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:
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.