A percentage compares a part to a whole out of 100, and this calculator answers the three questions people ask most often: what a percentage of a number equals, what percentage one number represents of another, and how much a value has increased or decreased. Enter your numbers below and get an instant result along with the exact formula used, so you can check the arithmetic yourself.
Enter your values to see the result.
15% of 80 → 12
Percentage of a number: 80 × 0.15 = 12.
20 is what percent of 80? → 25%
Part ÷ whole: (20 ÷ 80) × 100 = 25%.
Price rises from 80 to 100 → +25%
Percentage change: (100 − 80) ÷ 80 × 100 = 25%.
Price falls from 100 to 80 → -20%
Percentage change: (80 − 100) ÷ 100 × 100 = -20%.
Percentages appear everywhere, from sale prices and interest rates to exam scores and population statistics, yet nearly every percentage question boils down to one of three formulas.
To find a percentage of a number, divide the percentage by 100 to turn it into a decimal, then multiply that decimal by the number. For 15% of 80, divide 15 by 100 to get 0.15, then multiply by 80 to get 12. Reach for this formula whenever you are calculating a discount, a tip, a commission, an interest payment, or a tax amount, since all of these ask for a fraction of a base value.
When you need to know what share one number represents of another, divide the part by the whole and then multiply by 100. If you answered 20 questions correctly out of 80 on a test, dividing 20 by 80 gives 0.25, and multiplying by 100 gives 25%. This calculation shows up constantly in grading, budgeting, market share analysis, and any situation where you are comparing a portion to a total.
Percentage change tells you how much a value has grown or shrunk relative to where it started. Subtract the old value from the new value, divide that difference by the old value, and multiply by 100. Moving from 80 to 100 is a 25% increase, because the gain of 20 is measured against the smaller starting value of 80. Moving from 100 back down to 80 is only a 20% decrease, because the same gap of 20 is now measured against the larger value of 100. This asymmetry surprises many people the first time they notice it, but it follows directly from the formula: the denominator depends on which value you start from, not on the size of the gap itself.
The most frequent error is confusing percentage points with percentage change: an interest rate that moves from 10% to 12% has risen by 2 percentage points, but by 20% in relative terms, and using the wrong one in a financial report can be a costly mix-up. Another common mistake is applying the percentage-of-a-number formula when the question actually asked for a percentage change, which produces a plausible-looking but incorrect answer. A third mistake is assuming percentage increases and decreases are symmetrical: a 20% increase followed by a 20% decrease does not return a value to where it started, because each percentage is calculated against a different base. Finally, people sometimes forget to convert a percentage to a decimal before multiplying, which inflates results by a factor of 100.
Working through the three formulas above, and checking carefully which one matches the question being asked, resolves nearly every percentage problem you will encounter, whether you are splitting a restaurant bill, comparing exam results, tracking a household budget, or analyzing a company's quarterly growth. Keep the calculator open alongside these explanations to check your own arithmetic and to build confidence in doing the calculations by hand next time.
Convert the percentage to a decimal by dividing it by 100, then multiply that decimal by the number. For example, to find 15% of 80, divide 15 by 100 to get 0.15, then multiply 0.15 by 80 to get 12. This same method works for any percentage and any number, including percentages greater than 100 or percentages written with decimal places such as 7.5%.
Divide the part by the whole, then multiply the result by 100 to express it as a percentage. If you scored 20 points out of a possible 80, dividing 20 by 80 gives 0.25, and multiplying by 100 gives 25%. This tells you that 20 is 25% of 80, and the same formula applies to test scores, survey results, or any comparison between a portion and its total.
Percentage change measures how much a value has increased or decreased relative to its starting point. Subtract the old value from the new value, divide that difference by the old value, then multiply by 100. A positive result means an increase and a negative result means a decrease, so a price moving from 80 to 100 is a 25% increase, while a move from 100 back to 80 is a 20% decrease.
Because percentage change is always measured against the starting value, not a fixed reference point. Going from 80 to 100 is a 25% increase because the difference of 20 is measured against the smaller starting value of 80. Going back from 100 to 80 is only a 20% decrease because that same difference of 20 is now measured against the larger starting value of 100, which makes the percentage smaller.
Yes, discounts and tips both use the percentage-of-a-number formula: multiply the price by the rate written as a decimal to find the amount to subtract or add. For a 20% discount on a 50 dollar item, multiply 50 by 0.20 to get 10 dollars off, leaving a final price of 40 dollars. For a 15% tip on a 60 dollar bill, multiply 60 by 0.15 to get a 9 dollar tip.
A percentage point is the plain arithmetic difference between two percentages, while a percentage change describes that difference relative to the starting percentage. If an interest rate moves from 10% to 12%, that is a 2 percentage point increase, but expressed as a percentage change it is a 20% increase, since the 2 point gain is measured against the original 10%. Mixing up these two terms is one of the most common percentage mistakes.
Last updated on 2026-09-19 · Written by UtiliaTools