Karmel was educated at Caulfield Grammar School and the University of Melbourne, where he won a non-resident Exhibition to Trinity College in 1940. He graduated BA in the School of Economics in 1942, wining the Wyselaskie Scholarship and the Aitcheson Travelling Scholarship. After working at the Commonwealth Bureau of Census and Statistics in Canberra, Karmel accepted a lectureship in Economics and Economic History at the University of Melbourne in 1946. In that year, he was awarded the Rouse Ball studentship at Trinity College, University of Cambridge, where he completed a PhD on Male and Female Fertility Rates. He was awarded a Rockefeller Grant that enabled him to visit America before his return to Melbourne as Senior Lecturer in 1949.
At the age of 27, Karmel was appointment to the Chair of Economics at the University of Adelaide in 1950, later moving the Australian National University. He was a member of the board for the Centre for the Mind from 1997 to 1999.
His economic research included a focus on educational issues. In 1962, at the University of Melbourne during the third annual conference of the Australian College of Educators, he delivered the inaugural Buntine Oration, on the topic "Some Economic Aspects of Education". In 1971 he moved back to Canberra to head the Australian Universities Commission, becoming Chairman and head of its successor, the Commonwealth Tertiary Education Commission. Professor Karmel released a 1973 report commissioned by the Whitlam government named Schools in Australia which influenced the government's funding of state schools.
Karmel served as the Vice-Chancellor of both Flinders University (1966) and the Australian National University (1982-1987); he was the first person to hold the position at Flinders. The Peter Karmel Building at the ANU School of Music is named in his honour.
He died in Canberra on 30 December 2008, aged 86.
He was made a Commander of the Order of the British Empire in 1967, a Companion of the Order of Australia in 1976, and awarded a Centenary Medal in 2001 "for leadership in Australian higher education and for being a leading academic".
He was married to Lena, and they had six children. His daughter Pip Karmel was nominated for the 1996 Academy Award for Film Editing for her work on the film Shine. His son, Tom Karmel, is Adjunct Professor at Flinders University, where he works at the National Institute of Labour Studies.
- "College Scholarships, Exhibitions and Theological Studentships 1940", The Fleur-de-Lys, vol. 4, no. 40 (Oct. 1940): 12.
- "New Appointments and Resignations", University of Melbourne Gazette, vol. 6, no. 2 (29 Mar. 1950): 14–15.
- Centre for the Mind (2009). Who We Are. Retrieved 3 January 2009.
- "About Peter Karmel", accessed 13 June 2105.
- Smith, Bridie (3 January 2009). "Karmel's lessons heard". The Age.
- "GMB Architects, Peter Karmel Building Project". Retrieved 2008-12-13.
- It's An Honour (2008). Peter Henry Karmel. Retrieved 4 January 2009.
- Downie, Graham (2 January 2009). "'Gentleman scholar' Karmel dies". Canberra Times.
- Adjunct Staff, Flinders University.