Why a rise and its reversal aren't symmetric
A percentage change is always measured against the starting price, not the ending one — so raising a price and later reversing it uses two different bases, which is why the two percentages never match.
- Before — the price before the change
- After — the price after the change
More detail
A price increase and its full reversal use different percentages
Raising 100 to 120 is a +20% change, measured against the smaller base of 100. Bringing 120 back down to 100 is a −16.67% change, measured against the larger base of 120 — not −20%. The percentage that undoes an increase is always smaller in magnitude than the increase itself, because the base you're dividing by got bigger first.
Quick check. To find what percentage discount would fully cancel out a percentage increase, don't use the same number — divide the increase amount by the new (higher) price, not the original one.
Frequently asked questions
A price went from 100,000 to 120,000 — what's the percentage increase?
The change amount is +20,000 and the rate is (20,000 ÷ 100,000) × 100 = +20%.
If a price rises 20% and then falls back to the original, is that a 20% decrease?
No — it's about a 16.67% decrease. Going from 100 to 120 is +20% (divided by 100), but going from 120 back to 100 is −16.67% (divided by 120), because the base price used for the percentage is different each time.
Why isn't a 50% discount undone by a later 50% increase?
Because each percentage is calculated against a different starting price. A 50% discount from 100 gives 50; a 50% increase on that 50 only brings it to 75, not back to 100 — you'd need a 100% increase on 50 to return to the original price.
What if the price after the change is 0?
As long as the before-price is above 0, the amount lost equals the entire starting price, so the rate is −100%. If the before-price is itself 0, there's no base to divide by, the change rate is undefined, and the calculator shows "—" rather than −100%.