What Is a Percentage?
A percentage is a way of expressing a number as a fraction of 100. The word comes from the Latin "per centum," meaning "by the hundred." When you say 45%, you're saying 45 out of every 100, or 45/100, or 0.45 as a decimal.
Percentages are everywhere in daily life: sales tax, discounts, tips, interest rates, grades, statistics, battery levels, and more. Knowing how to calculate percentages quickly and accurately is one of the most practical math skills you can have.
This guide covers every common percentage calculation you'll encounter, with clear formulas and real-world examples.
Skip the math and use our free percentage calculator. Open Percentage Calculator →
The Three Basic Percentage Formulas
Nearly every percentage problem boils down to three basic types:
Type 1: Find a Percentage of a Number
Result = Number × (Percentage / 100)
Example: What is 15% of 240?
Result = 240 × (15 / 100) = 240 × 0.15 = 36
Type 2: Find What Percentage One Number Is of Another
Percentage = (Part / Whole) × 100
Example: 45 is what percentage of 180?
Percentage = (45 / 180) × 100 = 0.25 × 100 = 25%
Type 3: Find the Whole When You Know the Part and Percentage
Whole = Part / (Percentage / 100)
Example: 60 is 30% of what number?
Whole = 60 / (30 / 100) = 60 / 0.30 = 200
How to Calculate Percentage Increase
Percentage increase tells you how much a value has grown relative to its original amount. This is essential for tracking salary raises, investment returns, price inflation, and more.
Percentage Increase = ((New Value − Old Value) / Old Value) × 100
Examples
Salary raise: Your salary went from $52,000 to $56,000.
Increase = ((56,000 − 52,000) / 52,000) × 100 = (4,000 / 52,000) × 100 = 7.69% raise
Stock price: A stock went from $45 to $72.
Increase = ((72 − 45) / 45) × 100 = (27 / 45) × 100 = 60% increase
Population growth: A city grew from 250,000 to 310,000 people.
Increase = ((310,000 − 250,000) / 250,000) × 100 = 24% increase
How to Calculate Percentage Decrease
Percentage decrease measures how much a value has dropped. Useful for tracking weight loss, price reductions, declining sales, or market corrections.
Percentage Decrease = ((Old Value − New Value) / Old Value) × 100
Examples
Price drop: A laptop was $1,200, now it's $899.
Decrease = ((1,200 − 899) / 1,200) × 100 = (301 / 1,200) × 100 = 25.08% decrease
Weight loss: You went from 195 lbs to 175 lbs.
Decrease = ((195 − 175) / 195) × 100 = (20 / 195) × 100 = 10.26% decrease
How to Calculate Percentage Difference
Percentage difference compares two values without designating one as the "original." It's useful when comparing two competing products, test results, or any two quantities where neither is the baseline.
Percentage Difference = (|Value₁ − Value₂| / ((Value₁ + Value₂) / 2)) × 100
Example: Compare prices of two similar products: $45 and $52.
Difference = (|45 − 52| / ((45 + 52) / 2)) × 100 = (7 / 48.5) × 100 = 14.43% difference
Important: Percentage difference is not the same as percentage change. Use percentage change (increase/decrease) when one value is clearly the "before" and the other is "after."
Discount Calculations
Shopping discounts are one of the most common real-world percentage applications. Here's every scenario you might encounter:
Finding the Sale Price
Sale Price = Original Price × (1 − Discount% / 100)
Example: A $250 jacket is 35% off.
Sale Price = $250 × (1 − 0.35) = $250 × 0.65 = $162.50
Finding the Discount Amount
Discount Amount = Original Price × (Discount% / 100)
Example: A $250 jacket is 35% off.
Discount = $250 × 0.35 = $87.50 off
Finding the Original Price from Sale Price
Original Price = Sale Price / (1 − Discount% / 100)
Example: You paid $162.50 after a 35% discount. What was the original price?
