"What percentage is that?" comes up constantly — a discount at checkout, a grade on a test, a raise at work, a stat in the news. There isn't just one percentage formula; there are really five common ones, each answering a slightly different question. Here's all of them, with the math laid bare.
The Five Percentage Questions
| Question | Formula | Example |
|---|---|---|
| What is X% of Y? | (X ÷ 100) × Y | 20% of 250 = 50 |
| X is what % of Y? | (X ÷ Y) × 100 | 50 of 200 = 25% |
| % change from A to B | ((B − A) ÷ |A|) × 100 | 80 → 100 = 25% increase |
| Increase/decrease Y by X% | Y × (1 ± X ÷ 100) | 500 + 20% = 600 |
| X is Y% of what number? | X ÷ (Y ÷ 100) | 45 is 30% of 150 |
1. What Is X% of Y?
The most common one: finding a portion of a whole. Divide the percentage by 100 to get a decimal, then multiply by the total. 20% of 250 is (20 ÷ 100) × 250 = 50. This is the formula behind tips, discounts, and commission calculations.
2. X Is What Percent of Y?
The reverse question: you know the part and the whole, and want the percentage. Divide the part by the whole, then multiply by 100. If you scored 50 out of 200 on a test, that's (50 ÷ 200) × 100 = 25%.
3. Percentage Change (Increase or Decrease)
This one trips people up because the direction matters. Subtract the original value from the new value, divide by the original value, then multiply by 100. Going from 80 to 100 is ((100 − 80) ÷ 80) × 100 = 25% increase. Going from 100 back to 80 is ((80 − 100) ÷ 100) × 100 = −20% — not the same magnitude, which is exactly why you always divide by the original number, not the new one.
4. Increasing or Decreasing a Number by X%
To add a percentage on top of a number, multiply by (1 + the percentage as a decimal): $500 increased by 20% is 500 × 1.20 = $600. To subtract, multiply by (1 − the decimal): $500 decreased by 20% is 500 × 0.80 = $400. This is exactly how sales tax and discounts are calculated.
5. X Is Y% of What Number?
The least common but occasionally essential one: working backward to the original total. Divide the known part by the percentage (as a decimal): if 45 is 30% of some number, that number is 45 ÷ 0.30 = 150.
Step-by-Step: Use a Percentage Calculator
- Choose which of the five questions matches what you're trying to find
- Enter the numbers you already know
- Get the exact answer instantly, without doing the arithmetic by hand
Try It Yourself
Use our free Percentage Calculator — all five formulas in one place
Open Percentage Calculator →