By what percentage a value changed between two numbers.
Divide the difference between the new and old values by the old value and multiply by 100: (new − old) / old × 100. From 250 to 300 that is (300 − 250) / 250 × 100 = 20%. A negative result means a decrease. The denominator is always the starting value, never the new one.
If a rate rises from 5% to 7%, it has risen by 2 percentage points — but by 40 percent. A percentage point is the plain difference between two rates; the percentage is that difference relative to the starting rate. The two are frequently confused, and the gap between them is often severalfold.
Each change is taken from the value current at the time. 100 rises by 50% to 150, but 50% of 150 is 75, so you end at 75 — a quarter below where you started. Recovering from a 50% fall requires a 100% rise. That asymmetry is why averaged percentages mislead.
You cannot — a percentage change from zero is undefined, because zero would sit in the denominator. In practice such cases are reported as an absolute change (“from 0 to 8”) or noted as a figure appearing for the first time. The same applies to a move from a negative value to a positive one, where percentages stop meaning anything.