Khemani was born in India and was educated through high-school at La Martiniere Calcutta. She moved to the United States to study physics at Harvey Mudd College, where she completed a senior thesis on gravitational holography. Her undergraduate thesis was awarded the Thomas Benjamin Brown Memorial Award. Alongside her physics courses, Khemani completed courses in mathematics, computer science, economics, linguistics and creative writing. She also took part in robotics programs and competed at national robotics competitions. After completing her undergraduate degree in 2010, she moved to Princeton University as a graduate student. Following her PhD studies, Khemani was a Junior Fellow in the Harvard Society of Fellows.