I looked into formulae for this and found 11 for owned cats and 3 for feral cats. Most are based on the number of households, some on the number of people, and two on shelter intake. The resulting range for the US is 44,200,498 to 95,796,618 (maximum is over twice the minimum) for owned cats, 21,075,256 to 57,613,401 (maximum is almost 3 times the minimum) for feral cats.
In “Methods used to estimate the size of the owned cat and dog population: a systematic review” by Martin J Downes, Rachel S Dean, Jenny H Stavisky, Vicki J Adams, Douglas JC Grindlay and Marnie L Brennan (http://www.biomedcentral.com/1746-6148/9/121) the values from two different AVMA studies are given as 59,100,000 and 74,059,000.
This paper also include the results of a phone survey done for two Indiana Counties: Marion = 94,998 (74,348 to 115,648), Tippecanoe = 17,165 (12,569 to 21,761). My collection of formulae give the results much higher: Marion = 292,367 to 175,445, Tippecanoe = 54,598 to 34,053.
Did you want a formula? One that hits an average of all of them is:
cats = households *.664
You can get the number of households in your area from http://quickfacts.census.gov/qfd/index.html
Do I have a point here? Well, yes. All we have are estimates. Take them with a grain of salt.