison: Q1 2025: $500,000 revenue Q1 2026: $625,000 revenue
- YoY Growth = ((625,000 - 500,000) / 500,000) × 100 = 25%
Compound Annual Growth Rate (CAGR): Starting value: $10,000 Ending value: $25,937 (after 5 years)
- CAGR = ((25,937/10,000)^(1/5) - 1) × 100 = 21%
Percentage Word Problems Explained
Problem Type 1: Find the Percentage "What percent of 80 is 20?"
- Formula: (Part / Whole) × 100
- Solution: (20 / 80) × 100 = 25%
Problem Type 2: Find the Part "What is 35% of 240?"
- Formula: Whole × (Percent / 100)
- Solution: 240 × 0.35 = 84
Problem Type 3: Find the Whole "15 is 30% of what number?"
- Formula: Part / (Percent / 100)
- Solution: 15 / 0.30 = 50
Problem Type 4: Percentage Change "A price went from $80 to $92. What is the percent increase?"
- Formula: ((New - Original) / Original) × 100
- Solution: ((92 - 80) / 80) × 100 = 15%
Problem Type 5: Reverse Percentage "After a 20% discount, an item costs $64. What was the original price?"
- If 20% off, paying 80%
- Formula: Sale Price / 0.80
- Solution: $64 / 0.80 = $80 original
Problem Type 6: Successive Percentages "A store marks up by 25%, then offers 20% off. What's the final price of a $100 item?"
- After 25% markup: $100 × 1.25 = $125
- After 20% discount: $125 × 0.80 = $100
- Net effect: 0% change (1.25 × 0.80 = 1.00)
Percentage in Health, Sports, and Daily Life
Health and Nutrition Percentages:
| Measurement | Calculation | Healthy Range |
|---|---|---|
| Body Fat % | (Fat Mass / Total Mass) × 100 | Men: 10-20%, Women: 18-28% |
| Resting Heart Rate | % of Max HR (220-age) | 50-70% during rest |
| Target Heart Rate | 50-85% of max HR | For exercise |
| Daily Value (DV) | Nutrient / Recommended × 100 | 100% = full daily need |
Macronutrient Percentages: Typical balanced diet recommendations:
- Carbohydrates: 45-65% of calories
- Protein: 10-35% of calories
- Fat: 20-35% of calories
Sports Statistics:
| Sport | Common Percentage Stats |
|---|---|
| Basketball | Field goal %, Free throw %, 3-point % |
| Baseball | Batting average (actually a decimal), On-base %, Slugging % |
| Football | Completion %, Win % |
| Soccer | Possession %, Pass accuracy % |
Battery and Device Percentages:
- 100%: Fully charged
- 20%: Low battery warning typically starts
- 80%: Optimal charge level for lithium-ion longevity
- 0%: May have 5-10% reserve for safe shutdown
Weather Percentages:
- Humidity: % of water vapor in air relative to maximum
- Precipitation: Probability of rain at a point in the forecast area
- UV Index: Not a percentage, but often confused with one
Cooking and Recipes:
- Hydration % in bread: (Water weight / Flour weight) × 100
- Alcohol by Volume (ABV): (Pure alcohol / Total volume) × 100
- Butterfat %: Whole milk (3.25%), Cream (36%), Butter (80%)
Pro Tips
- 💡When calculating discounts, subtract the percentage from 100% first to find what you pay. A 30% discount means you pay 70% of the price.
- 💡For quick mental math, always start with 10% (move the decimal point one place left) and build from there.
- 💡Remember that percentage points and relative percentages are different. A rate going from 2% to 3% is a 1 percentage point increase but a 50% relative increase.
- 💡When comparing percentages, always check that they use the same base. 50% of $100 is very different from 50% of $1,000.
- 💡Use the "reverse percentage" to check your work: if you add 25%, you should be able to subtract 20% (not 25%) to get back to the original.
- 💡For successive discounts, multiply the remaining percentages: 20% off then 10% off = 0.80 × 0.90 = 72% of original (28% total discount).
- 💡To find what percentage X is of Y, divide X by Y and multiply by 100. Example: 15 is what % of 60? → (15/60) × 100 = 25%.
- 💡Remember: percentages multiply, not add. Two 50% increases don't make 100%; they make 125% (1.5 × 1.5 = 2.25).
- 💡For tip calculations, find 10% first, then adjust. 18% tip = 10% + 10% - 2% (or 10% + 8% = 10% + half of 10% + 3%).
- 💡When converting fractions to percentages, common ones to memorize: 1/4 = 25%, 1/3 ≈ 33.3%, 1/2 = 50%, 2/3 ≈ 66.7%, 3/4 = 75%.
- 💡For percentage change, always divide by the ORIGINAL value, not the new value.
- 💡APY (Annual Percentage Yield) is always higher than APR for the same rate because it includes compounding.
Frequently Asked Questions
To calculate a percentage of a number, convert the percentage to a decimal by dividing by 100, then multiply by the number. For example, to find 25% of 80: convert 25% to 0.25, then multiply 0.25 × 80 = 20. Alternatively, you can multiply the number by the percentage and divide by 100: (80 × 25) ÷ 100 = 20.
