Calculate percentages instantly with our simple, user-friendly calculator. Perfect for shopping discounts, test scores, tips, taxes, and more!
Calculate final prices after discounts, see how much you save on sales and special offers.
Add sales tax to prices or calculate tax amounts for any purchase.
Calculate tip amount and total bill with tip included.
Calculate profit margin percentage from cost and selling price.
Calculate selling price based on cost and desired markup percentage.
Calculate commission amount based on sales and commission rate.
A percentage represents a portion of 100. To calculate a percentage, you divide the part by the whole and multiply by 100. This fundamental concept is used in countless real-world applications, from calculating grades to determining sales tax.
(Part ÷ Whole) × 100 = Percentage
If you scored 85 out of 100 on a test, your percentage is: (85 ÷ 100) × 100 = 85%
A percentage increase shows how much a value has grown relative to its original amount. This calculation is essential for understanding price changes, salary raises, population growth, and investment returns.
New Value = Original × (1 + Percentage/100)
A $50 item with a 20% price increase: $50 × (1 + 20/100) = $50 × 1.20 = $60
A percentage decrease represents how much a value has reduced from its original amount. This is commonly used for discounts, depreciation, weight loss calculations, and analyzing declining trends.
New Value = Original × (1 - Percentage/100)
A $80 item with a 25% discount: $80 × (1 - 25/100) = $80 × 0.75 = $60
Percentage change measures the relative difference between two values. It's crucial for comparing data over time, analyzing growth rates, and understanding the magnitude of changes in various contexts.
((New - Old) ÷ Old) × 100 = % Change
Stock price changed from $40 to $50: ((50 - 40) ÷ 40) × 100 = 25% increase
When dealing with multiple percentage changes, you cannot simply add or subtract them. Each percentage change is applied to the result of the previous calculation, creating a compound effect.
Final = Initial × (1 + %1/100) × (1 + %2/100) × ...
A $100 investment grows 10% in year 1 and 15% in year 2: $100 × 1.10 × 1.15 = $126.50
Sometimes you need to work backwards from a final value to find the original amount before a percentage was applied. This is common in tax calculations and discount analysis.
Original = Final ÷ (1 + Percentage/100)
If a price including 20% tax is $120, the original price is: $120 ÷ 1.20 = $100
Percentage calculations are fundamental in financial planning and investment analysis:
Smart shoppers use percentages to maximize savings and compare deals:
Businesses rely on percentage calculations for data-driven decisions:
Students and educators use percentages throughout the learning process:
Track health improvements and fitness goals with precision:
Make informed property decisions with percentage calculations:
Percentages are a way to express numbers as parts of 100. The symbol '%' means 'per hundred', making percentages a universal language for comparing and understanding proportions.
Whether you're calculating shopping discounts, analyzing financial data, or determining grades, percentages simplify complex comparisons and make numbers more understandable.
Percentages are everywhere - from price tags in stores to economic news reports. Understanding how to work with percentages helps you make better decisions.
Calculate exact discounts, compare deals, determine final prices with tax, and understand the true value of loyalty programs and cashback offers.
Track interest rates, calculate investment returns, understand compound interest, and analyze financial growth over time.
Interpret surveys, understand market trends, analyze data changes, and present information in an understandable format.
Quick reference for converting between percentages, decimals, and fractions:
| Percentage | 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% | 0.3333 | 1/3 |
| 50% | 0.50 | 1/2 |
| 66.67% | 0.6667 | 2/3 |
| 75% | 0.75 | 3/4 |
| 100% | 1.00 | 1/1 |
$100 shirt with 30% off: Discount = $100 × 0.30 = $30. Final price = $100 - $30 = $70
$50 bill with 15% tip: $50 × 0.15 = $7.50 tip
To calculate a percentage of a number, multiply the number by the percentage and divide by 100. For example, to find 20% of 150: multiply 150 × 20 = 3,000, then divide by 100 = 30. Alternatively, convert the percentage to a decimal (20% = 0.20) and multiply: 150 × 0.20 = 30. This method works for any percentage calculation, whether you're calculating discounts, tips, taxes, or any other percentage-based value.
