Number of days feeding (be generous) multiplied by the total weight of the sheep times .04
Divide that by the weight of the bales gives you the number of bales you need.
Bales weigh between 35 and 120 lbs each so it's good to know how much your particular ones weigh. Don't let someone tell you that you need one bale per day...weights vary and you don't want to underfeed your sheep or any livestock that's depending on you for food. If you're using large round bales the calculations remain the same but I'd allow 10% more to account for wastage if you're not using a bale feeder.
Here's our calculations. 5, 200lb ewes eating for 150 days from 35 lb bales need 172 bales of hay for the winter. If the bales were 50 lbs then we'd only need 120. That's why it's important to know exactly how heavy your bales are and to make sure you buy the best hay you can, or make your own. Baled hay is a convenient way to store food and certainly more space efficient than loose hay. 6000 lbs of loose hay takes up an awful lot of room in a loft so bales are most common. We plan on feeding hay beginning in October and going through March with the sheep eating grass/hay in October and March but just hay for the colder months. The weather varies each year so you can never have too much hay in store. There are plenty of uses for old hay bales, animal bedding, gardening, compost, you name it.
A ewe needs about 4 lbs of hay for every 100 lbs of weight plus a half-1 lb grain in the last 6 weeks of pregnancy and nursing. For us that amounts to just a bit over a bale of hay per day plus grain so our feed costs for the winter work out to be $4 per day for hay, $2 for grain/pellet and of course you need straw for bedding and lots of fresh water. Our weekly average is probably $60 for food and bedding for the sheep and chickens. That cost will be offset by the eggs, chicks and lambs produced by our lovely ewes. Now that we have a barn with a hay loft we can buy our next years hay earlier in the year for probably half the price we're paying now which will save feed costs and if we build a rodent proof feed bin then we can get grain in bulk which is cheaper again. Something to think about if it saves us $600 in feed costs. I think we'll also plant some winter grazing crops like turnips and kale so they have some green stuff as far into the winter as they can manage which is good for their health and our pocket book. We'll see how it goes.