Down 20%, up 25%: why the same move doesn't undo itself

Take 100. Let it fall 20%, and it lands on 80. To get from 80 back to 100, you don’t need a 20% rise — you need 25%. The fall and the climb back cover the same distance, 20 points, but they’re not the same percentage, and the gap between them only widens as the fall gets steeper.

The example in full

Start at 100. A 20% decrease takes 20 off the total, leaving 80. That part is symmetric with how percentages of a starting number work: 20% of 100 is 20, so 100 minus that is 80.

The return trip is where it stops being symmetric. You’re now standing on 80, and you need to add 20 points to get back to 100. The question is what percentage of 80 that 20 represents — and 20 is 25% of 80, not 20% of it. So the rise from 80 back to 100 is a 25% increase, even though the fall from 100 to 80 was only a 20% decrease.

Both moves cover the same 20 points. Only the percentage attached to them differs.

Why

A percentage change is always measured against whatever number you’re starting from. The fall starts from 100, so 20 points off is 20% of 100. The rise starts from 80, so the same 20 points is a bigger slice of a smaller base — 25% of 80.

Same gap, smaller base, bigger percentage. That’s the whole mechanism. Nothing about the arithmetic is unusual or unfair — it’s just that “percentage” always has an implicit “of what”, and the fall and the rise are each measured against a different number.

There’s a separate, related figure worth knowing: if you want a single number that treats 80 and 100 symmetrically — comparing them without picking either one as the “start” — the percentage difference between them, measured relative to their average, is 22.22%. That’s a different question from “what rise reverses this fall”, and it deliberately splits the difference rather than favouring either direction.

The scale of the effect

The deeper the fall, the harsher this asymmetry gets. Losing 50% of 100 leaves 50 — and getting back from 50 to 100 needs a 100% rise, because you now have to double a number half the size of what you started with.

Push the fall further and the required rise grows faster still, without any upper limit. A fall that gets close to 100% would require a rise that’s enormous by comparison, because the base you’re climbing from has shrunk almost to nothing. There’s no floor on how small the recovery base can get, so there’s no ceiling on the percentage needed to climb back out.

Where you’ll feel it

This shows up anywhere a quantity drops and then recovers: a share price, a portfolio balance, monthly sales, event attendance, a currency’s value against another. Whatever the figure, the percentage needed to get back to where you started is always larger than the percentage that got you down there in the first place.

It’s also the quiet reason large investment losses take so long to recover from — the deeper the drawdown, the steeper the climb back, in percentage terms, even when the point-for-point distance looks the same on a chart.

Try your own numbers

Pick any starting figure, apply a percentage fall, then work out what percentage rise gets you back to where you began. The percentage calculator handles both directions and shows the difference directly, using the same percentage change logic as the 100-to-80 example above.