UPDATED 2022: the 6 weeks that previously had only the top 15 ratings available now have the top 20 available. Merry Christmas! I previously posted full ratings for summer 1981, but to celebrate the holiday season this year, I decided to fill out the entire 1980-81 season with all of the data I have. So I've removed the old post and all of those scans are available here.
Below are the weekly Nielsen ratings results for the 1980-81 television season. Viewership wasn't reported by Nielsen until the fall 1988 season, so up until that point the only metric widely available was the household rating (which is what is reported here in this article). To calculate the estimated number of households watching, just multiply each rating by 778,000 (through w/e June 28) or 799,000 (w/e July 5 onward) as that is what 1 rating point represents.
Full weekly household ratings for every show are available beginning with the week ending April 19, 1981 (from the Los Angeles Times), but only partial results are available prior to that point. Some weeks have only the top 20 weekly ratings (from Newsday), but most other weeks have the weekly top 20 and bottom 5 ratings (from Broadcasting Magazine). Additionally, the second document includes full rankings (without ratings) which are available for every week except for w/e Sept. 21, 1980, Dec. 7, 1980, Dec. 21, 1980, Jan. 4, 1981, and Jan. 11, 1981 (from the Fort-Worth Star-Telegram). Also note: the rankings for the w/e Dec. 28, 1980 is mislabeled as "Jan. 22-28".
ARCHIVED WEEKS (ratings - all weeks)
ARCHIVED WEEKS (full rankings - thru Apr. 12, 1981)
Source: Nielsen Media Research via Newsday, Broadcasting Magazine, and The Los Angeles Times