How long will my hay last?

Bales on hand and who's eating them → how many days of hay you have, the run-out date, and how many more bales get you to pasture.

98days of hay

Runs out about —

50.6 lb a day, waste included · 7.1 bales a week · 5,000 lb on hand

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How it's calculated

Hay on hand = bales × weight per bale.
Hay per day for each group = number of animals × body weight × daily intake (% of body weight) × (1 + waste %).
Days left = hay on hand ÷ hay per day (all groups). The run-out date is today plus the whole days left.
If you set a date when pasture is back, the shortfall is the days between the run-out date and that date, and bales to buy = shortfall days × hay per day ÷ bale weight, rounded up.
Starting intakes: horses 2%, cattle 2.5%, sheep and goats 3% of body weight a day. All are inside Extension ranges (University of Minnesota: horses willingly eat 2 to 2.5% when given free access; Oregon State: horses 1.5 to 3%, beef cattle 1 to 3%, sheep 2 to 5%, goats 2 to 6%). Change them to match your animals and your hay.
Waste depends on how you feed. University of Minnesota measured 57% waste feeding round bales to horses with no feeder versus 5 to 33% with a feeder. University of Missouri found 20% (open-bottom ring), 13% (sheeted-bottom ring) and 5% (cone feeder) for cattle. The 15% default is a middle value; pick yours.

Worked example

Two 1,100 lb horses at 2% intake with 15% waste eat 2 × 1,100 × 0.02 × 1.15 = 50.6 lb of hay a day. 100 bales × 50 lb = 5,000 lb, which lasts 5,000 ÷ 50.6 = 98.8 days, so 98 whole days. If that's 82 days short of pasture, you need 81.2 days × 50.6 lb ÷ 50 lb = 82.2, rounded up to 83 more bales.

Sources

Hay for horse diets — University of Minnesota Extension
Horses given free access to hay willingly eat 2 to 2.5% of body weight a day.
Calculating livestock winter hay needs — Oregon State University Small Farms Program
Dry matter intake by species as % of body weight, plus 10 to 50% extra for waste depending on the feeding system.
Feeding horses with a round-bale feeder — University of Minnesota Extension
5 to 33% hay waste with a feeder, 57% without.
How you feed hay this winter is more important than ever — University of Missouri Extension
Cattle feeder losses: 20% open-bottom ring, 13% sheeted-bottom ring, 5% cone feeder.