Original = $162.50 / (1 − 0.35) = $162.50 / 0.65 = $250.00
Stacking Discounts
Multiple discounts don't simply add up! A 20% discount followed by an additional 15% discount is NOT 35% off.
Example: $100 item with 20% off, then an additional 15% off:
- After 20%: $100 × 0.80 = $80
- After 15%: $80 × 0.85 = $68
Effective total discount: 32%, not 35%
Tip Calculations
Calculating tips is a daily use of percentages. Here are quick methods:
The Standard Method
Tip = Bill × (Tip Percentage / 100)
For a $85 bill:
- 15% tip: $85 × 0.15 = $12.75
- 18% tip: $85 × 0.18 = $15.30
- 20% tip: $85 × 0.20 = $17.00
- 25% tip: $85 × 0.25 = $21.25
Quick Mental Math Tricks
- 10% shortcut: Move the decimal point one place left. 10% of $85 = $8.50
- 20% shortcut: Calculate 10%, then double it. $8.50 × 2 = $17.00
- 15% shortcut: Calculate 10% + half of that. $8.50 + $4.25 = $12.75
- 25% shortcut: Divide by 4. $85 / 4 = $21.25
Tax Percentage Calculations
Calculating Sales Tax
Tax = Price × (Tax Rate / 100)
Total = Price × (1 + Tax Rate / 100)
Example: $49.99 item with 8.875% sales tax (NYC):
Tax = $49.99 × 0.08875 = $4.44
Total = $49.99 + $4.44 = $54.43
Finding Pre-Tax Price from Total
Pre-tax Price = Total / (1 + Tax Rate / 100)
Example: You paid $54.43 total with 8.875% tax. What was the pre-tax price?
Pre-tax = $54.43 / 1.08875 = $49.99
Grade and GPA Percentage Calculations
Converting Score to Percentage
If you scored 42 out of 50 on a test:
Percentage = (42 / 50) × 100 = 84%
Common US Grade Scale
| Letter Grade | Percentage Range | GPA Points |
|---|---|---|
| A+ | 97-100% | 4.0 |
| A | 93-96% | 4.0 |
| A− | 90-92% | 3.7 |
| B+ | 87-89% | 3.3 |
| B | 83-86% | 3.0 |
| B− | 80-82% | 2.7 |
| C+ | 77-79% | 2.3 |
| C | 73-76% | 2.0 |
| D | 60-69% | 1.0 |
| F | Below 60% | 0.0 |
Weighted Average Percentage
When different components have different weights (common in course grades):
Weighted Average = Σ(Score × Weight) / Σ(Weight)
Example: Your course has:
- Homework (20%): scored 92%
- Midterm (30%): scored 78%
- Final (50%): scored 85%
Weighted average = (92 × 0.20) + (78 × 0.30) + (85 × 0.50) = 18.4 + 23.4 + 42.5 = 84.3%
Percentage in Finance
Interest Rates
Interest rates are percentages applied to money. A 5% interest rate on a $10,000 savings account yields $500/year in simple interest. See our compound interest guide for exponential growth.
Inflation Rate
Inflation measures the percentage increase in prices over time. If inflation is 3%, a $100 item this year will cost $103 next year. Over 10 years at 3% inflation, that same item costs $134.39.
Profit Margin
Profit Margin = ((Revenue − Cost) / Revenue) × 100
Example: You sell a product for $80 that costs you $52 to make.
Margin = ((80 − 52) / 80) × 100 = 35% profit margin
Markup vs. Margin
Don't confuse markup with margin! Markup is based on cost; margin is based on selling price.
