What year did the us stop making pennies out of copper?

The simple answer would seem to be mid-1982. When the cost of the copper would have nearly exceeded one cent, the U.S. changed the penny to copper-plated zinc. You can identify these modern zinc cents because they do not "ring" when dropped onto a hard surface... mostly a dull thud.

But the best way to distinguish between the 95% copper pennies (mid-1982 and older) and the newer 97.5% zinc pennies (mid-1982 and newer) is by weight. The dull thud method can be very unreliable and requires a very trained ear. The 95% copper pennies weigh in at about 3.11 grams, while the 97.5% zinc pennies weigh in at about 2.5 grams. This difference in coins of this size is very significant and cannot be mistaken on any reasonable scale which displays at least one place behind the decimal point for grams.

EXCEPTIONS:

The composition of U.S. one-cent coins (the official name) was changed several times. While the earliest cents (1793 into mid-1857) were entirely copper, later cents (mid-1857 into mid-1982) contained 95% copper alloyed with 5% tin and zinc (bronze) or 5% zinc (brass). Before and during the U.S. Civil War, cents had more than twice as much zinc as usual. During World War 2, copper and brass were needed for military use, so the 1943 cents were made of a low-grade carbon steel and coated with zinc (these can be picked up with a magnet), giving them a grey color (they had no copper content). A similar war need for nickel led to the use of silver in the "nickels" made from mid-1942 through 1945 (these had no nickel content).

The final answer, then, would most correctly be: 1943. Since even the newest pennies still use at least 2.5% copper (mostly as the outer plating over the mostly zinc inner core), and all years except 1943 used at least 95% copper in the making of pennies, 1943 is the only year that no copper was used in the making of U.S. pennies.