Following his death, he was credited with collaborating with his doctoral advisor, Robert Millikan, on the Nobel-prize winning oil drop experiment which first determined the charge of the electron.

In 1911, Fletcher was the first physics student to earn a PhD summa cum laude from the University of Chicago.

This included the oil drop experiment commonly attributed to his advisor and collaborator, Robert Andrews Millikan.

Millikan took sole credit, in return for Fletcher claiming full authorship on a related result for his dissertation.

[9] Millikan went on to win the 1923 Nobel Prize for Physics, in part for this work, and Fletcher kept the agreement a secret until his death.

[11] He joined the Bell Telephone Laboratories' Engineering Staff Research Department where he found great interest in the physics of sound (acoustical science).

[13] He also developed the concepts of equal-loudness contours (commonly known as Fletcher–Munson curves), loudness scaling and summation, and the critical band.

[6] At Bell Labs, he worked with and was reportedly a tremendous influence on Harold Burris-Meyer, who developed advances in psychoacoustics.

Fletcher was elected an honorary fellow of the Acoustical Society of America in 1949, the second person to receive this honor after Thomas Edison, 20 years earlier.