Stocks in the United States plummeted today after a surprising plunge in the Shanghai market provoked worries worldwide about the global economy and the valuation of share prices.

The Dow Jones industrial average fell 416.02 points, or 3.3 percent, to 12,216.24, as all 30 stocks in Dow declined. The Standard & Poor’s 500-stock index dropped 50.33 points, or 3.5 percent, to 1,399.04. The Nasdaq composite index dropped 96.66 points, or 3.9 percent, to 2,407.86. This was the steepest one-day sell-off since September 2002. Asian and European markets closed sharply lower

The trigger was a nearly 9 percent slide in Chinese stocks, which had just reached a record high on Monday. The sudden reversal unnerved markets throughout Asia and into trading in Europe.

In the United States, markets had already been slumping in recent days on concerns about deterioration in the mortgage market for people with poor credit, as well as worries about the economy.