What is the term for extremely rapid and out-of-control inflation?

The term for extremely rapid and out-of-control inflation is hyperinflation.

Hyperinflation is not merely high inflation: it is a very rapid, typically accelerating rise in the general price level that rapidly destroys a currency’s purchasing power. As prices surge, people try to spend money quickly or exchange it for goods, foreign currency, or other stores of value. That loss of confidence can make the inflation spiral even faster.

Economist Phillip Cagan’s influential 1956 analysis treated an episode as beginning when monthly inflation exceeded 50 percent. That threshold is widely cited, although economists and institutions do not use one universally binding definition. Wars, political upheaval, collapsing production, and government deficits financed by money creation have all contributed to historical episodes.

Germany in 1923, Hungary in 1946, and Zimbabwe in 2008 are famous examples. Hyperinflation differs from deflation, which is a general fall in prices, and from disinflation, which means inflation is slowing. Stagflation combines persistent inflation with weak growth and high unemployment; it is severe, but not synonymous with hyperinflation.