The arithmetic behind the phrase
A run rate takes performance over a recent period, a month, a quarter, and scales it to twelve months: monthly recurring revenue of two million becomes a twenty-four million annual run rate. The same construction is applied to costs and, in transformation and M&A contexts, to savings, "run-rate synergies" being the annualised value of measures once fully implemented.
When annualising the present misleads about the future
The extrapolation is only as good as the period chosen, and the period is chosen by someone with a story to tell. A seasonal business annualised from its strongest quarter, a growth curve annualised from the month after a one-off contract landed, a cost base annualised the week after redundancies but before the rehiring: each produces a technically accurate number that misdescribes the year ahead. Run-rate savings deserve particular care in decision papers, because "achieving a run rate" and "banking the cash" are different events, often separated by a year or more, and announcements routinely celebrate the first as if it were the second.