Percentage Calculator Guide: Growth, Discounts and Ratios
The three percentage formulas that cover almost every real-world calculation you'll need.
Three formulas cover almost every percentage question: percentage of a number = (percentage ÷ 100) × number; what percentage one number is of another = (part ÷ whole) × 100; percentage change = ((new − old) ÷ old) × 100. A common mix-up: going from 20% to 25% is a 5 percentage-point change but a 25% relative increase — these mean different things and matter especially in finance and reporting.
Three formulas cover most cases
Finding a percentage of a number: (percentage ÷ 100) × number — for example, 15% of 200 is (15/100) × 200 = 30. Finding what percentage one number is of another: (part ÷ whole) × 100 — for example, 30 out of 200 is (30/200) × 100 = 15%.
Finding percentage change between two values: ((new − old) ÷ old) × 100 — for example, going from 200 to 230 is ((230−200)/200) × 100 = 15% increase. Almost every everyday percentage question, from a tip calculation to a sales report, is one of these three underlying formulas.
Percentage change vs percentage points
A common mix-up: if a rate goes from 20% to 25%, that's a change of 5 percentage points (25 − 20 = 5), but expressed as a percentage change relative to the original value, it's a 25% increase (((25−20)/20) × 100 = 25%). These describe the same underlying change but produce very different-sounding numbers.
Confusing the two changes the meaning of a statistic significantly, especially in finance and reporting — "interest rates rose by 5%" and "interest rates rose by 5 percentage points" describe genuinely different magnitudes of change, and financial news, in particular, is worth reading carefully for which one is meant.
Calculating a discount quickly
For a discount, multiply the original price by (100 − discount%) ÷ 100. An $80 item at 25% off: $80 × 0.75 = $60. The same logic in reverse lets you back into an original price if you only know the sale price and discount percentage — divide the sale price by (100 − discount%) ÷ 100 to recover the original.
Stacked discounts (25% off, then an additional 10% off) don't simply add to 35% off — each discount applies to the already-discounted price, so the combined effect is slightly less than the sum would suggest: $80 → $60 (25% off) → $54 (additional 10% off), a combined 32.5% off, not 35%.
This same principle explains why a 50% price drop followed by a 50% price increase doesn't return to the original price. $100 dropping 50% becomes $50; that $50 then rising 50% becomes only $75, not $100 — because each percentage is calculated against a different base value, not the original one.
Formula reference table
| What you need | Formula | Example |
|---|---|---|
| X% of a number | (X ÷ 100) × number | 15% of 200 = 30 |
| What % is part of whole | (part ÷ whole) × 100 | 30 of 200 = 15% |
| Percentage change | ((new − old) ÷ old) × 100 | 200 → 230 = 15% increase |
| Discounted price | price × (100 − X%) ÷ 100 | $80 at 25% off = $60 |
Common real-world use cases
Shoppers use percentage-of calculations constantly to figure out sale prices at checkout, and percentage-change calculations to compare deals across different discount structures. Employees calculating a tip use the same core formula as someone figuring out a raise's dollar value from a stated percentage increase.
Business owners and analysts use percentage change formulas to report growth (revenue up 15% year over year), while HR teams use the same math for salary adjustments and merit increases. Students encounter percentage calculations in test scoring, and anyone reading financial or economic news benefits from correctly distinguishing percentage change from percentage points when interpreting a headline statistic.
Common pitfalls and best practices
- Adding stacked percentages together. Two discounts of 25% and 10% don't combine to 35% off — each applies to the already-reduced price, so the true combined discount is always slightly less than the sum.
- Confusing percentage change with percentage points. "Increased by 5%" and "increased by 5 percentage points" describe different magnitudes unless the starting value happens to be 100 — always check which one a statistic actually means.
- Using the wrong base for a percentage-change calculation. Percentage change is always calculated relative to the original (old) value, not the new one — reversing this gives a mathematically different, incorrect answer.
- Assuming a 50% decrease and a 50% increase cancel out. They don't — a $100 item that drops 50% to $50 needs a 100% increase, not 50%, to get back to $100, since percentage change is always relative to a different base value.
Use the calculator
- Open the Percentage Calculator.
- Choose the calculation type you need (of, change, or ratio).
- Enter your values and get the instant result.