Percentage Calculator
Every common percentage problem in one tool: what is X% of Y, X is what percent of Y, percent increase or decrease and reverse percentage. Pick the mode, enter your numbers, get the answer with the working shown.
Five Percentage Problems, One Calculator
Almost every percentage question you'll ever face reduces to one of a small set of forms. Once you know the pattern, you can solve any of them on a napkin:
- What is P% of X? Formula:
X × P/100. Example: 18% tip on a $60 bill = $60 × 0.18 = $10.80. - X is what % of Y? Formula:
(X / Y) × 100. Example: 27 of 240 students passed = 27/240 × 100 = 11.25%. - What's the % change from A to B? Formula:
((B − A) / |A|) × 100. Example: stock went from $80 to $92 = +15%. - Increase / decrease X by P%. Formula:
X × (1 ± P/100). Example: $200 with 7% sales tax = $214. - X is the post-discount price at P% off — what was the original? Formula:
X / (1 − P/100). Example: paid $80 after 20% off → original was $100.
Why a 20% raise followed by a 20% pay cut doesn't break even
A salary goes from $50,000 → +20% → $60,000. Then the next year, the company gives a 20% pay cut. New salary: $60,000 × 0.80 = $48,000. Not $50,000.
The error is intuitive but real: the second 20% was applied to a different (larger) base than the first 20%. To exactly undo a 20% increase, you need a ~16.67% decrease. To exactly undo a 50% increase, you need a 33.3% decrease. The bigger the original change, the wider the gap.
This trap shows up everywhere: investment losses ("I lost 50%, but a 50% gain will get me back to even" — no, you need a 100% gain), discount stacking, restaurant bill tipping methods, and political claims about budget changes. Always work with the actual numbers, not the percentages.
Percentage vs Percentage Points — Mind the Difference
This is the most-confused distinction in news and economics writing:
- Going from 5% to 7% is a 2 percentage point increase.
- The same change is a 40 percent increase (because 2 / 5 = 40%).
A headline that says "unemployment rose 40%" sounds like a catastrophe. A headline that says "unemployment rose 2 percentage points, from 5% to 7%" tells you it's not great but not the end of civilization. Both can describe the same change; choose your reading carefully.
Real-World Percentage Use Cases
| Scenario | Problem Type | Quick Formula |
|---|---|---|
| Tip on a restaurant bill | P% of X | Bill × tip%/100 |
| Sales tax on a purchase | Increase X by P% | Price × (1 + tax%/100) |
| Quiz score | X is what % of Y | (Correct / Total) × 100 |
| Stock return | % Change A → B | ((End − Start) / Start) × 100 |
| Discount → original price | Reverse increase | Sale price / (1 − discount%/100) |
| Markup → wholesale price | Reverse increase | Retail / (1 + markup%/100) |
| Inflation adjustment | % Change over years | Old × (1 + inflation%/100)^years |
Mental Shortcuts
- 10% of any number: move the decimal one place left. 10% of 847 = 84.7.
- 5%: 10% divided by 2.
- 15% (standard tip): 10% + half of that. For $80 → 8 + 4 = $12.
- 20% (better tip): 10% × 2.
- X% of Y = Y% of X. 8% of 50 is the same as 50% of 8 (both are 4). Use whichever is easier.
- Doubling = +100%; halving = −50%. Sounds obvious but worth keeping straight.
Common Mistakes With Percentages
- Adding percentages of different bases. A 10% increase followed by a 10% increase is +21%, not +20%.
- Confusing decrease percentages with the "after" number. "30% off" doesn't mean the price is 30% — it means you save 30%, so you pay 70%.
- Mixing percentages and percentage points in arguments or news headlines.
- Forgetting that percentage changes are not symmetric. Losing 50% then gaining 50% leaves you at 75% of where you started.
- Using percentages instead of absolute numbers when the base is small. "Sales grew 200%" sounds great until you learn it was from 1 unit to 3 units.
Frequently Asked Questions
What is 0% of something?
Always zero. 0% of $1 million is $0. 0% of one molecule is also $0.
Can a percentage be greater than 100%?
Yes, when describing increase or a quantity that exceeds the reference. Stock returns can easily exceed 100% over multi-year horizons. A 150% increase means the new value is 2.5× the original.
Can a percentage be negative?
Yes — typically for losses or decreases. A −20% change means the value dropped 20% from the starting point.
What's the difference between percent and percentage?
"Percent" is used with a number (5 percent); "percentage" is used as a noun without a specific number (a small percentage of voters). The math is identical.
How do I convert a decimal to a percentage?
Multiply by 100. 0.75 = 75%. 0.043 = 4.3%. 1.20 = 120%.
How do I convert a fraction to a percentage?
Divide numerator by denominator, then multiply by 100. 3/8 = 0.375 = 37.5%. See our fraction calculator for help with the division.