Convert a ratio into a yearly pace
For consecutive positive quarterly levels, annualized growth equals 100 × ((ending level ÷ previous level)^4 − 1). A 1% quarterly increase corresponds to approximately 4.06% at an annualized pace. The exponent compounds the level ratio; multiplying 1% by four is only an approximation.
This conversion describes the pace of the measured quarter. It does not predict that the next three quarters will have identical growth. A single volatile quarter can produce a large annualized reading even when the change over a full year is quite different.
Three intervals that should stay distinct
Nonannualized quarter-to-quarter growth compares one quarter with the preceding quarter. Quarterly annualized growth compounds that ratio. Year-over-year growth compares a quarter with the same quarter one year earlier. Full-year growth compares an annual measure with the preceding annual measure. These labels are not interchangeable.
When using a published GDP headline, prefer the agency’s growth estimate instead of recomputing it from heavily rounded chart values. On the real GDP page, the default annualized series uses the growth values published in BEA Table 1.1.1, while raw levels come from Table 1.1.6.
An annual rate is also a level convention
A quarterly flow can be expressed at an annual rate. Four such quarterly levels should not be summed as though each were a nonannualized quarterly total. Annual averages, annual totals and fourth-quarter values answer different questions. The appropriate conversion depends on the source definition.
Do not annualize a growth rate that is already annualized. Nor should a ratio-growth formula be applied indiscriminately to negative or zero-valued measures. This site rejects invalid denominators and does not provide a universal frequency conversion. Keep the original unit, frequency and active transformation beside every chart and table.