Percentage Calculator
To calculate a percentage, divide the part by the whole and multiply by 100. Formula: Percentage = (part / whole) × 100. For example, 25 out of 100 = 25%. To find percentage change: ((new - old) / old) × 100.
Calculate percentages easily. Find what percent one number is of another, calculate percentage increase/decrease, or find the whole from a percentage. Includes formulas, worked examples, and educational content.
Fill any 2 fields and the 3rd will calculate automatically.
Formula: Value × Percentage% = Result
Worked Examples
1. Calculate a 15% tip on an $85 bill
Problem: You ate at a restaurant and your bill is $85. How much should you tip at 15%?
Tip = $85 × (15 / 100)
Tip = $85 × 0.15
Tip = $12.75
→ Enter Value=85, Percentage=15 to verify
2. Find the percentage increase from $50 to $65
Problem: A product price increased from $50 to $65. What is the percentage increase?
Percentage Increase = (Increase / Old Value) × 100
Percentage Increase = ($15 / $50) × 100
Percentage Increase = 30%
→ Enter Value=50, Result=15 to find 30%
3. What percent is 45 out of 180?
Problem: You scored 45 points out of 180 possible points. What percentage did you achieve?
Percentage = (45 / 180) × 100
Percentage = 0.25 × 100
Percentage = 25%
→ Enter Value=180, Result=45 to get 25%
4. Calculate sale price with 25% off a $120 item
Problem: A jacket originally costs $120 and is on sale for 25% off. What is the sale price?
Discount = $120 × (25 / 100) = $120 × 0.25 = $30
Sale Price = Original Price - Discount
Sale Price = $120 - $30 = $90
→ Enter Value=120, Percentage=25 to get $30 discount
5. Calculate a grade percentage
Problem: A student earned 87 points on a test worth 100 points. What is their grade percentage?
Grade % = (87 / 100) × 100
Grade % = 87%
→ Enter Value=100, Result=87 to verify 87%
Percentage Formulas
Basic Percentage Formula
Percentage = (Part ÷ Whole) × 100
or equivalently: Part = Whole × (Percentage ÷ 100)
Use this to find what percentage one number is of another, or to find a part given the whole and percentage.
Percentage Increase Formula
% Increase = ((New - Old) ÷ Old) × 100
Example: Price went from $80 to $100 → ((100-80) ÷ 80) × 100 = 25% increase
Percentage Decrease Formula
% Decrease = ((Old - New) ÷ Old) × 100
Example: Price dropped from $100 to $75 → ((100-75) ÷ 100) × 100 = 25% decrease
Percentage Difference Formula
% Difference = (|A - B| ÷ ((A + B) ÷ 2)) × 100
Use when comparing two values without a clear "original" value. Example: Compare 40 and 60 → (20 ÷ 50) × 100 = 40% difference
Common Percentages Quick Reference
| Percentage | Fraction | Decimal | Common Use |
|---|---|---|---|
| 10% | 1/10 | 0.10 | Standard tip, tax estimate |
| 15% | 3/20 | 0.15 | Restaurant tip |
| 20% | 1/5 | 0.20 | Good tip, common discount |
| 25% | 1/4 | 0.25 | Quarter off sale |
| 33.33% | 1/3 | 0.333 | One-third split |
| 50% | 1/2 | 0.50 | Half off, split in two |
| 66.67% | 2/3 | 0.667 | Two-thirds majority |
| 75% | 3/4 | 0.75 | Three-quarter completion |
| 100% | 1 | 1.00 | Full amount, doubling |
What Is a Percentage?
A percentage is a way of expressing a number as a fraction of 100. The word itself comes from the Latin phrase "per centum," meaning "by the hundred." When we say 50%, we mean 50 out of 100, or half of something. This standardized way of expressing proportions makes it easy to compare different quantities and understand relative sizes.
The percentage symbol (%) represents division by 100. So 25% is equivalent to 25/100, which simplifies to 1/4 or 0.25 as a decimal. This relationship between percentages, fractions, and decimals is fundamental to understanding how percentages work in everyday calculations.
A Brief History of Percentages
The concept of percentages has ancient roots. Ancient Romans calculated proportions in fractions of 100, even though they lacked our modern notation. The actual percent sign (%) evolved over centuries from an Italian abbreviation of "per cento." By the 17th century, mathematicians standardized the symbol we use today.
The widespread adoption of percentages in commerce, science, and everyday life came with the growth of banking and international trade. Merchants needed a standard way to express interest rates, profit margins, and discounts that could be understood across different number systems and currencies. Today, percentages are so ubiquitous that we encounter them dozens of times daily, from weather forecasts to nutrition labels.
Real-World Applications of Percentages
Finance and Banking
Percentages are the language of finance. Interest rates on savings accounts, mortgages, and credit cards are all expressed as percentages. When your bank offers a 4.5% APY on a savings account, that means for every $100 deposited, you earn $4.50 per year. Investment returns, stock market changes, and inflation rates all use percentages to communicate financial performance. Understanding these percentages directly impacts your wealth-building decisions.
Shopping and Discounts
Every sale sign uses percentages: "30% OFF," "Buy One Get One 50% Off," "Save Up to 70%." Being able to quickly calculate discounts helps you make informed purchasing decisions. If a $200 jacket is 35% off, you can calculate the $70 discount to know you'll pay $130. Similarly, understanding sales tax percentages (which vary by state from 0% to over 10%) helps you budget accurately.
