Percent Increase and Decrease
Drag the percent. Above zero the middle bar grows by that percent and the last bar shrinks by the SAME percent — but from the middle bar's bigger height. Below zero it shrinks first and grows back from the smaller height. Either way it lands short of the dashed line.
100 up 15% then down 15% = 97.8, not 100
The increase is 15% of 100, but the decrease is 15% of a bigger number.
- Start
- 100
- After the increase
- 115
- After the decrease
- 97.8
- Net change
- −2.3%
Try a percent
Ready to try some? Percent increase and decrease worksheets
Where it usually goes wrong
"Up 20%, then down 20%" sounds like it should cancel out, because plain addition and subtraction of the same amount does — $20 up and $20 down always gets back to the start. Percent does not work that way, and the reason is usually shown as a worked calculation rather than something a person watches actually happen to a quantity.
Try this
- Drag the percent up from small to large and read the two intermediate values as you go: the increase is always taken from the SAME start, but the decrease is always taken from a bigger number than that.
- Press 40%. The final bar is noticeably short of the dashed line — a 40% swing each way nets out to a 16% loss, not the 0% a same-amount round trip would give.
- Press −20%, then 20%. The bars swap colors — down comes first now — but the last bar lands on 96 both times: the order of the two steps changes the middle bar, never where the trip ends.
Where this goes next
The net result is always exactly −(percent²)/100 — 10% up-and-down loses 1%, 20% loses 4%, 50% loses 25% — which is why a stock that drops 50% needs a 100% gain, not 50%, to get back to where it started: the recovery percent has to be measured from the smaller, post-drop number.