Danes' father was born in Austin, Texas, in 1944 and, after studying Biology and Civil Engineering at Brown University, received a Bachelor of Fine Arts in Photography from Rhode Island School of Design (1968), where he studied with Harry Callahan. During Danes' childhood her father worked as a general contractor for 20 years, working on residential buildings in a company he ran called Overall Construction in New York. He also worked as a Photographer and computer consultant. He is the son of Gibson Andrew Danes, a former dean of the Yale School of Art and Architecture from 1958 to 1968. Danes is named after her paternal grandmother, Claire Danes (née Tomowske), who died in 1953.