On the left are the starting value and sliders for the percentage decrease and increase (0–90%). In the middle are the value after the decrease, the value after the increase and the difference from the start. Top right is the rise needed to recover; the card below it plots that rise as the decrease changes.
Take 20% off 100
20% of 100 is 20, so the value after the decrease is 100 × 0.8 = 80.
Add 20% to 80
Now raise 80 by 20%: 80 × 1.2 = 96. You are not back at 100.
The percentage is the same, but it is a percentage of a different number.
- The decrease — 20% of 100 = 20
- The increase — 20% of 80 = 16
Down 20, up 16: 100 − 20 + 16 = 96. The board's Difference from start reads −4.
What rise gets you back?
To go from 80 back to 100 you need 20 more. Divide that by where you are now, 80: 20 ÷ 80 = 25%.
Recovering from a 20% decrease takes a 25% increase. The board's Rise needed to recover shows 25% too.
The bigger the fall, the harder the climb back
Move only the percentage decrease and watch the rise needed.
- A 10% decrease — about 11.1% to recover
- A 20% decrease — 25%
- A 50% decrease — 100% (halved, so it has to double)
- An 80% decrease — 400% (down to a fifth, so it has to grow fivefold)
For small falls, the rise needed is close to the fall itself. As the fall grows, the gap widens fast. Press Draw on the bottom-right card and the line over 0–90% shoots up towards the right-hand end.
Written as a formula: rise needed = 1 ÷ (1 − decrease) − 1. It is the factor that takes the value after the decrease back to the start, minus 1.
The same holds for anything that moves by a percentage of its current value: prices, headcounts, sales, stock levels, body weight, share prices.
Try it yourself
Set the decrease and the increase to the same percentage — 10%, 20%, 30%, then 50% — with the starting value left at 100.
- Down 10%, up 10% — 99
- Down 20%, up 20% — 96
- Down 30%, up 30% — 91
- Down 50%, up 50% — 75
Equal percentages do not cancel out. The bigger they are, the further you end up from 100.
Then move only the decrease — 20%, 50%, 80% — and watch Rise needed to recover: 25%, 100%, 400%. It grows much faster than the decrease does.