It depends on the date.

Indian Head pennies dated 1864 to 1909 weigh 3.11 grams.

The Lincoln, Wheat Ears Reverse penny weighs 3.11 grams except for steel cents made only in 1943 that weigh 2.67 grams.

The Lincoln, Memorial Reverse penny (1959 to mid 1982) weighs 3.11 grams.

The Lincoln, Memorial Reverse penny (mid 1982 to present) weighs 2.5 grams.

It's not easy to tell the 1982s apart, so to figure out how many cents weigh a pound (or any other amount) you'd have to decide which date range you wanted to use and eliminate all 1982 coins. A pound is 453.6 gm so just divide that by the weight of the penny date that you decided to use.

See Related Links, below, for a list of all current specifications for other U.S. coins

Read more, below about the various pennies.