(new − old) / old.
Percent change = (New − Old) / Old × 100. Negative means a decrease, positive an increase.
Distinct from percentage-point change and from absolute difference.
A common mistake is applying percent change symmetrically — a 50% increase followed by a 50% decrease does not return you to the original number, since each percentage is calculated against a different base value.
Old 100, New 125: (125 − 100) / 100 × 100 = 25.0000%.
Percent change is relative (25% here); percentage points is subtraction of percentages (5% to 8% = 3 pp).
Yes — a doubling is +100%; tripling is +200%. Decreases are capped at −100%.
The gain is calculated on the smaller starting number, but the loss is calculated on the larger post-gain number — so the dollar loss ends up bigger than the dollar gain, leaving you below where you started.