Percentage Calculator
Calculate any percentage instantly. Find what is X% of Y, X is what percent of Y, percentage increase, decrease, difference, or change — with step-by-step formulas. Works worldwide.
Choose a calculation mode and enter your numbers. Results update live as you type, with the full formula shown for every answer.
| Step | Action | Calculation | Result |
|---|
| Percentage | Result | Percentage | Result |
|---|
* This calculator uses standard mathematical formulas and gives precise results. For very large numbers, results may be rounded to 6 decimal places for readability. All calculations are performed locally in your browser — no data is sent to any server.
Related Calculators
What Is a Percentage Calculator?
A percentage calculator is a free online tool that solves every common percent problem in seconds. Whether you need to find a percentage of a number, work out what percent one value is of another, calculate a percentage increase or decrease, or find the percentage change between two values — this calculator handles all six core calculation types in a single page.
Our percentage calculator is used worldwide by students working through homework, shoppers calculating discounts, employees figuring out tips, businesses calculating markups and margins, and professionals computing statistics. No matter your country or currency, the math is the same — and the answers are instant.
The 6 Types of Percentage Calculations
This calculator handles every percentage problem you'll ever encounter. Choose the mode that matches your question:
- What is X% of Y? — Find a percentage of a number. (Example: What is 20% of 250? → 50)
- X is what percent of Y? — Find what percent one number is of another. (Example: 10 is what percent of 50? → 20%)
- X is Y% of what? — Find the original whole when you know a part and its percentage. (Example: 30 is 15% of what? → 200)
- Percentage Increase / Decrease — Calculate how much a value has grown or shrunk in percentage terms.
- Percentage Difference — Find the symmetric difference between two values as a percentage.
- Percentage Change — Calculate the directional change from an old value to a new value.
Percentage Formulas Explained
Here are the standard mathematical formulas used by our calculator. These are universal and used worldwide in schools, businesses, and statistical work:
Result = (X / 100) × Y
2. X is what percent of Y?
Result = (X / Y) × 100
3. X is Y% of what?
Result = X / (Y / 100)
4. Percentage Increase / Decrease:
Result = ((New − Old) / Old) × 100
5. Percentage Difference:
Result = (|A − B| / ((A + B) / 2)) × 100
6. Percentage Change:
Result = ((New − Old) / |Old|) × 100
Real-World Examples
Here's how each calculation type is used in everyday life:
| Scenario | Question | Calculation | Answer |
|---|---|---|---|
| Shopping Discount | 20% off $250? | (20 ÷ 100) × 250 | $50 off → Pay $200 |
| Tip at Restaurant | 15% tip on $80? | (15 ÷ 100) × 80 | $12 tip |
| Test Score | 42 out of 50, what %? | (42 ÷ 50) × 100 | 84% |
| Sales Tax | $200 + 8% tax? | 200 + (8% × 200) | $216 |
| Salary Raise | $50K → $55K, what %? | ((55 − 50) ÷ 50) × 100 | 10% increase |
| Stock Drop | $120 → $90, what %? | ((90 − 120) ÷ 120) × 100 | 25% decrease |
| Business Markup | $30 cost + 40% markup? | 30 + (40% × 30) | $42 selling price |
| Reverse Discount | Sale price $80 was 20% off — original? | 80 ÷ (1 − 0.20) | $100 original |
How to Calculate Percentages by Hand (Mental Math Tricks)
These shortcuts will help you estimate percentages quickly without a calculator:
- The 10% trick: Move the decimal one place left. 10% of 350 = 35. 10% of 47 = 4.7.
- The 1% trick: Move the decimal two places left. 1% of 350 = 3.5. 1% of 47 = 0.47.
- 15% (common tip): Take 10%, then add half of it. 15% of 60 = 6 + 3 = 9.
- 20% (common tip/discount): Take 10% and double it. 20% of 75 = 7.5 × 2 = 15.
- 5%: Take 10% and halve it. 5% of 80 = 8 ÷ 2 = 4.
- Percentages are reversible: 8% of 50 = 50% of 8 = 4. This swap often makes mental math easier.
Percentage Increase vs. Percentage Difference: What's the Difference?
These two terms are commonly confused, but they answer different questions:
Percentage Increase (or Decrease) is directional. It tells you how much something went up or down from a starting point. Formula: ((New − Old) / Old) × 100. Example: A price going from $100 to $125 is a 25% increase.
Percentage Difference is symmetric. It tells you how far apart two values are, without caring which is "first" or "second". Formula: (|A − B| / average(A, B)) × 100. Example: The difference between $80 and $120 is 40%.
Use percentage change/increase when comparing before-and-after values (stock prices, salaries, weight, population). Use percentage difference when comparing two independent values that don't have an inherent order (like comparing two products' prices side-by-side).
Percentage vs. Percentile vs. Percentage Point
Three commonly-confused terms — here's the clean distinction:
- Percentage: A part out of 100. "30% of students passed." (30 out of every 100.)
- Percentile: A ranking position. "Scoring in the 90th percentile" means you scored higher than 90% of test-takers. Common in standardized tests.
- Percentage point: The absolute difference between two percentages. If interest rates rise from 4% to 6%, that's a "2 percentage point" increase, but a 50% percentage increase. Mixing these up is a classic mistake in news headlines.
Common Percentage Mistakes to Avoid
- Adding and subtracting percentages doesn't reverse. A 20% discount followed by a 20% increase does not bring you back to the original price. $100 → −20% → $80 → +20% → $96 (not $100).
- Confusing "increase by X%" with "increase to X%". "Increase by 50%" means add 50% of the original. "Increase to 50%" means the new value IS 50%.
- Dividing by the wrong base. For percentage change, always divide by the ORIGINAL value, not the new one.
- Compounding percentages incorrectly. Two consecutive 10% increases give a 21% total increase, not 20%. (1.10 × 1.10 = 1.21)
- Treating percentages as numbers. "50% of 50%" is 25%, not 100% — you multiply, not add.