The percentage increase formula is: ((New Value - Original Value) ÷ Original Value) × 100. For example, if a price increases from $50 to $75, the calculation is: ((75 - 50) ÷ 50) × 100 = (25 ÷ 50) × 100 = 0.5 × 100 = 50% increase. This formula is essential for calculating price changes, salary raises, growth rates, and investment returns. Always subtract the original from the new value first, then divide by the original value.
To calculate percentage decrease: 1) Find the difference between original and new value (Original - New). 2) Divide the difference by the original value. 3) Multiply by 100 to get the percentage. Example: Price drops from $80 to $60. Step 1: 80 - 60 = 20. Step 2: 20 ÷ 80 = 0.25. Step 3: 0.25 × 100 = 25% decrease. This method is perfect for calculating discounts, depreciation, weight loss, or any reduction in value.
To find what percent X is of Y, use the formula: (X ÷ Y) × 100. For instance, to find what percent 25 is of 200: (25 ÷ 200) × 100 = 0.125 × 100 = 12.5%. This calculation is useful for determining test scores (85 out of 100 = 85%), completion rates, market share, or any scenario where you need to express one value as a percentage of another. Always divide the partial value by the total value.
To calculate discount percentage: 1) Subtract the sale price from the original price to find the discount amount. 2) Divide the discount amount by the original price. 3) Multiply by 100. Example: Original price $120, sale price $90. Discount amount: $120 - $90 = $30. Discount percentage: ($30 ÷ $120) × 100 = 25% off. This helps you compare deals, understand savings, and make informed shopping decisions.
Reverse percentage calculation finds the original value when you know the final value and percentage. Formula: Original Value = Final Value ÷ (1 + Percentage/100) for increases, or Original Value = Final Value ÷ (1 - Percentage/100) for decreases. Example: If a price after 20% tax is $120, the original price is: $120 ÷ 1.20 = $100. This is crucial for calculating pre-tax amounts, original prices before discounts, or base salaries before raises.
To add a percentage to a number: 1) Convert the percentage to decimal (divide by 100). 2) Multiply the original number by (1 + decimal). Or use: Original × (1 + Percentage/100). Example: Add 15% to $200. Method 1: 15% = 0.15, so $200 × 1.15 = $230. Method 2: $200 × (1 + 15/100) = $200 × 1.15 = $230. This is used for calculating prices with tax, salary increases, markup pricing, and growth projections.
To calculate percentage difference between two numbers: 1) Find the absolute difference (larger - smaller). 2) Find the average of the two numbers. 3) Divide the difference by the average. 4) Multiply by 100. Formula: |A - B| ÷ ((A + B)/2) × 100. Example: Compare 80 and 100. Difference: 20. Average: 90. Percentage difference: 20 ÷ 90 × 100 = 22.22%. This method is ideal for comparing values without a clear 'before' and 'after' relationship.
Compound percentage applies multiple percentage changes sequentially. Formula: Final = Initial × (1 + %1/100) × (1 + %2/100)... Example: $100 increased by 10% then 20%. Step 1: $100 × 1.10 = $110. Step 2: $110 × 1.20 = $132. Total increase is 32%, not 30%! This is crucial for understanding compound interest, multi-year growth rates, sequential price changes, and investment returns. Each percentage is applied to the result of the previous calculation.
To calculate tip percentage quickly: 1) For 20% tip: Divide bill by 5. 2) For 15% tip: Divide bill by 10, then add half of that. 3) For 10% tip: Divide bill by 10. Example on $80 bill: 20% = $80 ÷ 5 = $16. 15% = $8 + $4 = $12. 10% = $8. Mental math trick: Move decimal one place left for 10%, double it for 20%. These shortcuts help you calculate tips instantly without a calculator.
To calculate sales tax: 1) Multiply the purchase amount by the tax rate (as a decimal). 2) Add the tax to the original amount for the total. Formula: Tax = Price × (Tax Rate/100), Total = Price + Tax. Example: $50 item with 8.5% tax. Tax amount: $50 × 0.085 = $4.25. Total price: $50 + $4.25 = $54.25. To find tax rate from total: Tax Rate = ((Total - Subtotal) ÷ Subtotal) × 100.
