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Percentage Calculator

Three questions people call the same thing. Pick which one you are asking and the calculator shows the working, including the step that decides percent change: which number goes on the bottom.

Numbers
Solution rule for each line
    Checked by Aziza Smailovic free · step by step · every formula shown

    How it works

    How the Percentage Calculator works

    the part a result on its own leaves out

    A percentage is a fraction with a fixed denominator

    Per cent means per hundred, so 15% is 15/100. That fixed bottom is the whole point: any two percentages can be compared directly without finding a common denominator. Every calculation below is fraction arithmetic wearing different notation.

    Why percent change needs the original value

    Percent change compares the difference with where you started, so the ORIGINAL number is always the denominator. Using the new one instead produces a different answer, which is why a 50% rise followed by a 50% fall does not return you to where you began.

    Common mistakes

    Common mistakes with percentages

    the errors that actually show up, not every possible slip

    1. Dividing by the new value in percent change

      From 50 to 75 is a 50% increase, because 25 is compared with the original 50. Dividing by 75 gives 33%, which answers a different question.

    2. Assuming a rise and a fall cancel

      100 raised by 50% is 150; 150 lowered by 50% is 75, not 100. The two percentages are taken of different bases.

    3. Confusing percent with percentage points

      Going from 20% to 25% is a rise of five percentage points, but a 25% increase. Both are correct statements about the same change, and they are not interchangeable.

    Questions

    Asked often enough to answer here

    answers that change how you work

    How do I find a percentage of a number?

    Divide the percentage by 100 and multiply. 15% of 80 is 0.15 × 80 = 12.

    How do I work out what percentage one number is of another?

    Divide the part by the whole and multiply by 100. 15 out of 80 is 15/80 × 100 = 18.75%.

    How is percent change calculated?

    Subtract the original from the new value, divide by the ORIGINAL, then multiply by 100. The original is always the denominator.

    What is the difference between percent and percentage points?

    Percentage points measure the gap between two percentages; percent measures the relative change. From 20% to 25% is five percentage points and a 25% increase.