Richard "Bill" Armstrong (July 16, 1873 – August 4, 1938) was an American college football player and coach.

He served as the head football coach at the College of William & Mary in 1896, the United States Naval Academy from 1897 to 1899 and the Hampton Institute—now known as Hampton University—in 1912, compiling a career college football coaching record of 24–8.

His uncle, Samuel C. Armstrong, was an American Civil War general who founded Hampton University.

He returned to his home in Hampton in June, where he died on August 4, 1938, after suffering a paralytic stroke.

This biographical article relating to a college football coach first appointed in the 1890s is a stub.