The family was one of only moderate means, and his early schooling limited. Among his school associates was James Wilson, who in after years became secretary of agriculture in the United States. When Samuel was eleven years old the family emigrated to the United States, living for three years near Saratoga in New York State and then moving on to the open prairie lands of Buchanan County, Iowa. The country was then largely a wilderness scantily peopled by a few hardy pioneers, and, owing to a lack of qualified teachers, educational facilities were few and poor. At the age of sixteen, Calvin was himself called upon to teach in the local district school, but is stated to have been also an expert carpenter and cabinet-maker. In 1861 or 1862 he entered Lenox College, in the town of Hopkinton.
Samuel became an instructor at Lenox College. It was one of the many small denominational colleges so abundant throughout the middle west, with scanty endowment, poor equipment, and affording opportunities for only the simplest and most fundamental training. There Calvin remained until 1864 when, in company with others of the faculty and student body, he enlisted. Before he was called into serious service, the war came to an end and Calvin returned to Lenox and labored under the discouraging conditions incidental to building up a nearly wrecked institution. In 1867 and 1868 he served as county superintendent of Delaware County, and from 1869 to 1873 was principal of one of the Dubuque schools. While at Lenox he found among other members of the faculty Thomas H. Macbride, a botanist, to whom he became warmly attached and with whom he made frequent excursions and collecting trips. In the course of this work he came in contact with Dr. C. A. White, then state geologist and later professor of geology at the State University. When Dr. White resigned to accept a call from an eastern college, Calvin in 1874 succeeded him as professor of natural history at the University and when the state survey was reorganized in 1892, became state geologist as well. It was with this organization that his name first became known to the country at large. This, it may be well to note, was the third attempt at a geological survey on the part of the state, and Calvin continued at its head until 1904, when he resigned, to be appointed again in 1906, serving until his death in 1911. Calvin's scientific training, as is evident, was largely self-acquired. When he entered upon his work as teacher, the geology of the upper Mississippi region was known only in the most general way and it is perhaps fortunate that he began with no preconceived notions. "He found his inspiration in a deep love and enthusiastic appreciation of nature and he brought to his work a critically keen judgment and an uncompromising allegiance to simple truth which made for thoroughness and accuracy". Calvin's individual research, quite aside from his teaching and executive duties, was largely paleontological and stratigraphic.
He was one of the founders of the American Geologist in 1888, and its editor-in-chief until 1894; a member of the Geological Society of America (president 1908); of the Paleontological Society of America; the American Association for the Advancement of Science; and other scientific societies.
In 1870 he was married to Louise Jackson by whom he had two children, a son and a daughter.