Chawla was born on March 17, 1962, in Karnal, India, but her official date of birth was altered to July 1, 1961, to allow her to become eligible for the matriculation exam. As a child, Kalpana liked to draw pictures of airplanes. She went to local flying clubs and watched planes with her father. Chawla said "Every once in a while we'd ask my dad if we could get a ride in one of these planes. And, he did take us to the flying club and get us a ride in the Pushpak and a glider that the flying club had."
In 1976, Chawla graduated from the Tagore School, where she was a high-performing student. After getting a Bachelor of Engineering degree in Aeronautical Engineering from Punjab Engineering College, India, she moved to the United States in 1982 and obtained a Master of Science degree in Aerospace Engineering from the University of Texas at Arlington in 1984. Chawla went on to earn a second Masters in 1986 and a PhD in aerospace engineering in 1988 from the University of Colorado Boulder.