What is a Percentage? Complete Guide to Percentage Calculations
A percentage is a mathematical concept that represents a number or ratio as a fraction of 100. The word itself comes from the Latin "per centum," meaning "by the hundred." Percentages are one of the most commonly used mathematical concepts in everyday life — from calculating discounts during shopping to understanding interest rates on loans, tax calculations, grade scoring, statistical data, nutritional information, and much more.
Our free percentage calculator handles all types of percentage calculations instantly. Whether you need to find what percentage one number is of another, calculate a percentage increase or decrease, figure out a tip, or determine a discount amount — this tool does it all in your browser with zero data collection and no signup required.
Understanding percentages is essential for financial literacy, academic success, and informed decision-making. This comprehensive guide below covers every type of percentage calculation with formulas, step-by-step examples, reference tables, and practical applications you can use immediately.
All Percentage Formulas You Need to Know
There are several fundamental percentage formulas that cover virtually every calculation you will ever need. Below is a comprehensive reference of every percentage formula, explained with clear examples.
| Calculation Type | Formula | Example | Result |
|---|---|---|---|
| X% of Y | (X / 100) × Y | 15% of 200 | 30 |
| What % is X of Y? | (X / Y) × 100 | 45 is what % of 180? | 25% |
| Percent Increase | ((New - Old) / Old) × 100 | 80 → 100 | 25% increase |
| Percent Decrease | ((Old - New) / Old) × 100 | 100 → 75 | 25% decrease |
| Percent Change | ((New - Old) / Old) × 100 | 50 → 65 | 30% change |
| Add X% to Y | Y × (1 + X/100) | Add 20% to 150 | 180 |
| Subtract X% from Y | Y × (1 - X/100) | Subtract 15% from 200 | 170 |
| Percent Difference | |A - B| / ((A + B) / 2) × 100 | Between 40 and 60 | 40% |
| Markup Percentage | ((Selling - Cost) / Cost) × 100 | Cost $50, Sell $75 | 50% markup |
| Margin Percentage | ((Selling - Cost) / Selling) × 100 | Cost $50, Sell $75 | 33.3% margin |
| Discount Amount | Original Price × (Discount% / 100) | 25% off $120 | $30 discount |
| Sale Price | Original × (1 - Discount% / 100) | 25% off $120 | $90 |
How to Calculate Percentage: Step-by-Step Guide
Type 1: Finding X% of a Number
This is the most common percentage calculation. You want to find a specific percentage of a given number. The formula is: Result = (Percentage / 100) × Number.
- 1Convert the percentage to a decimal by dividing by 100. For example, 25% becomes 0.25.
- 2Multiply the decimal by the number you want to find the percentage of. For example, 0.25 × 80 = 20.
- 3The result is your answer: 25% of 80 is 20.
| Percentage | Of 50 | Of 100 | Of 200 | Of 500 | Of 1000 |
|---|---|---|---|---|---|
| 5% | 2.50 | 5 | 10 | 25 | 50 |
| 10% | 5 | 10 | 20 | 50 | 100 |
| 15% | 7.50 | 15 | 30 | 75 | 150 |
| 20% | 10 | 20 | 40 | 100 | 200 |
| 25% | 12.50 | 25 | 50 | 125 | 250 |
| 30% | 15 | 30 | 60 | 150 | 300 |
| 33.3% | 16.67 | 33.33 | 66.67 | 166.67 | 333.33 |
| 40% | 20 | 40 | 80 | 200 | 400 |
| 50% | 25 | 50 | 100 | 250 | 500 |
| 60% | 30 | 60 | 120 | 300 | 600 |
| 75% | 37.50 | 75 | 150 | 375 | 750 |
| 80% | 40 | 80 | 160 | 400 | 800 |
| 90% | 45 | 90 | 180 | 450 | 900 |
| 100% | 50 | 100 | 200 | 500 | 1000 |
Type 2: Finding What Percentage X is of Y
When you need to express one number as a percentage of another, use: Percentage = (Part / Whole) × 100. For example, to find what percentage 35 is of 140: (35 / 140) × 100 = 25%. This means 35 is 25% of 140.
