How this calculator works
The consumer price index is a weighted average of the prices of a fixed basket of goods and services, expressed relative to a base period. Dividing one reading by another removes the base and leaves the change in the general price level. That ratio minus one is the inflation rate over the interval; a negative value is deflation. The result is a cumulative change between two points, not an annual rate, unless the two readings are exactly one year apart.
Formula
Inflation rate = (CPI later / CPI earlier) - 1, displayed as a percentage. The change in the index is CPI later - CPI earlier, and the price-level ratio is CPI later / CPI earlier. Both readings must be positive and come from one series.
Worked example
If the index moves from 100 to 130, the ratio is 1.30, the index change is 30 points and the inflation rate is 30%. Reading the same observations in reverse gives a price-level ratio of 0.769231 and an inflation rate of -23.0769%.
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Frequently asked questions
Is this an annual inflation rate?
Only if the two index readings are one year apart. For intervals of another length, the percentage is cumulative over that interval. Dividing by the number of years would be an approximation that ignores compounding.
Why can the rate differ from the index change?
Index points are not percentages. A move from 130 to 160 is 30 points but only 23.0769%, because the base is the earlier reading, not 100.
Can the index be seasonally adjusted?
Yes, provided both readings use the same treatment. A seasonally adjusted reading against an unadjusted one compares two different series and does not give a meaningful inflation rate.