What percent of appealed cases are heard by the US Supreme Court?

Approximately 1.2%

In 2010, there were 55,992 appeals filed with the US Court of Appeals Circuit Courts, and 8,159 cases petitioned to the US Supreme Court. Approximately 16% of the cases appealed to the US Supreme Court originate in the state court systems, and the other 84% (6,854) come from federal appellate courts (mostly the Circuit Courts).

Approximately 12% of the cases heard the US Court of Appeals Circuit Courts petition the US Supreme Court for a writ of certiorari; the court grants cert to approximately 1% of the petitions it receives, reducing the pool of federal cases to about 69 (based on 2010 estimates). Sixty-nine is roughly 1.2% of the cases appealed through the federal courts in 2010.