Type 3: Percentage Increase and Decrease
Percentage change is used to compare an old value with a new value. It is crucial for understanding price changes, salary increases, population growth, stock market movements, and more.
Percentage Increase Formula: ((New Value - Old Value) / Old Value) × 100. If a product price went from $40 to $52: ((52 - 40) / 40) × 100 = 30% increase.
Percentage Decrease Formula: ((Old Value - New Value) / Old Value) × 100. If your electricity bill dropped from $120 to $90: ((120 - 90) / 120) × 100 = 25% decrease.
Real-World Applications of Percentage Calculations
Shopping and Discounts
Percentage calculations are essential for smart shopping. When a store advertises "30% off," you need to calculate the actual savings and final price. Understanding how to quickly compute discounts helps you compare deals, identify genuine bargains, and make better purchasing decisions.
| Original Price | 10% Off | 20% Off | 25% Off | 30% Off | 40% Off | 50% Off |
|---|---|---|---|---|---|---|
| $25 | $22.50 | $20 | $18.75 | $17.50 | $15 | $12.50 |
| $50 | $45 | $40 | $37.50 | $35 | $30 | $25 |
| $75 | $67.50 | $60 | $56.25 | $52.50 | $45 | $37.50 |
| $100 | $90 | $80 | $75 | $70 | $60 | $50 |
| $150 | $135 | $120 | $112.50 | $105 | $90 | $75 |
| $200 | $180 | $160 | $150 | $140 | $120 | $100 |
| $300 | $270 | $240 | $225 | $210 | $180 | $150 |
| $500 | $450 | $400 | $375 | $350 | $300 | $250 |
Tips and Gratuity
Calculating tips at restaurants is one of the most common real-world uses of percentages. The standard tip in the United States ranges from 15% to 20% of the pre-tax bill, though customs vary by country.
| Bill Amount | 10% Tip | 15% Tip | 18% Tip | 20% Tip | 25% Tip |
|---|---|---|---|---|---|
| $20 | $2.00 | $3.00 | $3.60 | $4.00 | $5.00 |
| $30 | $3.00 | $4.50 | $5.40 | $6.00 | $7.50 |
| $50 | $5.00 | $7.50 | $9.00 | $10.00 | $12.50 |
| $75 | $7.50 | $11.25 | $13.50 | $15.00 | $18.75 |
| $100 | $10.00 | $15.00 | $18.00 | $20.00 | $25.00 |
| $150 | $15.00 | $22.50 | $27.00 | $30.00 | $37.50 |
| $200 | $20.00 | $30.00 | $36.00 | $40.00 | $50.00 |
Finance and Investments
- Interest rates: Banks express savings account yields and loan costs as annual percentage rates (APR). A 5% APR on a $10,000 savings account earns $500 per year in simple interest.
- Stock market returns: Investors track portfolio performance using percentage gains and losses. A stock that moves from $50 to $65 has gained 30%.
- GDP growth: Economists measure national economic health using GDP growth percentage. A 3% GDP growth rate indicates a healthy, expanding economy.
- Inflation rate: The consumer price index (CPI) measures how prices change over time as a percentage, helping you understand purchasing power.
- Tax calculations: Income tax brackets, sales tax, property tax, and capital gains tax are all expressed as percentages.
- Compound interest: The most powerful financial concept — earning interest on interest. The formula A = P(1 + r/n)^(nt) relies heavily on percentage calculations.
