Hinrichs graduated in 1860, between the First and Second Schleswig Wars. He emigrated later that year to the United States, settling initially in Davenport, Iowa, where he taught school, then in nearby Iowa City. In 1863 he was appointed a professor of natural philosophy, chemistry, and modern languages at the University of Iowa. He founded the first state weather and crop service in the United States and headed the Iowa Weather Service until 1886. He was first to identify and name the straight-line storm phenomenon he called the "derecho." He stayed at the University of Iowa until 1886, when he was fired by the state Board of Regents due to disputes with the university president and faculty colleagues. He became a professor at the St. Louis University in 1889 and taught there until his retirement in 1907.