Answer: The Percentage Calculator answers the three core percent questions — what is X% of Y, X is what percent of Y, and the percent change between two values — instantly, with the worked formula shown.
A percentage calculator answers the three core percent questions — what is X% of Y, X is what percent of Y, and percent change from X to Y — without mental math.
Calculate percentages, percentage change, discounts, and more
This percentage calculator handles every common percentage task in one place: finding a percent of a number, computing percent increase or decrease, and converting between fractions, decimals, and percentages. Results update as you type, right in your browser.
Percentages appear everywhere — discounts, taxes, tips, grades, interest, statistics — yet the underlying arithmetic is only three small formulas. Once you see them, the tool becomes a fast check on everyday numbers.
Percent of a number: x% of N = (x ÷ 100) × N. For example, 15% of 240 = 0.15 × 240 = 36. Percent change: ((new − old) ÷ old) × 100. A price rising from 240 to 300 changes by (300 − 240) ÷ 240 × 100 = 25%.
The reverse — what percent is A of B — is (A ÷ B) × 100: 36 is 15% of 240. Note that percent change is not symmetric: going from 240 to 300 is a 25% increase, but falling from 300 back to 240 is only a 20% decrease, because the base (denominator) changed.
The table lists quick reference values computed exactly from the formulas above, including sales-tax-like and tip-like amounts people reach for daily. Each value is (percent ÷ 100) × 240, shown to two decimals where relevant.
Mental math shortcut: 10% of a number is just the number with the decimal moved one place left (24 for 240), and 5% is half of that (12), so 15% = 24 + 12 = 36 without touching a calculator.
| Percent | x% of 240 | 240 minus x% |
|---|---|---|
| 5% | 12 | 228 |
| 10% | 24 | 216 |
| 15% | 36 | 204 |
| 20% | 48 | 192 |
| 25% | 60 | 180 |
| 50% | 120 | 120 |
A common trap: saying an interest rate 'went up 2%' when it moved from 3% to 5%. That is a rise of 2 percentage points but a 66.7% relative increase ((5−3)÷3 × 100). Financial and medical reporting usually means percentage points when they say 'percent,' but relative change when they say 'percent increase.'
| Rate move | Percentage points | Relative change | Everyday reading |
|---|---|---|---|
| 3% → 5% | +2 pts | +66.7% | "Up 2 points" or "up two-thirds in relative terms" |
| 5% → 3% | −2 pts | −40.0% | Fell 2 points, but 40% of the rate is gone |
| 4% → 6% | +2 pts | +50.0% | Same 2 points, smaller relative jump than 3→5 |
| 10% → 12% | +2 pts | +20.0% | Headline says 2 points; the borrower pays 20% more interest |
Notice how the points column stays flat while the relative column swings with the starting rate — which is why headlines about "a 2-point hike" and "rates up 66%" can both be true. Whichever convention a source uses, the number that matters to your wallet is usually the points one for rates, and the relative one for prices.
The same care applies to repeated changes. A 20% discount followed by a 20% price increase does not return the original price: 100 → 80 → 96. Multiplicative changes compose, so to undo x% up you need a different percent down (a 20% rise is undone by a 16.7% fall).
Reverse percentages trip up almost everyone, and the instinct — subtract the percent back off — is wrong. If a price rose 25% to $250, the original wasn't 250 − 62.50; it was 250 ÷ 1.25 = $200. The increase was 25% of the original, so you divide the end value by (1 + rate as a decimal). Markdowns flip the sign: an item now $250 after a 20%-off tag started at 250 ÷ 0.8 = $312.50.
This shows up everywhere once you look: pre-tip bill amounts, list prices "after savings," salaries quoted as take-home, and tax-inclusive prices abroad (a €100 VAT-inclusive dinner at 20% VAT holds only €83.33 of food). The pattern never changes — divide by the multiplier — and running the forward calculation to check (200 × 1.25 = 250 ✓) catches slips.
In statistics, percentages describe proportions of a whole, but small samples mislead: 4 out of 5 dentists is 80%, yet it might come from a survey of five people. Percentages from samples under 100 jump in whole-point steps (each person is worth several points), which is why reliable survey results report sample sizes alongside.
Percentile is another distinct idea — a percentile rank places a value within a distribution (a 90th-percentile test score beats 90% of takers), which says nothing about percent correct. Keep the two straight and most standardized-test and growth-chart reporting becomes easy to read.
Retail discounts stack multiplicatively, not additively: a "take an extra 20% off already-reduced 30% off" item costs 0.7 × 0.8 = 56% of the original price — a 44% total discount, not 50%. Sales tax applies to the discounted price, so a $100 item at 30% off with 8% tax costs $70 × 1.08 = $75.60.
Tips are pure percent-of-bill arithmetic: 18% of a $45 check is $8.10, 20% is $9.00. Splitting a bill with tip across a group is the same formula per person. Tax is sometimes excluded from the tip base by custom, though practice varies by country.
Grades and goals work the same way: a test score of 87 out of 120 is 72.5% — divide earned by possible. And "percent of goal" tracks progress identically: 63 units sold against a 90-unit target is 70% to goal. Every one of these is a single divide-and-multiply, which is all a percentage ever is.
How do I calculate a percentage of a number?
Convert the percent to a decimal (divide by 100) and multiply: 15% of 240 = 0.15 × 240 = 36. For mental math, take 10% (move the decimal one place left) and scale — 5% is half of 10%, 15% is 10% plus 5%.
How is percentage increase calculated?
Percentage increase = ((new − old) ÷ old) × 100. If a value goes from 240 to 300, the increase is 60 ÷ 240 × 100 = 25%. Decrease uses the same formula; the result is negative.
What is the difference between percent and percentage points?
Percentage points measure absolute change between two percentages: moving from 3% to 5% is +2 points. Percent change measures relative change: that same move is a 66.7% increase ((5−3)÷3 × 100).
Why doesn't a 20% discount plus 20% markup cancel out?
Each percentage applies to a different base. 100 with 20% off is 80; adding 20% to 80 gives 96, not 100. To exactly undo a 20% increase you need a 16.7% decrease (1 ÷ 1.2 − 1).
How do I convert a fraction to a percentage?
Divide the numerator by the denominator and multiply by 100: 3/8 = 0.375 = 37.5%. Going the other way, a percentage becomes a fraction by putting it over 100 and simplifying — 45% = 45/100 = 9/20.
How do I find the original number before a percentage change?
Divide, don't subtract. If a price rose 25% to $250, the original was 250 ÷ 1.25 = $200 — subtracting 25% of 250 gives the wrong $187.50. After a decrease to $250 from a 20% markdown, the original was 250 ÷ 0.8 = $312.50. The divisor is always (1 ± rate as a decimal).
What's the difference between percent and percentile?
Percent is a share of a whole; percentile is a position in a ranked distribution. A 90th-percentile test score beat 90% of takers and says nothing about the percent of questions answered correctly — a 90th-percentile result could be a 62% raw score on a hard exam.