Descriptive statistics
Percentage Change Calculator
How much something went up or down, in percentage terms — and why the reverse change is not the same number.
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How to read this result
Percentage change is always relative to where you started. 80 to 100 is a 25% increase; 100 back to 80 is a 20% decrease. The same absolute move, two different percentages, because the denominator changed. This asymmetry is the single most common source of confusion with percentages.
Percentage points are not percent. A conversion rate moving from 4% to 5% has risen by one percentage point and by 25 percent. Both are true; quoting the larger one without saying which is how a small change gets sold as a big one.
Percentage difference is symmetric, and is a different thing. It divides by the average of the two values rather than by the first, so it gives the same answer in both directions. Use it when neither value is naturally "the original" — comparing two measurement methods, for example.
From zero, percentage change is undefined. Any increase from zero is infinite in percentage terms. Quote the absolute change instead.
The formula
Positive is an increase, negative a decrease. The absolute value in the denominator keeps the sign meaningful when the original value is negative.
Percentage difference — the symmetric version
Same answer whichever value you start from, which is why it is preferred when neither is the baseline.
Worked example
A price rise, and the fall that would undo it
A subscription rises from £80 to £100. How large is that increase — and what discount would take it back?
- Subtract to get the absolute change.100 − 80 = 20
- Divide by the original value.20 / 80 = 0.25
- Express as a percentage.+25%
- Now go the other way: the change from 100 back to 80.(80 − 100) / 100 = −0.20 → −20%
- The multiplier form of each.×1.25 up, ×0.80 back
A 25% rise needs a 20% cut to reverse it. This is why a stock that falls 50% must then gain 100% to break even, and why “we cut costs by 30% after growing them 30%” leaves you worse off than you started.
Checked against arithmetic — (100 − 80)/80.
The calculator above is loaded with these numbers by the Load the worked example button.
Assumptions, and when to use something else
The original value must not be zero, and both values should be on the same scale and in the same units. Percentage change on a quantity that crosses zero — a profit that becomes a loss — is arithmetically computable and close to meaningless; report the absolute change instead.
- The change is compounded over several periodsCompound growth rateThe per-period rate that produces a given total change.
- You are comparing two conversion ratesA/B test calculatorA percentage change between two rates needs a significance test before it means anything.
- The values are a series over timeLine graph makerPlot the series and see the shape of the change.
Questions people ask
What is the difference between percentage change and percentage difference?
Percentage change divides by the original value and is directional: 80 to 100 is +25%, 100 to 80 is −20%. Percentage difference divides by the average of the two and is symmetric: both comparisons give 22.2%. Use change when there is a clear before and after, difference when there is not.
How do I calculate a percentage decrease?
The same formula — the result simply comes out negative. From 100 to 75: (75 − 100)/100 = −25%.
Why can't I calculate percentage change from zero?
Because the formula divides by the original value. Any rise from zero is infinitely large in relative terms, which is why growth from a zero base is always quoted in absolute numbers.
What does a 200% increase mean?
Three times the original: the value increased by 200% of itself, so 50 becomes 150. This is a common ambiguity — “increased by 200%” and “increased to 200%” are different statements, and the second means doubling.