Grades and Academic Performance
Academic grading systems worldwide use percentages. A score of 85% means you answered 85 out of every 100 points correctly. GPA calculations convert letter grades into numerical equivalents based on percentage ranges. Understanding how individual assignment scores weighted by percentages contribute to your final grade is essential for academic planning.
Statistics and Data Analysis
Researchers, journalists, and data analysts use percentages to communicate findings. Election polls report that "52% of voters support candidate A." Medical studies might find that "a treatment reduced symptoms by 40%." Sports statistics track shooting percentages, win percentages, and improvement percentages. In all these cases, percentages help standardize comparisons across different sample sizes and contexts.
Health and Nutrition
Nutrition labels display percentages of daily recommended values. When a food label says "20% Daily Value of Iron," it means one serving provides 20% of the iron you need daily. Body fat percentages, medication dosages relative to body weight, and treatment efficacy rates all rely on percentage calculations to communicate health information effectively.
Tips and Gratuities
Calculating tips is one of the most common everyday uses of percentages. Standard tipping ranges from 15-20% in the United States. For a quick 20% calculation, find 10% (move the decimal one place left) and double it. On an $85 bill, 10% is $8.50, so 20% is $17. Mental percentage shortcuts like this make daily calculations faster.
Tips for Quick Mental Percentage Calculations
- 10% — Simply move the decimal point one place to the left. 10% of 85 = 8.5
- 5% — Find 10% and halve it. 5% of 80 = 8 ÷ 2 = 4
- 15% — Find 10%, then add half of it. 15% of 80 = 8 + 4 = 12
- 20% — Find 10% and double it. 20% of 85 = 8.5 × 2 = 17
- 25% — Divide by 4. 25% of 80 = 80 ÷ 4 = 20
- 50% — Simply halve the number. 50% of 86 = 43
- 1% — Move the decimal two places left. 1% of 250 = 2.5
How to Use
- Enter your value in the input field
- Click the Calculate/Convert button
- Copy the result to your clipboard
Frequently Asked Questions
- How do I calculate percentage of a number?
- To calculate a percentage of a number, multiply the number by the percentage and divide by 100. Formula: (Number × Percentage) / 100. For example, 25% of 200 = (200 × 25) / 100 = 50. Alternatively, convert the percentage to a decimal (25% = 0.25) and multiply: 200 × 0.25 = 50.
- How do I find what percent one number is of another?
- To find what percent one number is of another, divide the part by the whole and multiply by 100. Formula: (Part / Whole) × 100 = Percentage. For example, to find what percent 30 is of 150: (30 / 150) × 100 = 20%. So 30 is 20% of 150.
- How do I calculate percentage increase or decrease?
- To calculate percentage change, use the formula: ((New Value - Old Value) / Old Value) × 100. A positive result is an increase, negative is a decrease. For example, if a price goes from $80 to $100: ((100 - 80) / 80) × 100 = 25% increase. If it drops to $60: ((60 - 80) / 80) × 100 = -25% decrease.
- What is the formula for calculating percentages?
- The basic percentage formula is: Percentage = (Part / Whole) × 100. To find the part: Part = (Percentage × Whole) / 100. To find the whole: Whole = (Part × 100) / Percentage. These three variations let you solve any percentage problem depending on which values you know.
- How do I convert fractions to percentages?
- To convert a fraction to a percentage, divide the numerator by the denominator and multiply by 100. For example, 3/4 = 0.75 × 100 = 75%. Common conversions: 1/2 = 50%, 1/4 = 25%, 1/5 = 20%, 1/3 ≈ 33.33%, 2/3 ≈ 66.67%.
- How do I calculate percentage difference between two numbers?
- Percentage difference compares two values relative to their average: |Value1 - Value2| / ((Value1 + Value2) / 2) × 100. For example, the percentage difference between 40 and 60: |40 - 60| / ((40 + 60) / 2) × 100 = 20 / 50 × 100 = 40%. This differs from percentage change, which uses one value as the base.
- How do I calculate a tip percentage?
- To calculate a tip, multiply the bill amount by the tip percentage divided by 100. For a 15% tip on an $85 bill: $85 × (15/100) = $85 × 0.15 = $12.75. Quick mental math: find 10% by moving the decimal ($8.50), then add half of that for 15% ($8.50 + $4.25 = $12.75).
- How do I calculate discount and sale price?
- To find the discount amount, multiply the original price by the discount percentage divided by 100. Then subtract from the original price. For 25% off a $120 item: Discount = $120 × 0.25 = $30. Sale price = $120 - $30 = $90. Alternatively, multiply by (1 - discount%): $120 × 0.75 = $90.
- What is the difference between percentage and percentile?
- A percentage is a portion out of 100 (e.g., scoring 85% on a test means 85 out of 100 points). A percentile indicates rank relative to others (e.g., being in the 85th percentile means you scored higher than 85% of test-takers). Percentage measures performance; percentile measures relative standing.
- How do I reverse a percentage to find the original number?
- To find the original number before a percentage was applied, divide the result by the percentage as a decimal. If 30 is 25% of a number: Original = 30 ÷ 0.25 = 120. For increases: if a price after a 20% increase is $120, the original was $120 ÷ 1.20 = $100.