Percentage Calculator

A percentage is simply a fraction with 100 as the denominator, dressed up in more convenient clothing. When you see 45%, you're looking at 45 parts out of 100, or 0.45 as a decimal. This tool takes that simple concept and applies it to the four scenarios people encounter most often: finding a percentage of a number, calculating how much something increased or decreased, figuring out what portion one number represents of another, and working backward from a final value to find the original.

The confusion usually starts when people mix up which number goes where. Is the discount calculated from the original price or the sale price? Do you divide the small number by the big one, or the other way around? These questions matter because getting them backward gives you answers that seem plausible but are completely wrong. A 25% discount followed by a 25% markup doesn't return you to the original price, for instance. This calculator handles the setup so you can focus on the actual problem you're solving.

The first formula answers "what is X% of Y?" Multiply the percentage by the number and divide by 100. So 15% of 240 becomes (15 × 240) / 100 = 36. You can also convert the percentage to a decimal first: 0.15 × 240 = 36. Same answer, slightly different mental path.

Percentage increase and decrease use the same underlying logic but compare two values. The formula is ((New - Old) / Old) × 100. If your electricity bill went from 85 dollars to 102 dollars, you calculate (102 - 85) / 85 × 100 = 20% increase. For decreases, the result comes out negative, or you can swap the order: (85 - 102) / 85 × 100 = -20%.

The third formula tells you what percentage one number is of another. Divide the part by the whole and multiply by 100. If 18 students passed out of 72 who took the exam, that's (18 / 72) × 100 = 25% pass rate. The fourth formula reverses a percentage change. If something costs 84 dollars after a 20% discount, the original was 84 / (1 - 0.20) = 105 dollars.

Your manager announces a 4% raise effective next month. You currently earn 52,000 dollars annually. The straightforward calculation gives you 52,000 × 0.04 = 2,080 dollars more per year, bringing your new salary to 54,080 dollars. That breaks down to roughly 173 dollars extra per month before taxes.

But here's where percentages get interesting in real life. Inflation last year ran at 3.2%. Your real purchasing power increase is actually closer to 0.8%, not 4%. To find that, subtract the inflation rate from your raise: 4% - 3.2% = 0.8% real increase, which translates to about 416 dollars in actual additional buying power over the year.

Now imagine you're comparing two job offers. One pays 58,000 with no bonus. Another pays 54,000 with a potential 12% performance bonus. The bonus-eligible position maxes out at 54,000 × 1.12 = 60,480 dollars. If you realistically expect to hit 75% of that bonus target, you're looking at 54,000 + (6,480 × 0.75) = 58,860 dollars. Suddenly the comparison becomes clearer.

Retailers know most shoppers can't quickly calculate whether 30% off plus an extra 15% off beats a flat 40% discount. Here's the truth: stacked discounts multiply, they don't add. A 200 dollar item at 30% off becomes 140 dollars. Then 15% off that 140 gives you 119 dollars—a total savings of 40.5%, which barely edges out the flat 40% (which would be 120 dollars). The difference is a single dollar, but the principle matters on bigger purchases.

Another overlooked use: checking restaurant bills. If your meal costs 67 dollars and you want to leave 18% tip, find 10% (6.70), halve it for 5% (3.35), and add them with another 3% (2.01). That gives you roughly 12.06 dollars. Alternatively, calculate 20% (13.40) and subtract a bit. Either way, you'll catch a server who accidentally adds automatic gratuity when you've already tipped. Percentage fluency protects your wallet in small daily ways that compound over time.

The most common error is dividing by the wrong number when calculating percentage change. If sales dropped from 500 units to 400 units, the decrease is (500 - 400) / 500 × 100 = 20%. Many people accidentally divide by 400 (the new value), getting 25% instead. Always divide by the original value, the starting point before the change happened.

Another frequent mistake involves adding percentages that shouldn't be added. If an investment gains 50% one year and loses 50% the next, you don't break even. Starting with 1,000 dollars, you'd have 1,500 after year one, then 750 after year two. You've lost 25% overall. Percentages applied sequentially multiply as decimals (1.50 × 0.50 = 0.75), they don't simply cancel out.

Finally, people regularly confuse percentage points with percentages. If interest rates rise from 4% to 5%, that's a 1 percentage point increase but a 25% relative increase. Financial news often uses these interchangeably, which misleads readers. When precision matters—and with money it usually does—clarify which one you mean.