Unable to find work as an engineer, Clarke went to work for General Electric as a supervisor of computers in the Turbine Engineering Department. During this time, she invented the Clarke calculator, an early graphing calculator, this simple graphical device solved equations involving electric current, voltage and impedance in power transmission lines. The device could solve line equations involving hyperbolic functions ten times faster than previous methods. She filed a patent for the calculator in 1921 and it was granted in 1925.
In 1921, Clarke took a leave of absence from GE to teach physics at the Constantinople Women's College in Turkey because she was not allowed to do electrical engineering work, was not earning the same salary and had a lower professional status as men doing the same work. The next year, when she returned from Turkey, she was offered a job by GE as a salaried electrical engineer in the Central Station Engineering Department – the first professional female electrical engineer in the United States. She retired from General Electric in 1945.