In short

  • Use percentage change when one value is the starting reference.
  • Use percentage difference when neither value is the reference and order should not matter.
  • A zero starting value makes ordinary percentage change undefined.

Percentage change has a direction

Percentage change compares a new value with an old value: (new − old) ÷ |old| × 100. The old value is the reference, so swapping the two values changes the result. A positive answer is an increase and a negative answer is a decrease.

Percentage difference is symmetric

Percentage difference is useful when two observations have equal status. CalcQuick divides the absolute gap by the average of their absolute magnitudes. Swapping the values does not change the result. NIST Dataplot documents this average-based definition as one accepted alternative.

Worked comparison

From 80 to 100, percentage change is (100 − 80) ÷ 80 = 25%. The symmetric percentage difference is 20 ÷ 90 = 22.22%. The answers differ because the formulas ask different questions.

Handle zero explicitly

If the old value is zero, an ordinary percentage change would divide by zero and is undefined. If both values are zero, CalcQuick reports a percentage difference of zero; otherwise the symmetric formula uses the average magnitude.

Sources

These primary or official references support the formulas, definitions or scope used in this guide.