Percentage points compare rates directly

When both inputs are already percentages, subtract the old rate from the new rate. For 30% minus 20%, the difference is 10 percentage points. The word 'points' matters: it signals a direct distance on a percentage scale. A fall from 8% to 5% is a decrease of 3 percentage points, regardless of the size of the original population.

Percentage change uses the old value as denominator

Use percentage change = (new − original) ÷ original × 100. With 20 and 30, the absolute change is 10; 10 ÷ 20 × 100 equals 50%. Reversing the order gives (20 − 30) ÷ 30 × 100, or about −33.33%. The two directions are not opposites because each calculation uses a different original denominator.

State the unit in the result

Writing 'up 10%' is ambiguous when the underlying values are rates. Prefer 'up 10 percentage points, from 20% to 30%' for the direct difference, or 'up 50% relative to the prior rate' for the relative comparison. Include the input period and population as well; arithmetic alone cannot establish whether two measurements were collected on a comparable basis.

Watch for a zero baseline

Relative change from zero is undefined because the original value would be the denominator. A move from zero orders to ten orders is an absolute increase of ten, but it is not an ordinary finite percentage increase. Do not substitute an arbitrary tiny denominator to manufacture a percentage. Report the absolute change, explain that the baseline was zero, and provide context such as the observation period.

Interpret negative baselines cautiously

The standard formula still produces a number when the original value is negative, but the usual language of growth can become counterintuitive. Moving from −20 to −10 gives (−10 − (−20)) ÷ −20 × 100 = −50%, even though the numerical value increased toward zero. The calculator warns in this case. State the raw values and formula, or choose an application-specific convention that your audience recognizes.

Verify with a substitution

Before publishing a result, replace each formula symbol with the displayed inputs and recompute the numerator and denominator. Check that the old value, not the new value, is underneath the fraction. Then ask whether the source values are counts, currency amounts, or already percentages. A percentage-point answer applies only when comparing rates directly; a percent-of calculation answers yet another question, such as 20% of 150 = 30.