Percentage Calculator

A percentage is a number expressed as a fraction of 100, written with the % sign. 75% means 75 out of every 100, which is the same as the fraction 3/4 or the decimal 0.75. Percentages make things easy to compare even when the totals differ, which is why they're used so widely in finance, school grades and statistics.

Think of the percent sign as "divided by 100." So 20% of 50 is 0.20 x 50 = 10. To convert a decimal to a percentage, multiply by 100. To convert a percentage to a decimal, divide by 100. Every percentage problem involves three values: the part, the whole and the percent. If you know two, you can find the third.

Multiply the number by the percent, written as a decimal. To find 18% of $250, multiply 250 by 0.18 to get $45. A handy mental shortcut is to find 10% by moving the decimal one place, then scale. 10% of $250 is $25, so 20% is $50, and 5% is $12.50.

Subtract the old value from the new value, divide by the old value and multiply by 100. If a price goes from $40 to $50, the change is $10, and $10 / $40 x 100 = 25%. A negative answer means a decrease. To apply this to an investment, enter your numbers in the simple ROI calculator, which uses the same math.

A percentage point is the plain difference between two percentages. If a loan's rate rises from 4% to 5%, that's a rise of one percentage point, but it's a 25% increase in the rate itself. News reports and lenders can use these terms loosely, so check which one is meant. On interest costs, the difference matters a lot.

Percentage error shows how far an estimate is from the true value. Subtract the true value from the estimate, ignore any minus sign, divide by the true value and multiply by 100. If you estimated 110 and the true value was 100, your error is 10%. It's common in science classes and when checking financial forecasts against actual results.

Multiply the price by the discount to find the savings, then subtract. A $120 jacket at 30% off saves $36, leaving $84. Or multiply directly by what remains: 120 x 0.70 = $84. Two stacked discounts don't add up. 20% off and then another 10% off gives 28% off in total, not 30%, because the second discount applies to the reduced price.

Multiply the bill by the tip rate. For a 20% tip on $64, 64 x 0.20 = $12.80. A quick way is to take 10% by moving the decimal to get $6.40, then double it. For 15%, take 10% and add half of it. The calculator's increase option can give you the total including the tip, which is 64 x 1.20 = $76.80.

A common guideline is to save about 15% of your income for retirement, counting any employer match. At minimum, many people try to contribute enough to get the full match, since otherwise they're leaving part of their pay behind. Use our 401(k) calculator to see how different percentages change your balance at retirement.

Percentages stack on top of each other, not side by side. A 10% gain followed by another 10% gain is a 21% total gain, since the second one applies to the higher amount. A 10% gain followed by a 10% loss leaves you with 99% of what you started with. That's why our investment calculators use compounding and not simple addition.

Historians trace it to Italian merchants, who abbreviated "per cento" in their account books. Over time, the abbreviation wore down into a symbol resembling two small circles with a line between them, which eventually became the modern %. Long before that, Roman taxes were already charged in hundredths, such as a 1/100 tax on goods sold at auction.