Academic Grading
Grade percentages help students understand their academic standing. If you scored 42 out of 50 on a test, your percentage score is (42/50) × 100 = 84%. Most grading scales use the following ranges:
| Percentage Range | Letter Grade | GPA (4.0 Scale) | Description |
|---|---|---|---|
| 93-100% | A | 4.0 | Excellent / Outstanding |
| 90-92% | A- | 3.7 | Excellent |
| 87-89% | B+ | 3.3 | Very Good |
| 83-86% | B | 3.0 | Good |
| 80-82% | B- | 2.7 | Above Average |
| 77-79% | C+ | 2.3 | Average Plus |
| 73-76% | C | 2.0 | Average |
| 70-72% | C- | 1.7 | Below Average |
| 67-69% | D+ | 1.3 | Poor |
| 60-66% | D | 1.0 | Barely Passing |
| Below 60% | F | 0.0 | Failing |
Mental Math Tricks for Quick Percentage Calculations
Being able to calculate percentages mentally is a valuable life skill. These proven tricks make percentage math fast and easy, even without a calculator:
- 1To find 10%: Simply move the decimal point one place to the left. 10% of 250 = 25.0. This is the foundation for most mental percentage calculations.
- 2To find 5%: Find 10% first, then halve it. 5% of 250 = 25 ÷ 2 = 12.50.
- 3To find 1%: Move the decimal point two places to the left. 1% of 250 = 2.50.
- 4To find 15%: Calculate 10% + 5%. For 15% of 80: 10% = 8, 5% = 4, total = 12.
- 5To find 20%: Calculate 10% and double it. 20% of 350 = 35 × 2 = 70.
- 6To find 25%: Divide by 4. 25% of 200 = 200 ÷ 4 = 50.
- 7To find 33%: Divide by 3. 33% of 90 = 90 ÷ 3 = 30.
- 8To find 50%: Simply halve the number. 50% of 180 = 90.
- 9To find 75%: Find 50% + 25%. 75% of 200 = 100 + 50 = 150.
- 10Swap trick: X% of Y = Y% of X. So 8% of 25 = 25% of 8 = 2. Choose whichever is easier to calculate!
Understanding Markup vs. Margin: Why It Matters
One of the most common sources of confusion in business is the difference between markup and margin. While both express profit as a percentage, they use different denominators and produce very different numbers for the same transaction.
| Cost Price | Selling Price | Profit | Markup % | Margin % |
|---|---|---|---|---|
| $10 | $15 | $5 | 50% | 33.3% |
| $20 | $30 | $10 | 50% | 33.3% |
| $50 | $75 | $25 | 50% | 33.3% |
| $100 | $120 | $20 | 20% | 16.7% |
| $100 | $150 | $50 | 50% | 33.3% |
| $100 | $200 | $100 | 100% | 50% |
| $100 | $300 | $200 | 200% | 66.7% |
Markup = ((Selling Price - Cost) / Cost) × 100. It tells you how much you added on top of the cost. Margin = ((Selling Price - Cost) / Selling Price) × 100. It tells you what percentage of the revenue is profit. Markup is always higher than margin for the same transaction. A 100% markup equals a 50% margin.
Compound Percentage Growth Explained
Compound growth is when growth is calculated on both the original amount and any accumulated growth from previous periods. This concept is critical for understanding investment returns, population growth, inflation effects, and the power of consistent saving.
| Years | 3% Annual | 5% Annual | 7% Annual | 10% Annual | 12% Annual |
|---|---|---|---|---|---|
| 1 | $1,030 | $1,050 | $1,070 | $1,100 | $1,120 |
| 5 | $1,159 | $1,276 | $1,403 | $1,611 | $1,762 |
| 10 | $1,344 | $1,629 | $1,967 | $2,594 | $3,106 |
| 15 | $1,558 | $2,079 | $2,759 | $4,177 | $5,474 |
| 20 | $1,806 | $2,653 | $3,870 | $6,727 | $9,646 |
| 25 | $2,094 | $3,386 | $5,427 | $10,835 | $17,000 |
| 30 | $2,427 | $4,322 | $7,612 | $17,449 | $29,960 |
Frequently Asked Questions About Percentages
How do I calculate what percentage one number is of another?▼
Use the formula: Percentage = (Part / Whole) × 100. For example, to find what percentage 30 is of 120: (30 / 120) × 100 = 25%. This means 30 is 25% of 120. This formula works for any two numbers — just divide the part by the whole and multiply by 100.
