Kendall was born in Boston to Evelyn Way and Henry P. Kendall, an industrialist. Kendall grew up in Sharon, Massachusetts and attended Deerfield Academy. He enrolled in the U. S. Merchant Marine Academy in 1945, and served on a troop transport on the North Atlantic in the winter of 1945 - 1946.

In 1946, he enrolled at Amherst College where he majored in mathematics, graduating in 1950. While at Amherst, he operated a diving and marine salvage company during two summers. He co-authored two books, one on shallow water diving and the other on underwater photography.

He did graduate research at the Massachusetts Institute of Technology, involving an experimental study of positronium, and he obtained his PhD in 1955. He then spent the next two years as a postdoctoral fellow at Brookhaven National Laboratory. He then spent five years in Robert Hofstadter's research group at Stanford University in the late 50's and early 60's, where he worked with Jerome Friedman and Richard Taylor, studying the structure of protons and neutrons, using the university's 300 feet long linear electron accelerator. He developed a close working relationship with Wolfgang K. H. Panofsky at Stanford.

Kendall was one of the founding members of the Union of Concerned Scientists (UCS) in 1969. He served as Chairman of the UCS from 1974 until his death in 1999. His public policy interests included avoiding nuclear war, the Strategic Defense Initiative, the B2 bomber, nuclear reactor safety and global warming.

Kendall was not only a very accomplished Physicist, but also a very skilled mountaineer and Photographer. He did extensive rock climbing in Yosemite Valley, followed by expeditions to the Andes, Himalaya and Antarctica, photographing his experiences with large format cameras. He was elected a Fellow of the American Academy of Arts and Sciences in 1982. On April 7, 2012, the American Alpine Club inducted Kendall into its Hall of Mountaineering Excellence at an award ceremony in Golden, Colorado.