Both RPI and CPI are measures of inflation, RPI stands for retail price index and CPI for consumer price index. The essential difference is in how they are calculated. RPI takes a simple average, or arithmetic mean, by adding up the price of certain items and then dividing by the number of those items.
CPI uses a geometric mean to identify the factor by which prices have increased. This involves multiplying the numbers, rather than adding them up, and then finding the ‘nth root’. If it is just two numbers this would be the square root, if it is three number it is the cube root and so on.
The advantage of this method is that the mean is not distorted by the large numerical increases. However, it is therefore typically lower than the mean used in RPI, which reflects how much more people are likely to be spending overall, rather than per product.
The difference between the two is very useful for governments, who like to peg pay rises to CPI, currently 2.5%, and tax incomes to RPI, currently 3.6%.