What term describes an exchange rate set by a government or central bank rather than left to the market?

An exchange rate set by a government or central bank rather than left to market forces is a fixed exchange rate.

Under a fixed, or pegged, exchange-rate regime, a monetary authority links its currency to another currency, a basket of currencies, or sometimes a commodity such as gold. The authority announces a target value and may buy or sell currencies in the foreign-exchange market to defend it. Those transactions require foreign-exchange reserves and can increase or reduce the domestic money supply.

Fixed rates became especially prominent under the Bretton Woods system established after World War II. That framework tied many currencies to the U.S. dollar, which was convertible into gold for official purposes. The system effectively ended in 1971–1973, after which many major economies moved toward floating rates.

“Fixed” does not always mean absolutely immovable: some regimes use a narrow band or periodically adjust the peg. It is different from a spot rate, which describes delivery timing, and a forward rate, which applies to a future contract. A floating rate, by contrast, changes with market conditions.