GlossaryStatistics and interpretation
Percentage change
Percentage change measures movement relative to a starting value. Learn the formula, zero-base limitation, and difference from percentage points.
Percentage change expresses the difference between two values relative to the starting value. For a positive starting value, subtract the earlier value from the later value, divide by the earlier value, and multiply by 100. A positive result indicates an increase; a negative result indicates a decrease.
The starting value is the base
The formula is: percentage change = (later value − earlier value) ÷ earlier value × 100. The Bureau of Labor Statistics uses this arithmetic in its explanation of changes in price indexes. The same arithmetic can describe comparable public-safety counts, although the meaning of those counts still needs checking. BLS calculation guidance.
Always show the starting and ending values alongside a percentage when practical. The percentage describes relative movement; the values reveal its size in actual records.
Example
Hypothetical example: An agency records 80 eligible calls in one month and 100 in the comparable month the following year. The increase is 20 calls. The percentage change is (100 − 80) ÷ 80 × 100 = 25%.
If the count later falls from 100 to 80, the decrease is 20%, because the starting value is now 100. Equal numerical changes in opposite directions do not necessarily produce equal percentage changes.
Common confusion
A percentage change is different from a percentage-point change. If a share rises from 20% to 25%, it rises by five percentage points and by 25% relative to its original share. The two descriptions use different calculations.
A zero starting value makes the ordinary percentage-change formula undefined. Moving from zero incidents to three should be reported as “from zero to three,” rather than as a 300% increase. Moving from a positive count to zero is a 100% decrease under the ordinary formula.
What the calculation does not establish
A large percentage can come from a small base. A rise from two to four records is 100%, while a rise from 200 to 220 is 10%. The first percentage is larger even though its numerical increase is smaller.
Before comparing, keep periods, categories, geography, and counting rules compatible. Missing data cannot be substituted for zero. A change caused by newly included agencies or revised classifications needs explanation. The arithmetic can be correct even when a comparison is not meaningful.