Carl Ryder was born in Copenhagen. He was the son of Frederik Valentiner Ryder (1821-1909) and his wife Henriette Sophie Cathrine Husmann (1836-1896). He entered a military career in the Royal Danish Navy becoming a Second Lieutenant in 1879 and Captain 1897. 
He led an expedition to the Upernavik Distrikt in 1886-1887 and, most famously, the 1891-1892 expedition to East Greenland by the vessel Hekla. The way north from Ittoqqortoormiit was effectively blocked by ice. Instead, Ryder made the first comprehensive mapping of the entire Scoresby Sund fjord system, except for the inner part of Nordvestfjord.
He was a member of several other expeditions:
- The meteorological expedition 1882-83 to Nuuk led by Adam Paulsen
- The naturalist expedition to West Greenland with Eugenius Warming and Theo Holm in 1884 on the schooner Fylla
- J. A. D. Jensen's 1885 expedition
He married Ida Caroline Helene Clara Wolff (1864–1933) in 1888.
The Ryder Glacier in NW Greenland is named in his honour.
- Spencer Apollonio, Lands That Hold One Spellbound: A Story of East Greenland, 2008
- "Carl Hartvig Ryder". gravsted.dk. Retrieved April 1, 2019.
- Ryder, C. H. (1895–1925). Den Østgrønlandske Expedition udført i Aarene 1891-92 under Ledelse af C. Ryder, vol. 1-3 [The East Greenland Expedition in the years 1891-92 led by C. Ryder]. Meddelelser om Grønland (in Danish). 17-19.
- The Danish Scientific Expedition of 1884 in the Gunboat "Fylla". Proceedings of the Royal Geographical Society and Monthly Record of Geography, 7 (3), (1885): pp. 177-180 full text
- Ostermann, H. (1982). Ryder, C. H.. In: Dansk biografisk Leksikon v. 12: pp 485-86.