What is X% of Y?
X is what percent of Y?
X is Y% of what?
Percentage increase / decrease
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The three percentage formulas
Every percentage question is one of three rearrangements of the same relationship - part = percent × whole:
| Question | Formula | Example |
|---|---|---|
| What is 20% of 150? | (20 ÷ 100) × 150 | = 30 |
| 30 is what % of 150? | (30 ÷ 150) × 100 | = 20% |
| 30 is 20% of what? | 30 ÷ (20 ÷ 100) | = 150 |
Mental math shortcuts
Start from 10%: move the decimal one place left (10% of 64 = 6.4). Then build: 20% is double, 5% is half, 15% is one-and-a-half times. And use the symmetry trick when it helps: X% of Y always equals Y% of X - 8% of 50 feels hard, but 50% of 8 is obviously 4.
Fractions, decimals, and percentages
| Fraction | Decimal | Percent |
|---|---|---|
| 1/10 | 0.1 | 10% |
| 1/8 | 0.125 | 12.5% |
| 1/5 | 0.2 | 20% |
| 1/4 | 0.25 | 25% |
| 1/3 | 0.333… | 33.33% |
| 1/2 | 0.5 | 50% |
| 2/3 | 0.667… | 66.67% |
| 3/4 | 0.75 | 75% |
| 1/1 | 1.0 | 100% |
Percentage change vs. percentage points
When a rate moves from 4% to 5%, two true statements sound contradictory: it rose 1 percentage point, and it rose 25 percent. Points compare by subtraction (5 − 4 = 1); percent change compares by division ((5 − 4) ÷ 4 = 0.25). Interest rates, poll numbers, and unemployment figures are almost always quoted in points; growth and prices in percent. When a headline says "rates jumped 25%", check which one the writer actually meant - it is one of the most common numerical errors in news.
One more asymmetry worth knowing: gains and losses don't cancel. A 50% loss needs a 100% gain to get back to even, because the second change is measured from a smaller base. That is also why "up 25%, then down 20%" lands exactly where it started.
Frequently asked questions
How do I calculate a percentage of a number?
Divide the percentage by 100 and multiply by the number: X% of Y = (X ÷ 100) × Y. For example, 20% of 150 = 0.20 × 150 = 30. Mental shortcut: find 10% by moving the decimal point one place left, then scale - 20% is double that, 5% is half of it.
How do I find what percent one number is of another?
Divide the part by the whole and multiply by 100: (part ÷ whole) × 100. So 30 out of 150 is 30 ÷ 150 × 100 = 20%. This is the formula for test scores, market share, progress toward a goal - any "out of" question.
What is the formula for percentage increase or decrease?
Percentage change = (new − old) ÷ old × 100. From 80 to 100: (100 − 80) ÷ 80 × 100 = +25%. From 100 to 80: (80 − 100) ÷ 100 × 100 = −20%. Note the asymmetry - the change is always measured relative to the starting value, which is why +25% and −20% undo each other.
What is the difference between a percentage change and percentage points?
If an interest rate rises from 4% to 5%, it rose by 1 percentage point but by 25 percent (1 is a quarter of 4). Percentage points compare two percentages by subtraction; percent change compares them by division. News reports mix these up constantly - when a change of rates is described, check which one is meant.
How do I calculate a discount price quickly?
Multiply the price by (100 − discount) ÷ 100. A $80 item at 25% off: 80 × 0.75 = $60. Mental shortcut: 25% off means you pay 3/4; 20% off means you pay 4/5. For odd percentages, find 10% and build from there.
How do I find the original price before a discount?
Divide the sale price by (100 − discount) ÷ 100. If something costs $60 after 25% off, the original was 60 ÷ 0.75 = $80. A common mistake is adding 25% back to $60, which gives $75 - wrong, because the 25% was taken from the larger original price.
How much should I tip?
In the United States, 15-20% of the pre-tax bill is standard for table service, with 20% signaling good service; counter service is commonly 0-10%. In much of Europe, service is included and rounding up or 5-10% is generous. The tip calculator above splits the total per person too.
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