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.

How can I check percentage change with a free calculator?

Open the CalcQuick percentage calculator linked above and select Percentage change. Enter the old and new values; no signup is required. For a positive starting value, calculate (new − old) ÷ old × 100. Use the steps below to check what the result means.

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.

Percentage increase: show each step

Suppose a weekly count rises from 80 to 100. Use 80 as the original value.

  • Subtract: 100 − 80 = 20.
  • Divide by the original value: 20 ÷ 80 = 0.25.
  • Multiply by 100: 0.25 × 100 = 25%.
  • The new count is 25% higher than the original count.

Percentage decrease: why reversing the numbers changes the answer

From 100 to 80, subtract 100 from 80 to get −20. Divide by the original 100 to get −0.20, then multiply by 100 to get −20%. That is a 20% decrease. An increase from 80 to 100 is 25%, but returning from 100 to 80 is a 20% decrease because the starting value has changed.

Are percentage points the same as percentage change?

No. If a rate rises from 20% to 25%, it rises by 5 percentage points. The relative percentage change is (25 − 20) ÷ 20 × 100 = 25%. State which measure you mean when comparing rates.

Which formula does CalcQuick use for negative starting values?

CalcQuick divides by the absolute magnitude of the old value: (new − old) ÷ |old| × 100. For −80 to −60, this convention gives +25%. Dividing by the signed old value instead gives −25%, so calculators can disagree for negative baselines. State the convention and the absolute change when a negative starting value is involved.

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.