Math & Statistics · 百分比变化（Percentage Change） · Updated 2026-10-25
What Is Percentage Change?
Definition
Percentage change = (new − old)/old — the denominator is always the baseline. Two frequent traps: first, asymmetry — 100→110 is +10% while 110→100 is −9.1%; up 10% then down 10% gives 100×1.1×0.9 = 99 (−1% net), and recovery needs 1/(1−drop)−1. Second, units: "A grew 20%, B grew 10%, so A grew 10% more" is wrong — A grew 10 percentage points more; a percentage point and a percent are different units.
Formula
Change = (new − old)/old × 100%; recovery = 1/(1−drop) − 1
Worked Example
A stock falling 80→40 (−50%) needs +100% to recover; 80→120 (+50%) then −50% leaves 60 — order does not change the net loss.
Common Misconception
"Equal rise and fall cancel out" — commutativity keeps the net identical but nonzero (1.1×0.9 = 0.99). And swapping points for percent: inflation falling from 3% to 2% drops 1 percentage point, not 1% (a 33% relative drop).
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