Befriended by Joseph Holt, Schoepf served as a clerk first in the U.S. Coastal Survey and later in the U.S. Patent Office and the War Department (working under Holt).
In 1890 he and Thomas Corwin Mendenhall of the U.S. National Geodetic Survey campaigned to establish the United States Board on Geographic Names to create official names for locations in the United States.
He was astronomer to the United States Coast Survey in 1857, and instructor in mathematics to naval cadets in 1860.
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The United States Department of Transportation, in conjunction with the Federal Highway Administration, the Federal Railroad Administration and the National Geodetic Survey appointed the Coast Guard as the maintaining agency for the U.S. Nationwide DGPS network (NDGPS).
He was a pupil of Louis Agassiz, whom he accompanied in 1840 on glacial expeditions in the Alps and in 1847 to the United States, where in 1848 he entered the government Coast Survey.