The best way to calculate the answer is to use AUM (Animal Unit Month) calculations. What that will be is estimate the amount of forage the cow will eat in a year, then, you will need to determine how many acres of forage it will take to produce that amount of forage.
Here are some websites that will help explain the system.
http://www.ag.ndsu.nodak.edu/dickinso/research/1997/animal.htm
http://www1.agric.gov.ab.ca/$department/deptdocs.nsf/all/agdex1201
http://mbforagecouncil.mb.ca/foragegrasslandmanual/8agrazingmanagementsystemsgrazingmanagement/82aanimalunitmonthsstockingrateandcarryingcapacity/default.aspx
An example calculation follows:
1,000 lb cow weaning a 550 lb calf will need 13 AUM's to sustain the grazing system
13 AUM time 780 lb/AUM equals 10,140 lb of forage, let's estimate 35% harvest efficiency of the forage so the cow will need 10,140 / .35 = 28,971 lb of forage.
If your pasture can produce 3 tons of forage/acre (6,000 lb/acre), then 28,971/6000=4.82 acres/cow
Cross-fencing, supplemental feeding, winter hay, silage, etc. will adjust the number of acres.
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