About This Percentage Calculator
Welcome to the most comprehensive percentage calculator online. Whether you need to calculate what percentage one number is of another, find the percentage increase or decrease, or solve any percentage-related problem, this free tool provides instant, accurate results with step-by-step formulas.
Our percentage calculator supports 6 calculation modes to handle every percentage scenario you encounter in daily life, business, academics, or professional work. From calculating discounts and tips to analyzing financial data and academic scores, this tool is designed for speed, accuracy, and ease of use.
100% free, no sign-up required. All calculations are performed instantly in your browser with results accurate to 10 decimal places. Perfect for students, teachers, business professionals, shoppers, and anyone who works with percentages.
What Is a Percentage?
A percentage (from Latin "per centum" meaning "by the hundred") is a number or ratio expressed as a fraction of 100. It is denoted using the percent sign %. For example, 25% means 25 per 100, or 25/100, or 0.25 as a decimal.
Percentages are used to express how large or small one quantity is relative to another quantity. They're essential in finance, statistics, science, and everyday calculations like discounts, taxes, tips, interest rates, and test scores.
How to Use the Percentage Calculator
This calculator offers 6 different calculation modes to solve any percentage problem. Here's how to use each mode:
1. Percentage of a Number (What is X% of Y?)
Calculate what a specific percentage of a number equals. Perfect for discounts, tips, taxes, and commissions.
- Example: What is 20% of 150? → Answer: 30
- Formula: (Percentage ÷ 100) × Number = Result
- Use Cases: Calculate 15% tip on a $60 meal, find 30% off a $200 item, determine 5% sales tax
2. What Percent? (X is what % of Y?)
Find what percentage one number represents of another. Useful for calculating scores, completion rates, and proportions.
- Example: 30 is what % of 150? → Answer: 20%
- Formula: (Part ÷ Whole) × 100 = Percentage
- Use Cases: Calculate test scores (18 out of 20 correct), project completion (45 of 60 tasks done), market share
3. Percentage Increase
Calculate the percentage increase when a value grows from an original amount to a larger amount.
- Example: Increase from 50 to 75 → Answer: 50% increase
- Formula: ((New Value - Original Value) ÷ Original Value) × 100 = % Increase
- Use Cases: Calculate salary raises, price increases, population growth, investment gains
4. Percentage Decrease
Calculate the percentage decrease when a value drops from an original amount to a smaller amount.
- Example: Decrease from 100 to 80 → Answer: 20% decrease
- Formula: ((Original Value - New Value) ÷ Original Value) × 100 = % Decrease
- Use Cases: Calculate discounts, price reductions, weight loss, depreciation
5. Percentage Difference
Calculate the percentage difference between two values without designating one as "original." Uses the average of both values as the reference point.
- Example: Difference between 100 and 120 → Answer: 18.18% difference
- Formula: (|Value1 - Value2| ÷ ((Value1 + Value2) ÷ 2)) × 100
- Use Cases: Compare sales between two products, compare test scores, analyze data sets
6. Percentage Change
Calculate the overall percentage change (increase or decrease) from an original value to a new value. Shows positive change for increases and negative for decreases.
- Example: Change from 80 to 100 → Answer: +25% change
- Formula: ((New Value - Original Value) ÷ Original Value) × 100
- Use Cases: Track stock price changes, analyze year-over-year growth, monitor KPI changes
Percentage Formulas & Worked Examples
Understanding the formulas behind percentage calculations empowers you to solve problems mentally or verify calculator results. Here are the core formulas with detailed examples:
Basic Percentage Formula
Percentage = (Part ÷ Whole) × 100
This is the fundamental formula. It tells you what percentage a part is of a whole.
Example: In a class of 40 students, 10 got an A grade. What percentage got an A?
Percentage = (10 ÷ 40) × 100 = 0.25 × 100 = 25%
Answer: 25% of students got an A.
Finding X% of a Number
Result = (Percentage ÷ 100) × Number or Result = Number × (Percentage / 100)
Example: A jacket costs $80. It's on sale for 35% off. How much is the discount?
Discount = (35 ÷ 100) × 80 = 0.35 × 80 = $28
Final price = $80 - $28 = $52
Answer: The discount is $28; you pay $52.
Percentage Increase Formula
% Increase = ((New - Original) ÷ Original) × 100
Example: Your rent was $1,200/month and increased to $1,320/month. What's the percentage increase?
