Percentage Calculator
Find a percentage, or what percent one number is of another.
Find a percentage, or what percent one number is of another.
Percentages appear everywhere: discounts in shops, marks in exams, interest rates, tax, tips, nutrition labels, battery levels and news headlines. The idea is simple, but small misunderstandings cause expensive and confusing mistakes. This guide explains what a percentage really is, shows the formulas you need most often, and points out the traps that catch many people. You can check every example with the calculator above.
The word percent means out of one hundred. When you say 20 percent, you mean 20 parts out of every 100, which is the same as the fraction 20/100, the decimal 0.20, or one fifth. Converting between these forms is the key skill. To turn a percentage into a decimal, divide by 100. To turn a decimal into a percentage, multiply by 100.
To find X percent of Y, multiply Y by X and divide by 100. For example, 20 percent of 250 is 250 times 20 divided by 100, which equals 50. In the calculator, enter 20 as Number X and 250 as Number Y, and the first line of the result gives the answer. This is the calculation you use for discounts, tax, commission and tips.
To find what percent X is of Y, divide X by Y and multiply by 100. If you scored 42 out of 60 in a test, divide 42 by 60 to get 0.7, then multiply by 100 to get 70 percent. The second line of the calculator does this for you. This is the formula for exam scores, completion rates and shares of a budget.
Percentage change compares a new value with an old one. The formula is new minus old, divided by old, multiplied by 100. If your monthly sales rise from 80 to 100, the change is 20 divided by 80, which is 25 percent. If they fall from 100 to 80, the change is minus 20 divided by 100, which is a 20 percent decrease. The size of the change is different because the starting point is different. You can use the calculator for this too: type the new value as X and the old value as Y, read the second line, and subtract 100 from the answer.
Suppose a price goes up by 25 percent and later falls by 25 percent. Many people expect to be back where they started, but they are not. A price of 100 becomes 125 after the rise. A 25 percent fall from 125 is 31.25, leaving 93.75. The second percentage was applied to a bigger number. The same effect explains why a 50 percent loss needs a 100 percent gain to recover.
News reports often mix up these two ideas. If an interest rate moves from 10 percent to 12 percent, it has risen by two percentage points. The relative increase is two divided by ten, which is 20 percent. Both statements are correct, but they mean different things. When you read a headline, ask whether the figure refers to a change in points or a relative change.
Sometimes you know the final amount and the percentage that was added or removed, and you need the original value. If a price of 1,170 includes 17 percent tax, the original price is 1,170 divided by 1.17, which equals 1,000. If an item costs 3,400 after a 15 percent discount, the original price is 3,400 divided by 0.85, which equals 4,000. The common error is to subtract or add the percentage from the final figure, which gives the wrong answer because the percentage was based on the original amount.
If you sell products, you will meet two similar terms. Markup is profit as a percentage of cost, and margin is profit as a percentage of the selling price. Buy an item for 600 and sell it for 1,000. The profit is 400. The markup is 400 divided by 600, about 66.7 percent. The margin is 400 divided by 1,000, which is 40 percent. A shop that wants a 40 percent margin cannot get it by adding 40 percent to cost. It would need to charge cost divided by 0.6, which is 1,000 in this example.
Most percentage errors come from a short list. People forget which number is the base. They add percentages that should be multiplied, such as two discounts or two years of growth. They confuse percentage points with percent. They type 0.15 when the tool expects 15. And they round too early in a long calculation. Slow down, check the base number, and use a rough estimate to see if the answer is sensible.
Enter two numbers. The first line shows X percent of Y, and the second line shows what percent X is of Y. The calculator works in your browser and does not save your numbers. For anything involving money, double check the final figure against your invoice, receipt or bank statement.
Can a percentage be more than 100? Yes. 150 percent of a number is one and a half times that number.
How do I find the percent increase? Use new minus old, divided by old, times 100.
Is 20 percent off then 10 percent off the same as 30 percent off? No. It equals 28 percent, because the second discount applies to the reduced price.