Percentage Calculator
Find percentages, increases, decreases, ratios & reverse percentages instantly
About the Percentage Calculator
This free percentage calculator handles six common percentage problems in one place — finding a percentage of a number, working out what percentage one number is of another, calculating percentage increase or decrease, reversing a percentage to find the original value, converting a ratio to a percentage, and applying discounts or sales taxes to a price.
- Switch between six calculation modes using the tabs — no need to remember different formulas.
- Get a clear breakdown showing the formula used and step-by-step values.
- Percentage change mode automatically detects whether a value increased or decreased.
- Discount and sales tax mode shows the final price and the exact amount added or removed.
- Works with decimals and negative numbers for accurate real-world results.
How to Calculate a Percentage
To find a percentage of a number, divide the percentage by 100 and multiply it by the number: percentage ÷ 100 × number. To find what percentage one number is of another, divide the part by the whole and multiply by 100.
"Percent" literally means "per hundred" — a percentage is simply a fraction expressed out of 100. Whether you're calculating a discount at checkout, working out exam scores, comparing year-over-year revenue growth, or splitting a restaurant bill, the underlying math is always the same: converting between a part, a whole, and a ratio expressed as a fraction of 100.
This calculator covers the six most common percentage problems people search for, each with its own formula and a step-by-step breakdown so you can see exactly how the result was reached.
The Six Percentage Formulas Explained
1. Finding a Percentage of a Number
Example: What is 25% of 200? → (25 ÷ 100) × 200 = 0.25 × 200 = 50.
2. Finding What Percentage One Number Is of Another
Example: 50 is what percent of 200? → (50 ÷ 200) × 100 = 0.25 × 100 = 25%.
3. Percentage Increase or Decrease
Example: A value rises from 80 to 100 → ((100 − 80) ÷ 80) × 100 = (20 ÷ 80) × 100 = 25% increase. A positive result means an increase; a negative result means a decrease.
4. Reverse Percentage (Finding the Original Number)
Example: 50 is 25% of what number? → 50 ÷ (25 ÷ 100) = 50 ÷ 0.25 = 200. This is useful when you know a discounted price or a partial amount and need to work backward to the full value.
5. Ratio to Percentage
Example: A ratio of 3:4 → 3 ÷ (3 + 4) × 100 = 3 ÷ 7 × 100 ≈ 42.86% for the first part, and the remainder for the second.
6. Discount and Sales Tax Calculations
Sales Tax / Markup: Final Price = Price × (1 + Percentage ÷ 100)
Example: A $1,000 item with a 20% discount → $1,000 × (1 − 0.20) = $1,000 × 0.80 = $800, a savings of $200. To add a 8.5% sales tax to a $50 item → $50 × 1.085 = $52.50.
Common Real-World Uses for Percentage Calculations
| Scenario | Mode to Use |
|---|---|
| Working out a discount or sale price | Discount / Tax |
| Adding U.S. sales tax to a price | Discount / Tax |
| Calculating a test score from correct answers | X is what % |
| Comparing salary, revenue, or population growth | % Change |
| Finding the original price before a discount was applied | Reverse % |
| Splitting a budget or converting odds/ratios | Ratio → % |
| Calculating commission or interest on an amount | % of a Number |
Tips for Working with Percentages
- Percentage points vs. percent: Going from 20% to 25% is a 5 percentage point increase, but it's a 25% relative increase (5 ÷ 20 × 100). These two phrasings describe different things and are often confused — particularly in financial and political reporting.
- Negative percentages in change calculations: A negative result in the percentage change formula means the value decreased — for example, going from 100 to 80 gives −20%, a 20% decrease.
- Order matters for sequential percentages: Applying a 10% increase followed by a 10% decrease does not return you to the original number, because the second percentage is calculated on a different base value.
- U.S. sales tax varies by state: Unlike a fixed national rate, U.S. sales tax rates differ by state and sometimes by county or city. Five states — Alaska, Delaware, Montana, New Hampshire, and Oregon — have no statewide sales tax.
- Rounding: For financial calculations, round only at the final step to avoid compounding small rounding errors across multiple calculations.
Frequently Asked Questions
About This Tool & Editorial Standards
This percentage calculator uses standard arithmetic formulas for percentage, ratio, and proportional calculations. The educational content on this page is written and periodically reviewed by the Toolriz tools team for accuracy. This tool is provided for general informational purposes only and is not a substitute for professional financial, tax, or accounting advice. For tax-related questions, consult a CPA or refer to the IRS website at irs.gov.