Percentage Change Calculator
Type the old value and the new one, and the change appears as a percentage, worked out exactly, with the arithmetic beneath it. Fill in a different pair of boxes to turn the sentence around: the new value after a 15% rise, or what a price was before a 20% cut. One sentence, “From 300 to 240 is a change of −20%”, does all three.
What it does
- A rise past 100% is allowed and means more than double: from 50 to 150 is a change of 200%.
- A fall of 100% takes any value above 0 to 0, so the start behind that 0 cannot be worked out.
- From below 0 the change is measured against the start’s size, so −50 to −25 is a rise of 50%.
- A change from 0 has no percentage, and the answer says why rather than showing infinity.
- A change that never ends, such as 3 to 4, says it repeats rather than passing off 33.33% as exact.
- Two changes in a row multiply: 10% and then 10% again is 21% from the start, as 100 to 121 shows.
How to use it
- Type the starting value in the first box and the new one in the second.
- Read the change, and the working under it.
- For a new value or an old one, type the other value and the percentage: the box left alone is worked out.
- Copy the answer.
What it does not do
- A column of figures at once: it works out one pair at a time, so a list of changes belongs in a spreadsheet.
- Average yearly growth across several years: it compounds, so it is not the total change divided by the years.
Questions
How do I work out a percentage increase?
Subtract the old value from the new one, divide by the old value and multiply by 100: from 80 to 92 is 12 ÷ 80 × 100 = 15%. Type 80 and 92 here and the same working appears with your numbers.
Why does a 20% fall need a 25% rise to recover?
Because each percentage is taken from a different starting value. 300 less 20% is 240, and getting back to 300 takes 60 more, which is 25% of 240.
What does a change of 100% mean?
The value doubled: from 40 to 80 is a change of 100%. A change of −100% is a fall to zero, and a change of 200% is three times the start, which is where the two are often confused.
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