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MATH & NUMBERS

Percentage Calculator

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Enter both values to see the percentage

How the percentage calculation works

A percentage is a way of expressing a number as a share of 100. The word comes from the Latin "per centum", meaning "by the hundred". To find what percentage one number is of another, divide the first number (the value) by the second (the total) and multiply by 100. In formula form: percentage = value ÷ total × 100.

This calculator does exactly that. Enter the value in the first box and the total in the second, and it shows the percentage straight away. For example, 15 out of 200 gives 15 ÷ 200 = 0.075, and 0.075 × 100 = 7.5%. Another example: a student who scores 42 out of 50 has 42 ÷ 50 × 100 = 84%. The result updates as you type, so you can test several values against the same total without starting over.

Everyday uses

Percentages appear almost everywhere. Teachers express grades as a percentage of the total marks, shops advertise savings as a percentage off, surveys report results as a share of respondents, and businesses describe profit margins and growth in percentages. Because a percentage always compares a part to a whole of 100, it makes different quantities easy to compare. A score of 18 out of 24 and a score of 30 out of 40 look different as raw numbers, but as percentages (75% each) you can see immediately that they are equal. Percentages also run through everyday money matters such as sales tax, tips, interest rates, and loan fees, which is why a quick and reliable way to check them is so useful.

Related percentage problems you can solve by hand

This tool answers one question: what percentage is X of Y? Several related questions come up often, and each has a simple formula you can use with a basic calculator.

To find a percentage of a number, multiply the number by the percentage divided by 100. For example, 20% of 80 is 80 × 0.20 = 16. A discount works the same way: a 25% discount on an item priced at 80 takes off 20, leaving 60.

To find a percentage change, subtract the old value from the new value, divide by the old value, and multiply by 100. If a price rises from 80 to 100, the change is (100 − 80) ÷ 80 × 100 = +25%. Note that the reverse is not symmetrical: a fall from 100 back to 80 is a 20% decrease, not 25%, because the starting point is different. This is one of the most common sources of confusion with percentages.

Reading the result

A result above 100% simply means the value is larger than the total. For example, 250 is 125% of 200. This is perfectly valid and often appears when comparing growth, overspending against a budget, or output against a target. A result of exactly 100% means the two numbers are equal, and anything below 100% means the value is smaller than the total. If you enter 0 as the total, no result is shown, because dividing by zero is not possible.

COMMON QUESTIONS

What is the difference between "percentage of" and "percentage change"?
This calculator answers "what percentage is X of Y", which compares a part to a whole at one point in time. A percentage change compares an old value with a new one, using the formula (new − old) ÷ old × 100. They are separate calculations.
How do I find 20% of a number?
Multiply the number by 0.20, or divide it by 5. For example, 20% of 80 is 16. For any percentage, divide it by 100 first and then multiply, so 35% of 80 is 80 × 0.35 = 28.
Can I use decimals?
Yes. Both fields accept decimals, which is useful for amounts like 15.50 or for scores with half marks. The result is shown to two decimal places.
What if my result is over 100%?
It means the value is greater than the total. For example, 250 is 125% of 200. This is mathematically valid and comes up whenever something exceeds its target or budget.
Why is a 20% rise followed by a 20% fall not back to the start?
Because each percentage applies to a different base. If 100 rises by 20% it becomes 120, and a 20% fall from 120 takes off 24, leaving 96. To return from 120 to 100 you need a drop of about 16.7%.
What is the difference between a percentage and a percentage point?
A percentage point is the plain difference between two percentages. If an interest rate goes from 5% to 7%, it has risen by 2 percentage points, but by 40% in relative terms (2 ÷ 5 × 100).
Why does the calculator show nothing when the total is zero?
Dividing by zero has no defined answer, so the calculator waits for a total that is not zero. Enter any other number in the "Of total" box to see a result.

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