Percentage error measures the accuracy of a measurement or estimate. Formula: |Actual Value - Expected Value| ÷ |Expected Value| × 100. Example: You estimate 250 people will attend an event, but 280 actually come. Error: |280 - 250| ÷ 250 × 100 = 30 ÷ 250 × 100 = 12% error. The absolute value ensures error is always positive. This is essential in science, forecasting, quality control, and any field requiring precision measurement.
To calculate percentage of total in Excel: 1) Divide the part by the total using formula =Part/Total. 2) Format as percentage (Ctrl+Shift+%). Example: If cell A1 contains 25 and B1 contains 200, enter =A1/B1 in C1, which gives 0.125 or 12.5%. For running totals: =A2/SUM($A$2:$A$10). The dollar signs create absolute references. Excel automatically multiplies by 100 when you apply percentage formatting. Use for budgets, sales analysis, and data reports.
Markup and margin are different: Markup = ((Selling Price - Cost) ÷ Cost) × 100. Margin = ((Selling Price - Cost) ÷ Selling Price) × 100. Example: Cost $50, Selling Price $75. Markup: (($75 - $50) ÷ $50) × 100 = 50% markup. Margin: (($75 - $50) ÷ $75) × 100 = 33.33% margin. Markup is based on cost (how much you add), margin is based on selling price (your profit percentage). Retailers use markup for pricing, while investors focus on margin.
To calculate percentage change over time, use: ((End Value - Start Value) ÷ Start Value) × 100 ÷ Number of Time Periods = Average % Change per Period. For compound annual growth rate (CAGR): ((End Value ÷ Start Value)^(1/Years) - 1) × 100. Example: Investment grows from $1,000 to $1,500 over 3 years. Simple: 50% ÷ 3 = 16.67% per year average. CAGR: ((1,500 ÷ 1,000)^(1/3) - 1) × 100 = 14.47% annual compound growth.
For easier calculations, convert percentages to decimals by dividing by 100. For example, 25% becomes 0.25, making multiplication simpler and reducing errors.
To quickly estimate percentages, find 10% first (move decimal one place left), then multiply. For 30%, calculate 10% and multiply by 3.
Memorize common percentage equivalents: 50% = 1/2, 25% = 1/4, 20% = 1/5, 10% = 1/10. This speeds up mental calculations significantly.
Verify your results by working backwards. If you calculated 20% of 150 as 30, check: is 30 ÷ 150 = 0.20? This catches errors quickly.
A change from 10% to 15% is a 5 percentage point increase, but a 50% relative increase. Know when each measurement matters.
For compound percentages, multiple discounts, or tax calculations, use our calculator to ensure accuracy and save time.
The concept of percentages has evolved over millennia, becoming an essential tool in modern mathematics and daily life.
Ancient civilizations like the Egyptians and Babylonians used fraction systems that laid the groundwork for percentage concepts. They calculated proportions for taxation, trade, and architectural projects.
Islamic mathematicians advanced the understanding of ratios and proportions. The word 'percent' derives from the Latin 'per centum,' meaning 'by the hundred,' which gained use in medieval commerce.
As trade expanded during the Renaissance, Italian merchants popularized percentage calculations for interest rates and profit margins. The % symbol evolved from the Italian 'per cento.'
Today, percentages are universal in finance, statistics, science, and everyday life. Digital calculators and computers have made complex percentage calculations accessible to everyone.
Many people mix up finding 'X% of a number' with 'increasing by X%'. These are different calculations that yield different results.
Remember: 20% of 100 is 20, but increasing 100 by 20% gives you 120.
You cannot simply add or subtract percentage changes. A 50% increase followed by a 50% decrease doesn't return to the original value.
Calculate each percentage change sequentially: 100 → +50% = 150 → -50% = 75 (not 100).
Confusing these terms leads to major misunderstandings, especially in finance and statistics reporting.
Interest rate rising from 2% to 3% is a 1 percentage point increase, but a 50% relative increase.
Multiplying by the percentage number instead of its decimal equivalent is a frequent calculation error.
Always convert: 15% = 0.15, not 15. So 15% of 200 is 200 × 0.15 = 30, not 200 × 15 = 3000.