% Increase = ((1320 - 1200) ÷ 1200) × 100 = (120 ÷ 1200) × 100 = 0.10 × 100 = 10%
Answer: 10% rent increase.
Percentage Decrease Formula
% Decrease = ((Original - New) ÷ Original) × 100
Example: A laptop originally priced at $1,000 is now $750. What's the percentage decrease?
% Decrease = ((1000 - 750) ÷ 1000) × 100 = (250 ÷ 1000) × 100 = 0.25 × 100 = 25%
Answer: 25% price reduction.
Percentage Difference Formula
% Difference = (|Value1 - Value2| ÷ Average) × 100 where Average = (Value1 + Value2) ÷ 2
Example: Product A costs $90, Product B costs $110. What's the percentage difference?
Average = (90 + 110) ÷ 2 = 100
Difference = |90 - 110| = 20
% Difference = (20 ÷ 100) × 100 = 20%
Answer: 20% difference between the two products.
Common Percentage Conversions
- Decimal to Percentage: Multiply by 100. (0.75 → 75%)
- Percentage to Decimal: Divide by 100. (45% → 0.45)
- Fraction to Percentage: Divide numerator by denominator, multiply by 100. (3/4 → 0.75 → 75%)
- Percentage to Fraction: Write as X/100, then simplify. (60% → 60/100 → 3/5)
Frequently Asked Questions
How do I calculate percentage of a number?
Multiply the number by the percentage and divide by 100. Formula: (Percentage ÷ 100) × Number. For example, 20% of 150 = (20 ÷ 100) × 150 = 30. Alternatively, convert the percentage to decimal (20% = 0.20) and multiply: 0.20 × 150 = 30.
How do I find what percentage one number is of another?
Divide the first number by the second number, then multiply by 100. Formula: (Part ÷ Whole) × 100 = Percentage. For example, 30 is what % of 150? (30 ÷ 150) × 100 = 20%. This tells you that 30 represents 20% of 150.
How do I calculate percentage increase?
Subtract the original value from the new value, divide by the original value, then multiply by 100. Formula: ((New - Original) ÷ Original) × 100. For example, an increase from 50 to 75: ((75 - 50) ÷ 50) × 100 = 50% increase.
How do I calculate percentage decrease?
Subtract the new value from the original value, divide by the original value, then multiply by 100. Formula: ((Original - New) ÷ Original) × 100. For example, a decrease from 100 to 80: ((100 - 80) ÷ 100) × 100 = 20% decrease.
What is the difference between percentage change and percentage difference?
Percentage change compares a new value to an original value: ((New - Original) ÷ Original) × 100. Percentage difference compares two values without designating one as 'original': (|Value1 - Value2| ÷ ((Value1 + Value2) ÷ 2)) × 100. Use percentage change for before/after comparisons; use percentage difference for comparing two independent values.
How do I calculate reverse percentage?
To find the original number before a percentage increase/decrease, divide the final amount by (1 + percentage/100) for increases, or by (1 - percentage/100) for decreases. Example: If $120 is after a 20% increase, the original is: 120 ÷ 1.20 = $100. For a 20% decrease to $80, the original is: 80 ÷ 0.80 = $100.
What is 20% of 150?
20% of 150 is 30. Calculation: (20 ÷ 100) × 150 = 0.20 × 150 = 30. This is one of the most common percentage calculations used in discounts, tips, and everyday math.
How do I calculate percentage in Excel or Google Sheets?
In Excel/Google Sheets, use formulas: Percentage of a number: =A1*(B1/100) or =A1*0.20 for 20%. What percent is X of Y: =(A1/B1)*100. Percentage increase: =((B1-A1)/A1)*100. Format cells as Percentage (%) to automatically multiply by 100 and display the % symbol.
Why do percentages sometimes add up to more than 100%?
Percentages can exceed 100% in cases like: multiple percentage increases applied sequentially (compound growth), percentage changes relative to different base values, or when measuring multiple categories that overlap. For example, a 50% increase followed by another 50% increase results in a 125% total increase (not 100%).
How accurate is this percentage calculator?
Our percentage calculator is accurate to 10 decimal places using JavaScript's native math operations. Results are rounded to 2 decimal places for display but maintain full precision for chained calculations. It handles edge cases like division by zero and provides mathematically correct results for all percentage operations.