Percentage Calculator
Calculate percentages instantly — find X% of Y, what percent one number is of another, percentage change, increase, and decrease.
📊 Percentage Calculator
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A percentage is a way of expressing a number as a fraction of 100, denoted by the symbol %. The word comes from the Latin per centum, meaning "by the hundred." Introduced to Europe through medieval Italian merchants who needed a standardized way to calculate trade profits and taxes, percentages are now the universal language of comparison — used in finance, science, medicine, education, and everyday life.
This percentage calculator handles all five of the most common percentage operations: finding a percentage of a number, finding what percent one number is of another, calculating percentage change between two values, and computing percentage increase or decrease. Each calculation is shown with its formula and step-by-step solution.
The 5 Percentage Formulas You Must Know
| Operation | Formula | Example | Result |
|---|---|---|---|
| X% of Y | (X ÷ 100) × Y | 15% of 240 | 36 |
| X is what % of Y | (X ÷ Y) × 100 | 45 is what % of 180 | 25% |
| % Change | ((New − Old) ÷ |Old|) × 100 | 80 → 100 | +25% |
| % Increase | Y × (1 + X/100) | 200 increased by 15% | 230 |
| % Decrease | Y × (1 − X/100) | 200 decreased by 15% | 170 |
How to Calculate X% of a Number — Step by Step
This is the most common percentage question: "What is 20% of 350?" The method is straightforward:
Step 2: Multiply by the number → 0.20 × 350 = 70
Shortcut: Move the decimal point two places left. 20% becomes 0.20, then multiply.
Real-world uses: calculating a 20% restaurant tip on a $85 bill ($17), finding 8.5% sales tax on a $1,200 purchase ($102), or determining a 30% discount on a $250 jacket ($75 off → you pay $175).
How to Find What Percentage One Number Is of Another
This answers: "36 is what percent of 150?"
Example: (36 ÷ 150) × 100 = 0.24 × 100 = 24%
Common applications: calculating your exam score as a percentage (you scored 78 out of 90 → 86.7%), finding what percentage of your monthly income goes toward rent ($1,200 rent ÷ $4,500 income × 100 = 26.7%), or working out a company's market share (company sales $8M ÷ total market $50M × 100 = 16%).
How to Calculate Percentage Change
Percentage change measures the relative difference between two values — showing whether something increased or decreased and by how much. This is critical in finance, economics, and data analysis.
Increase example: Price went from $80 to $100 → ((100 − 80) ÷ 80) × 100 = +25%
Decrease example: Stock dropped from $150 to $120 → ((120 − 150) ÷ 150) × 100 = −20%
A positive result means the value increased; a negative result means it decreased. The absolute value of the original (|Old Value|) ensures the formula works correctly even when the old value is negative (such as when a company moves from a loss to a profit).
Percentage in Real-Life Finance — Key Applications
Understanding percentages is the foundation of financial literacy. Here's how percentages appear in the most important financial decisions:
- Interest rates: A personal loan at 12% per annum means you pay 12% of the outstanding principal each year as interest. On a $10,000 loan, that's $1,200/year.
- Income tax brackets: Tax rates are percentages applied to income ranges. If the 25% bracket applies to income between $40,000–$85,000, you pay 25% of any income in that range (not 25% of your total income).
- Investment returns (CAGR): A mutual fund with 12% CAGR turns $10,000 into $31,058 over 10 years, using the compound growth formula: 10,000 × (1 + 0.12)^10.
- Inflation: 6% annual inflation means goods costing $100 today will cost $106 next year and $179 in 10 years.
- GST/VAT/Sales tax: 18% GST on a ₹5,000 product adds ₹900, making the final price ₹5,900.
- Discount and markup: A 40% markup on a $50 item costs the retailer adds $20 → selling price $70. A 30% discount at checkout reduces the price by 30%.
How to Reverse a Percentage (Find the Original Value)
Often you know the result after a percentage was applied, but need the original. This is called the "reverse percentage" or "working backwards from a percentage."
| Situation | Formula | Example |
|---|---|---|
| Price after X% increase | Original = Final ÷ (1 + X/100) | $120 after 20% increase → $120 ÷ 1.20 = $100 |
| Price after X% decrease | Original = Final ÷ (1 − X/100) | $85 after 15% discount → $85 ÷ 0.85 = $100 |
| Amount includes X% tax | Pre-tax = Total ÷ (1 + X/100) | $118 includes 18% GST → $118 ÷ 1.18 = $100 |
Common Percentage Mistakes to Avoid
Even people comfortable with numbers make these errors:
- Percentage points vs percentages: If interest rates rise from 4% to 6%, that's an increase of 2 percentage points — but a 50% increase in the rate itself. These are very different statements.
- Reversing isn't symmetric: A 50% increase followed by a 50% decrease does NOT return to the original. $100 → +50% = $150 → −50% = $75. You've lost $25.
- Using the wrong base: Percentage change always uses the original value as the base, not the new one. Going from 80 to 100 is a 25% increase (using 80 as base), not a 20% increase (using 100 as base).
- Cumulative percentages: Two successive 10% increases do not equal a 20% increase. $100 → +10% = $110 → +10% = $121. The combined effect is 21%, not 20%.