He spent two terms taking a special course in mathematics taught by Joseph Roberts, a prominent mathematician, and a course in architectural drawing under John Haviland at the Franklin Institute.

William pursued a career in civil engineering on the advice of Samuel Mifflin, the then president of the Union Canal Company of Pennsylvania and friend of his father.

[3][4] Roberts served as an assistant in survey and construction at the Lehigh Canal, between Mauch Chunk, Pennsylvania, and Philadelphia.

From 1834 to 1840 Roberts was in charge of extensions of the Pennsylvania Canals; Bellefontaine and Indiana, Allegheny Valley, Atlantic and Mississippi, and Iron Mountain.

Roberts served as associate chief engineer for the construction of the Eads Bridge across Mississippi River at St. Louis in 1868.

[6] From 1879 to 1881 Roberts served as a member of the Mississippi River Jetty Commission and chief engineer, all public works in Brazil.