Percentage calculator

Three percentage questions with different bases

Choose the operation before entering numbers. “What is A% of B?” multiplies a percentage by a base number. “A is what percent of B?” divides a part by a whole. “Percentage change from A to B” compares a new value with an original value. The same two numbers can produce very different answers depending on the question.

In percentage-of mode, A is the written percentage: enter 15 for 15%, not 0.15. In share mode, A is the part and B is the whole. In change mode, A is the original positive value and B is the new value. The labels change with the mode to make the denominator clear.

Formulas and worked examples

Percentage of a number = A × B ÷ 100. Fifteen percent of 240 is 15 × 240 ÷ 100 = 36. If that represents a discount, the discounted amount is 240 − 36 = 204; the calculator's direct answer is the discount portion, not the final price.

Part as a percentage of whole = A ÷ B × 100. A quantity of 45 out of 180 is 25%. A part larger than the whole produces a percentage over 100; that can be mathematically valid, for example when comparing an achieved quantity with a smaller target.

Percentage change = (new − original) ÷ original × 100. Moving from 80 to 100 is a 25% increase. Moving from 100 back to 80 is a 20% decrease. The different bases explain why equal absolute changes need not have equal percentage changes.

Percentage points and repeated changes

A rate increasing from 20% to 25% rises by five percentage points. Its relative percentage increase is (25 − 20) ÷ 20 × 100 = 25%. Use the word points when subtracting two percentages directly; use percentage change when comparing the difference with the original rate.

Repeated changes multiply. Increasing 100 by 10% gives 110. Decreasing that new value by 10% gives 99, not 100. The reverse operation uses the new base. Similarly, two consecutive 20% discounts leave 0.8 × 0.8 = 0.64 of the original price, equivalent to a 36% total reduction rather than 40%.

A zero whole has no defined part-to-whole percentage. A zero original value also has no defined relative change. This tool reports those inputs instead of displaying an infinity or an arbitrary 100%. For change mode it requires a positive original value because interpreting growth from a negative base needs a separate convention. Signed arithmetic remains available in the other modes.

Frequently asked questions

What is the difference between percent and a decimal?

A percentage divides by 100: 25% is 0.25. Enter the written percentage in the percentage field.

Can the result exceed 100%?

Yes in share mode when the part is larger than the comparison whole. Check whether that interpretation fits your task.

Why are increase and decrease not symmetrical?

They use different starting values as their denominators.

Using and checking the result

All inputs and arithmetic on this page stay in the current browser. Switching between English and Chinese keeps the current form values in memory during navigation. Reloading the site restores the example. The toolkit does not save calculation inputs in cookies or browser storage, and the usage event records only that a calculation was completed, not the values or answer.

The initial values are a worked example, not a suggestion about your personal situation. Replace every relevant field before using the answer. Editing a field clears the previous result so it is not mistaken for a calculation using the new values. Use Reset example to return to the starting illustration.

If a result appears unexpected, repeat a small example by hand. Check units, signs, endpoints, and whether a percentage was entered as 30 rather than 0.30. To report an issue, use the contact form with non-sensitive sample inputs, the answer you expected, and the steps that produced the difference. Do not include private academic records or identifying details.

Compare quantities without changing the question

Before comparing two percentages, verify that their underlying quantities mean the same thing. A completion rate for ten tasks and a completion rate for one hundred tasks are not equally weighted when you want the completion rate of all tasks combined. Suppose one group completes nine of ten and another completes fifty of one hundred. Their rates are 90% and 50%, but the combined rate is fifty-nine out of one hundred ten, approximately 53.6364%, not the simple average of 70%.

That example illustrates why a percentage often needs its original numerator and denominator alongside it. If you receive only a rounded percentage, you may not be able to reconstruct the exact count. A displayed one-third share rounded to 33.33% can produce a small difference when multiplied back into the original total. Retain unrounded values for intermediate work and round the final display according to the precision the task needs.

A useful check for percentage-of mode is proportionality. Doubling the base while holding the percentage fixed should double the result. Doubling the percentage with a fixed base should also double the result. In share mode, multiplying both the part and whole by the same nonzero factor should leave the percentage unchanged. These checks help identify a misplaced decimal or a swapped input without relying on a second calculator.

For percentage change, confirm the direction in words. A negative answer means the new value is below the positive original value. It does not automatically mean the outcome is undesirable: a lower cost and a lower score may have different practical meanings. The calculator describes the arithmetic change, while you decide what that change means in context.

When comparing discounts, taxes, or fees, identify which subtotal each percentage applies to. Applying a fee before a discount can differ from applying it afterward if the fee uses a different base. Write the sequence explicitly and calculate each step from the appropriate subtotal rather than adding all percentages into one number.