Percentage Calculator

What a percentage calculator actually does

A percentage is just a fraction out of 100, so "20%" always means 20 out of every 100 units of whatever you're measuring. A percentage calculator takes the three related numbers in any percentage problem — the part, the whole, and the percentage itself — and works out whichever one you don't have. That covers almost every real-world question people type into a search box: what is X% of Y, one number as a percentage of another, and how much something has gone up or down.

The reason a dedicated tool is useful rather than just doing the division yourself is that percentage problems come in several different shapes, and it's easy to divide by the wrong number or forget to multiply by 100. This page runs through the exact formulas for each common case, with numbers plugged in, so you can check your own math or just trust the calculator above and understand why the answer looks the way it does.

Finding X% of Y

This is the most common percentage question: what is 15% of 200? The formula is (X ÷ 100) × Y. So 15% of 200 is (15 ÷ 100) × 200 = 0.15 × 200 = 30. You can also flip the order and multiply 200 × 0.15 — it comes out the same because multiplication doesn't care about order.

This shows up constantly with discounts, tax, and tips: an 8% sales tax on a $45 purchase is (8 ÷ 100) × 45 = $3.60, making the total $48.60. A 15% off sale on a $60 jacket saves (15 ÷ 100) × 60 = $9, bringing the price to $51. Once you can do this one calculation confidently, most everyday percentage problems become easy [5](https://thiscalc.com/calculators/percentage).

Finding what percent X is of Y

The reverse question is: 25 is what percent of 200? Here the formula is (X ÷ Y) × 100. Divide the part by the whole first, then multiply by 100 to turn the decimal into a percentage: (25 ÷ 200) × 100 = 0.125 × 100 = 12.5%.

A practical example: if you scored 42 out of 50 on a test, your percentage score is (42 ÷ 50) × 100 = 0.84 × 100 = 84%. Or if 18 out of 120 items in a batch were defective, that's (18 ÷ 120) × 100 = 15% defective. The key thing to remember is that the "whole" — the number you're comparing against — always goes on the bottom of the fraction.

Percentage increase and decrease

Percentage change measures how much a value has grown or shrunk relative to where it started. The formula is ((New − Old) ÷ Old) × 100. If a value goes up, the result is positive (an increase); if it goes down, the result is negative (a decrease) [4](https://www.mathsisfun.com/numbers/percentage-change.html).

Example: a product's price rises from $40 to $52. The change is 52 − 40 = 12, and 12 ÷ 40 = 0.3, so that's a 30% increase. Now say a company's headcount drops from 250 employees to 210. The change is 210 − 250 = −40, and −40 ÷ 250 = −0.16, which is a 16% decrease [3](https://www.calculatorsoup.com/calculators/algebra/percent-change-calculator.php).

It's worth noting that percentage increase and decrease are not symmetrical. If a $100 item increases by 50% it becomes $150, but if that $150 item then decreases by 50% it only drops to $75, not back to $100. That's because each percentage change is calculated on a different starting value.

Adding or subtracting a percentage from a number

Sometimes you already know the percentage change and want the resulting value, rather than the change itself. To increase a number by a percentage: New Value = Old Value × (1 + percentage ÷ 100). To increase $80 by 25%: 80 × (1 + 0.25) = 80 × 1.25 = $100.

To decrease a number by a percentage: New Value = Old Value × (1 − percentage ÷ 100). To decrease $80 by 25%: 80 × (1 − 0.25) = 80 × 0.75 = $60. This one-step method is faster than calculating the percentage separately and then adding or subtracting it, and it's exactly what most discount and markup calculations boil down to.

Worked examples you can check by hand

Restaurant bill split with tax: a $86 bill has 9.5% sales tax already included in the menu prices isn't standard, so if tax is added separately: 86 × 0.095 = $8.17 tax, for a total of $94.17.

Salary raise: your salary goes from $52,000 to $56,160. The increase is 56,160 − 52,000 = 4,160, and 4,160 ÷ 52,000 = 0.08, so that's an 8% raise.

Investment loss: a $3,000 investment drops to $2,550. The change is 2,550 − 3,000 = −450, and −450 ÷ 3,000 = −0.15, a 15% loss. To recover back to $3,000 from $2,550, you'd actually need a gain of 450 ÷ 2,550 = 17.6%, not 15% — a good illustration of why percentage changes aren't reversible one-for-one.

Percentage points vs percent

One mistake that trips up even careful writers is confusing percentage points with percent. If an interest rate moves from 5% to 7%, that's a rise of 2 percentage points, but expressed as a percentage change it's (7 − 5) ÷ 5 × 100 = 40%. Both statements are true, but they mean very different things, and mixing them up in a headline or a report can make a change look much bigger or smaller than it is.

When you're reading statistics — approval ratings, tax rates, unemployment figures — check which one is being used. "Up 2 percentage points" and "up 2 percent" are not the same claim, and government and news reports don't always spell out which they mean.

Common mistakes when calculating percentages

The most frequent error is dividing by the wrong number in a percent-of calculation, especially mixing up the part and the whole. Always ask: which number is the total, and which is the piece of it? The total goes on the bottom.

Another common slip is forgetting to convert the percentage to a decimal before multiplying — using 15 instead of 0.15 gives an answer 100 times too large. And when chaining multiple percentage changes (like a discount followed by a tax), remember each percentage applies to the result of the previous step, not to the original number.

Rounding too early is also a problem in multi-step calculations. If you round 0.125 to 0.13 halfway through a longer calculation, your final answer will drift off. Keep full precision until the very last step, then round for display.

Where percentage calculations show up in everyday life

Shopping: working out sale prices, comparing discounts, and adding sales tax. Finance: interest rates, investment returns, loan APRs, and salary raises. Health and fitness: body fat percentage changes, calorie deficits, and progress tracking. School and testing: grade calculations and score comparisons.

Business: profit margins, growth rates, conversion rates, and year-over-year comparisons all rely on the same handful of formulas covered above. Once you know the three basic patterns — percent of a number, one number as a percent of another, and percentage change — you can handle almost any percentage question that comes up without needing to look up a new formula each time [2](https://www.pearson.com/channels/calculators/percentage-calculator).