Christopher Moore has a doctorate in physics from MIT and has worked on projects ranging from tracking the world’s oil supply to searching for new cancer drugs. His latest gig is turning out to be the hardest: Helping shoppers find their correct clothing size.

There are no standard clothing sizes, something that anyone who has stood in a dressing room trying on jeans, tops or dresses can attest. As shopping has shifted online, the problem has worsened. Size and fit are among the top reasons for returning online orders, according...