Percentage change, percentage difference, and percentage points are not interchangeable. Use percentage change for an ordered original-to-new movement, percentage difference for two peer values with no original, and percentage points for direct subtraction between two rates already written as percentages. For 80 and 100, change from 80 is 25% while symmetric difference is 22.222222%; for a rate moving from 20% to 25%, the answer is 5 percentage points or a 25% relative increase.

Choose the denominator before the formula

For ordinary positive values, percentage change = (new − original) ÷ original × 100. Percentage difference = |a − b| ÷ ((a + b) ÷ 2) × 100 when neither value is the base. Percentage-point change = new rate − old rate when both inputs are already percentages. Change requires a nonzero original; symmetric difference requires a nonzero average. The operation is chosen by the meaning of the values, not by whichever formula gives the preferred number.

Use percentage change when direction matters

From 80 to 100 is a 25% increase because 80 is the original base. From 100 back to 80 is a 20% decrease because 100 is now the base. The two answers differ because the reference changed. This asymmetry is expected, not a rounding error.

Use percentage difference when neither value is original

For two measurements or peer values, divide the absolute difference by their average. For 80 and 100: 20 ÷ 90 × 100 = 22.222222%. Swapping the values leaves the answer unchanged. When both values are zero, the result cannot be calculated because the average base is zero.

Use percentage points for two percentages

A rate rising from 20% to 25% gains 5 percentage points. Relative to the original 20%, that is a 25% increase. Reporting only “up 5%” is ambiguous. Name percentage points for the direct subtraction and percentage change for the relative comparison.

Percentage points do not convert to percent by themselves

A point change becomes a relative percent change only after the original rate is known: relative change = point change ÷ original rate × 100. Moving from 20% to 25% is +5 points and 5 ÷ 20 × 100 = 25% relative. Moving from 50% to 55% is the same +5 points but only 5 ÷ 50 × 100 = 10% relative. If the original rate is zero, this relative conversion is undefined even though the point difference can still be stated.