Answer: The Percentage Change Calculator answers the three core percent questions — what is X% of Y, X is what percent of Y, and the percent change between two values — instantly, with the worked formula shown.
Calculate percentage increase or decrease
Percentage change measures how much a value rose or fell relative to where it started. The formula is (new − old) ÷ old × 100: a change from 80 to 100 is (100−80)/80 = 25% increase, while a fall from 100 to 80 is (80−100)/100 = 20% decrease. The same absolute move gives different percentages depending on the starting point — that asymmetry is the whole point of the metric.
This calculator handles both directions, plus percentage difference — the comparison of two values without a 'before' — which uses the average of the two as the base: |a−b| ÷ ((a+b)/2) × 100. Choose the right mode for your question: change requires a starting value; difference treats both values symmetrically.
A 50% loss and a 50% gain do not cancel. $100 that falls 50% lands at $50; a subsequent 50% gain brings it to only $75, because each percentage applies to a different base. Recovering a 50% loss requires a 100% gain. This asymmetry is why investment drawdowns are so costly and why 'it went up 10% then down 10%' always ends below the start.
The table below lists the gain required to break even after various losses. Small losses need nearly symmetric recoveries, but large losses need multiples: after a 90% drop, the investment must double more than nine-fold — a 900% gain — just to return to the original value.
Percentage change drives headlines and reports: quarterly revenue growth, inflation readings, population change, price moves, and poll swings. The Consumer Price Index, the US inflation measure published monthly by the Bureau of Labor Statistics, is typically reported as a percentage change versus a year earlier — a number computed exactly as this page computes it.
The classic pitfall is the shifting base. If a stock rises 25% one month (from $80 to $100) and falls 20% the next (from $100 to $80), you cannot average 25% and −20% to get +2.5%; the true change over both months is 0%, because changes compose multiplicatively: 1.25 × 0.80 = 1.00. Always chain percentage changes by multiplication, never by addition.
Another trap is small denominators. A village of 200 people gaining 10 residents grew 5%; a city of 2 million gaining 10 grew 0.0005%. The same absolute change yields wildly different percentages, so always pair a percentage with the absolute numbers when the base is small.
| Loss | Value left (from $100) | Gain needed to break even |
|---|---|---|
| 10% | $90 | 11.1% |
| 20% | $80 | 25% |
| 33.3% | $66.70 | 50% |
| 50% | $50 | 100% |
| 75% | $25 | 300% |
| 90% | $10 | 900% |
Percentage points measure the absolute difference between two percentages. If an interest rate rises from 3% to 5%, that is a 2-percentage-point increase but a 66.7% relative increase (2 ÷ 3). Confusing the two distorts meaning: 'mortgage rates rose 2%' versus 'rose 2 percentage points' are entirely different statements about the same move from 3% to 3.06% versus 3% to 5%.
Financial reporting usually means points when discussing rates — the Federal Reserve raising rates 'by 25 basis points' means 0.25 percentage points. When you need the relative comparison instead, this calculator's percentage-change mode converts any before-and-after pair, rates included.
How do I calculate percentage change?
Subtract the old value from the new value, divide by the old value, and multiply by 100. From 80 to 100: (100 − 80) ÷ 80 × 100 = 25%, an increase. If the result is negative, it is a decrease — the formula is identical either way, and this page labels the direction for you.
What is the difference between percentage change and percentage difference?
Percentage change uses the original value as the base and requires a before-and-after. Percentage difference compares two values symmetrically using their average as the base. Use change for 'how much did it grow?'; use difference for 'how far apart are these two?' when neither is the starting point.
Why doesn't a 50% loss need just a 50% gain to recover?
Each percentage applies to a different base. A 50% loss on $100 leaves $50; a 50% gain on $50 adds only $25, reaching $75. Full recovery needs a 100% gain on the $50. Break-even gains grow faster than the losses: a 90% loss needs a 900% gain.
What are percentage points?
Percentage points are the simple arithmetic difference between two percentages. A rate moving from 3% to 5% rises 2 percentage points, which is a 66.7% relative increase. Keeping points and percent distinct prevents the most common misreading of statistics about rates, polls, and interest.
How do I chain two percentage changes?
Multiply the growth factors, then subtract one. A 25% rise followed by a 20% fall is 1.25 × 0.80 = 1.00 — net zero — not +5%. Averaging percentage changes is wrong because each is computed against a different base.
When is percentage change misleading?
When the base is small or unstable. Growing from 2 customers to 4 is a 100% jump that sounds dramatic but is trivial in absolute terms. Conversely, huge bases make big absolute moves look tiny. Report the absolute numbers alongside the percentage whenever the denominator is small or the stakes are high.