- Markup = ((80 − 52) / 52) × 100 = 53.8% markup
- Margin = ((80 − 52) / 80) × 100 = 35% margin
Common Percentage Conversions
Fractions to Percentages
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333... | 33.33% |
| 1/4 | 0.25 | 25% |
| 1/5 | 0.2 | 20% |
| 1/8 | 0.125 | 12.5% |
| 1/10 | 0.1 | 10% |
| 2/3 | 0.667... | 66.67% |
| 3/4 | 0.75 | 75% |
| 3/8 | 0.375 | 37.5% |
| 5/8 | 0.625 | 62.5% |
| 7/8 | 0.875 | 87.5% |
Decimal to Percentage
Multiply by 100 and add the % sign: 0.742 = 74.2%
Percentage to Decimal
Divide by 100: 74.2% = 0.742
Percentage Mistakes to Avoid
- Adding percentages incorrectly: A 50% increase followed by a 50% decrease does NOT return to the original. $100 + 50% = $150, then $150 − 50% = $75 (a 25% net loss!).
- Confusing percentage points with percentages: Going from 10% to 15% is a 5 percentage point increase, but a 50% relative increase.
- Stacking discounts: As shown above, 20% off + 15% off ≠ 35% off.
- Forgetting the base: "50% more" depends on what you're measuring. 50% more than 20 = 30, but 50% more than 100 = 150.
- Reversing the base in percentage change: Always divide by the original (starting) value, not the new value.
Explore More Tools
- Percentage Calculator -- Calculate any percentage instantly
- Tax Calculator -- Estimate your taxes
- ROI Calculator -- Calculate return on investment
- Compound Interest Guide -- When percentages grow exponentially
- Mortgage Calculator Guide -- Understand mortgage interest rates
Use our free percentage calculator for all your calculations. Open Percentage Calculator →
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Frequently Asked Questions
How do you calculate a percentage of a number?
To find a percentage of a number, multiply the number by the percentage and divide by 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 you calculate percentage increase?
Percentage increase = ((New Value − Old Value) / Old Value) × 100. For example, if a stock goes from $50 to $65: ((65 − 50) / 50) × 100 = 30% increase.
How do you calculate percentage decrease?
Percentage decrease = ((Old Value − New Value) / Old Value) × 100. For example, if a price drops from $80 to $60: ((80 − 60) / 80) × 100 = 25% decrease.
How do you find what percentage one number is of another?
Divide the part by the whole and multiply by 100. For example, what percentage is 35 of 200? (35 / 200) × 100 = 17.5%. This tells you that 35 is 17.5% of 200.
How do you calculate a tip percentage?
Multiply the bill amount by the tip percentage divided by 100. For a 20% tip on a $85 bill: $85 × 0.20 = $17 tip. Quick trick: find 10% ($8.50) and double it ($17) for 20%.
How do you calculate a discount percentage?
If you know the original and sale price: Discount % = ((Original − Sale Price) / Original) × 100. If you know the discount percentage: Sale Price = Original × (1 − Discount/100). A $120 item at 30% off = $120 × 0.70 = $84.
How do you calculate percentage difference between two numbers?
Percentage difference = (|Value1 − Value2| / ((Value1 + Value2) / 2)) × 100. For example, the percentage difference between 40 and 60: (20 / 50) × 100 = 40%. This is different from percentage change, which has a clear "before" and "after."
How do you convert a fraction to a percentage?
Divide the numerator by the denominator and multiply by 100. For example, 3/8 as a percentage: (3 ÷ 8) × 100 = 37.5%. Common fractions: 1/4 = 25%, 1/3 ≈ 33.33%, 1/2 = 50%, 2/3 ≈ 66.67%, 3/4 = 75%.
How do you calculate GPA percentage?
GPA percentage conversion depends on the scale. Common US conversions: A (4.0) = 93-100%, B (3.0) = 83-86%, C (2.0) = 73-76%. To calculate weighted GPA, multiply each course grade by its credit hours, sum them, and divide by total credit hours.
How do you calculate tax percentage?
Tax amount = Price × Tax Rate / 100. For an 8.5% sales tax on a $50 item: $50 × 0.085 = $4.25 tax. Total: $54.25. To find the pre-tax price from a total: Pre-tax = Total / (1 + Tax Rate/100).