Percentage Change Calculator
Change, and the reverse move needed to undo it.
Work out Percentage Change. Change, and the reverse move needed to undo it. Exact where exactness is possible.
Percentage change
50.00%
100 → 150, a increase
Percentage changes do not reverse symmetrically. This increase of 50.00% would need 33.33% in the opposite direction to undo — a 50% fall famously needs a 100% rise to recover. Multiplying by 1.5 is the same operation stated without that trap.
How the Percentage Change Calculator works
Percentage changes do not reverse symmetrically, and that asymmetry is the point this page makes. A 50% fall needs a 100% rise to recover, not another 50%. The reverse figure is shown alongside the change for that reason.
Also known as: percent change formula · how to calculate percentage change · percent increase or decrease · percentage change between two numbers
The asymmetry
Percentage changes do not reverse symmetrically, because each one is measured against a different base.
A fall from 100 to 50 is −50%, measured against 100. Getting back to 100 is +100%, measured against the 50 you now have. The same 50 units of movement reads as two different percentages depending on which end you start from.
In practice
From 200 to 150 is a 25% decrease. Recovering it takes a 33.3% rise, not 25%.
The effect compounds as the fall deepens: a 50% drop needs 100% to recover, an 80% drop needs 400%, and a 90% drop needs 900%.
This is the arithmetic behind a great many misleading charts and recovery claims. A fund that falls 50% and then rises 50% has not broken even — it is down 25%.
Change against difference
Percentage change divides by the original value and carries a direction. Percentage difference divides by the average of the two and has none, so swapping the inputs gives the same answer.
Between 100 and 150 the change is +50% while the difference is 40%. Neither is wrong — they answer different questions. Use change when one value is genuinely the starting point, and difference when neither is.
Frequently asked questions
How do I calculate percentage change?
Subtract the old value from the new, divide by the old, and multiply by 100. From 200 to 150 is a 25% decrease.
Why does a 50% loss need a 100% gain to recover?
Because the gain is measured against the smaller number. Falling from 100 to 50 loses 50; getting that 50 back is a 100% rise on the 50 you have left.
What is the difference between percentage change and percentage difference?
Change has a direction and divides by the original. Difference has none and divides by the average of the two, so swapping the inputs gives the same answer.
Can I calculate a change from zero?
No — there is no base to measure against, so the percentage is undefined. Report the absolute change instead.
Put this calculator on your own site
Free to use, on any site, commercial or not. Paste this where you want it to appear. It is a plain iframe, so it works in WordPress, Squarespace, Wix, Webflow, Ghost and anything else that accepts HTML.
<iframe src="https://www.thecalclibrary.com/embed/percentage-change-calculator" width="100%" height="640" style="border:1px solid #e2e8f0;border-radius:12px" loading="lazy" title="Percentage Change Calculator"></iframe>The only condition is that the credit line stays visible. It sits inside the frame, so you do not have to do anything to keep it.
Related calculators
Percentage Increase Calculator
How much something went up, and the multiplier behind it.
OpenPercentage Decrease Calculator
How much something fell, and what it takes to recover.
OpenPercentage Difference Calculator
A symmetric comparison, where neither value is the reference.
Open