How to Calculate Any Percentage in 3 Formulas
Every percentage problem falls into one of three patterns. Once you know which formula to reach for, the math takes seconds.
“What is X% of Y?” — Multiply Y by X, divide by 100. What is 15% of 200? 200 × 15 ÷ 100 = 30. Use this for tips, sales tax, discounts, commission, and any time you need a fraction of a whole number expressed as a percentage.
“Percentage change from A to B” — Subtract the old value from the new, divide by the absolute value of the old, multiply by 100. Going from $80 to $100: ((100 − 80) / 80) × 100 = 25% increase. Going from $100 to $80: ((80 − 100) / 100) × 100 = −20% decrease. Notice that a 25% increase followed by a 20% decrease brings you back to the starting point — the percentages are not the same because the base number changes.
“A is what percent of B?” — Divide A by B, multiply by 100. 25 is what percent of 200? (25 / 200) × 100 = 12.5%. Use this for test scores, budget ratios, savings rates, and any part-to-whole comparison.
| Mode | Formula | Example | Result |
|---|---|---|---|
| X% of Y | (X / 100) × Y | 20% of 150 | 30 |
| % Change | ((B − A) / |A|) × 100 | 50 → 75 | 50% increase |
| A is what % of B | (A / B) × 100 | 30 of 120 | 25% |
| X% of Y | (X / 100) × Y | 8.875% of $85 | $7.54 (sales tax) |
| % Change | ((B − A) / |A|) × 100 | $2,000 → $2,300 rent | 15% increase |
| A is what % of B | (A / B) × 100 | $1,500 rent of $5,000 income | 30% |
Why “Going Up 50% Then Down 50%” Doesn't Get You Back to Where You Started
This is the single most misunderstood concept in percentage math. Start with $100. A 50% increase brings you to $150. Now a 50% decrease takes you to $75 — not $100. The base changed. The first 50% was calculated on $100; the second 50% was calculated on $150.
The formula to reverse a percentage increase is: Reverse % = Original % / (1 + Original % / 100) × 100. To undo a 50% increase, you need a 33.33% decrease. To undo a 25% increase, you need a 20% decrease. To undo a 100% increase (doubling), you need a 50% decrease (halving).
This matters when landlords raise rent, when investments drop after gains, and when retailers mark up then “discount.” A store that marks a $100 item up 40% to $140, then offers a 40% off sale, sells it for $84 — pocketing the $16 difference while the customer thinks they got the original price back.
Common Percentage Reversals
| Increase | Decrease Needed to Reverse | $100 Example |
|---|---|---|
| 10% | 9.09% | $100 → $110 → $100 |
| 20% | 16.67% | $100 → $120 → $100 |
| 25% | 20% | $100 → $125 → $100 |
| 50% | 33.33% | $100 → $150 → $100 |
| 100% | 50% | $100 → $200 → $100 |
Percentages in Everyday Money Decisions
Percentages show up in almost every financial transaction. Your rent-to-income ratio (aim for under 30%), credit card APR (divide by 12 for the monthly rate), savings rate (the percentage of income you keep), tip on a restaurant bill, sales tax added at checkout, and investment returns. This calculator handles all of these — pick the mode that matches your question.
For tipping, “what is 20% of $85” is the most common percentage question people search for. The answer: $17. For rent budgeting, “$1,800 is what percent of $6,000 income” tells you your rent-to-income ratio: 30%. For salary negotiations, “percentage change from $75,000 to $82,000” shows you exactly what that raise is worth: 9.33%.
For restaurant tips specifically, the tip calculator handles splitting between people and rounding up. To reverse-engineer a discount, use the discount calculator. For markup vs. margin conversions, the markup calculator shows both sides of the equation.