Every everyday percentage in one place
Tips, sales, raises, budget shares, test scores and growth figures all use percentages, and it is easy to grab the wrong formula. This calculator takes two numbers, X and Y, and shows the five most common calculations at once. Just read the line that answers your question.
The five formulas
| Question | Formula | With X = 15 and Y = 80 |
|---|---|---|
| What is X% of Y? | X ÷ 100 × Y | 12 |
| What percent of Y is X? | X ÷ Y × 100 | 18.75% |
| What is the percent change from X to Y? | (Y − X) ÷ X × 100 | +433.33% |
| What is Y increased by X%? | Y × (1 + X ÷ 100) | 92 |
| What is Y decreased by X%? | Y × (1 − X ÷ 100) | 68 |
Everyday examples
- A 15% tip on an $80 bill: 80 × 15 ÷ 100 = $12.
- 15 correct answers out of 80: 15 ÷ 80 × 100 = 18.75%.
- A subscription that goes from $15 to $80: (80 − 15) ÷ 15 × 100 ≈ +433%.
- An $80 bill plus 15%: 80 × 1.15 = $92.
- An $80 item at 15% off: 80 × 0.85 = $68.
Common percentages applied to 80
| Percent | X% of 80 | 80 increased | 80 decreased |
|---|---|---|---|
| 5% | 4 | 84 | 76 |
| 10% | 8 | 88 | 72 |
| 18% | 14.4 | 94.4 | 65.6 |
| 20% | 16 | 96 | 64 |
| 25% | 20 | 100 | 60 |
| 50% | 40 | 120 | 40 |
Classic traps
- Successive percentages don’t add up: two 10% increases make 21%, not 20% (1.1 × 1.1 = 1.21).
- A cut doesn’t undo a rise of the same size: +50% then −50% takes 100 to 75.
- Percent or percentage points? A rate moving from 4% to 5% rises by 1 point, which is a 25% relative increase.
- Working backwards: if a price rose 20% to reach $96, the original price was 96 ÷ 1.2 = $80, not 96 minus 20% ($76.80).
Mental math shortcuts
For 10%, move the decimal point one place left. For 5%, halve the 10% figure. For 20%, double it. For 25%, divide by 4, and for 50%, by 2. For 1%, move the decimal point two places. Combining these handles most tips and discounts in your head: 15% = 10% + 5%, 18% = 20% − 2%. A lesser-known trick: X% of Y equals Y% of X, so 8% of 50 is the same as 50% of 8, which is 4.
Percent change versus percent difference
Percent change has a direction: it compares a new value with an old one. Percent difference compares two values with no starting point, using their average as the base: |A − B| ÷ ((A + B) ÷ 2) × 100. Use percent change for prices over time and percent difference to compare two products or measurements side by side.