How do I calculate percentage increase between two numbers?▼
Use the formula: Percentage Increase = ((New Value - Old Value) / Old Value) × 100. For example, if a stock price went from $40 to $52: ((52 - 40) / 40) × 100 = 30% increase. Always divide by the OLD (original) value, not the new value.
How do I reverse a percentage to find the original number?▼
To find the original number before a percentage was applied, divide by (1 + percentage/100) for increases, or by (1 - percentage/100) for decreases. For example, if a price after a 20% increase is $120, the original was $120 / 1.20 = $100. If a price after a 25% discount is $75, the original was $75 / 0.75 = $100.
What is the difference between percentage and percentile?▼
A percentage is a ratio out of 100 that shows a proportion (e.g., "you scored 85% on the test"). A percentile indicates your ranking relative to others (e.g., "you scored in the 90th percentile" means you scored higher than 90% of test takers). Percentage measures your performance, percentile measures your position.
How do I calculate percentage change when the original value is zero?▼
Percentage change from zero is mathematically undefined because you would be dividing by zero. In practice, when the starting value is zero, you can report the change as an absolute number rather than a percentage, or use a small positive starting value as an approximation.
How do I add or subtract percentages?▼
You can only directly add or subtract percentages if they are percentages of the same base number. 10% of 200 plus 5% of 200 = 15% of 200 = 30. However, 10% of 200 plus 10% of 300 is NOT 10% of 500 — you must calculate each one separately (20 + 30 = 50) and then express as a percentage of the combined total if needed.
What is a basis point?▼
A basis point (bp or bps) is 1/100th of a percentage point, or 0.01%. It is commonly used in finance to describe small changes in interest rates or bond yields. For example, if an interest rate moves from 3.25% to 3.50%, it increased by 25 basis points. Using basis points avoids confusion between "percentage" and "percentage point" changes.
How do I calculate tax percentage?▼
To find the tax amount: Tax = Price × (Tax Rate / 100). For a $50 item with 8.5% sales tax: $50 × 0.085 = $4.25 in tax. Total price = $50 + $4.25 = $54.25. To find the pre-tax price from a total: Original = Total / (1 + Tax Rate / 100). From $54.25 with 8.5% tax: $54.25 / 1.085 = $50.
Is this percentage calculator free to use?▼
Yes, this percentage calculator is completely free to use with no limits. There is no signup required, no account needed, no ads, and no hidden costs. All calculations are performed instantly in your browser for complete privacy — your data never leaves your device.
How do percentage points differ from percentages?▼
A percentage point is the arithmetic difference between two percentages. If unemployment rises from 5% to 7%, it increased by 2 percentage POINTS (the difference). However, it increased by 40% in PERCENTAGE terms ((7-5)/5 × 100). This distinction matters greatly in economics, finance, and statistics.
Percentage, Decimal, and Fraction Conversion Chart
Converting between percentages, decimals, and fractions is a fundamental math skill. Use this comprehensive reference table for quick conversions:
| Percentage | Decimal | Fraction | Percentage | Decimal | Fraction |
|---|---|---|---|---|---|
| 1% | 0.01 | 1/100 | 50% | 0.50 | 1/2 |
| 5% | 0.05 | 1/20 | 60% | 0.60 | 3/5 |
| 10% | 0.10 | 1/10 | 66.67% | 0.6667 | 2/3 |
| 12.5% | 0.125 | 1/8 | 70% | 0.70 | 7/10 |
| 15% | 0.15 | 3/20 | 75% | 0.75 | 3/4 |
| 20% | 0.20 | 1/5 | 80% | 0.80 | 4/5 |
| 25% | 0.25 | 1/4 | 87.5% | 0.875 | 7/8 |
| 30% | 0.30 | 3/10 | 90% | 0.90 | 9/10 |
| 33.33% | 0.3333 | 1/3 | 95% | 0.95 | 19/20 |
| 40% | 0.40 | 2/5 | 100% | 1.00 | 1/1 |