Kuhn was born in Takoma Park, Maryland, the son of Alice Waring (Roberts) and Louis Charles Kuhn, a fuel company executive. His father was a Bavarian (German) immigrant, and his mother had deep roots in Maryland. Kuhn grew up in Washington, D.C., and graduated from Theodore Roosevelt High School. He then attended Franklin and Marshall College in the V-12 Navy College Training Program before going to Princeton in 1945. Kuhn graduated from Princeton with honors in 1948 with a Bachelor of Arts degree in Economics. He then received his law degree in 1950 from the University of Virginia where he served on the editorial board of the law review.