What the economic order quantity is
The economic order quantity (EOQ) is the order size that minimizes the total cost of managing inventory. Ordering in large batches means few orders but a lot of stock sitting on shelves; ordering in small batches keeps stock low but multiplies shipping and paperwork. The EOQ is the balance point, where the yearly ordering cost equals the yearly holding cost.
The formula
EOQ = √(2 × D × S ÷ H)
- D: annual demand in units
- S: cost of placing one order (shipping, receiving, admin time)
- H: cost of holding one unit for a year, here a percentage of the unit purchase cost
The calculator also gives the number of orders per year (D ÷ EOQ), the days between orders, the total annual cost and the reorder point:
Reorder point = daily demand × lead time + safety stock
Worked example
A shop sells 12,000 units a year. Each order costs $75 to place. Each unit costs $20, and holding stock costs 20% of its value per year, so H = $4.
- EOQ = √(2 × 12,000 × 75 ÷ 4) = √450,000 ≈ 671 units
- Orders per year = 12,000 ÷ 671 ≈ 17.9, about one every 20 days
- Reorder point with a 7-day lead time and 100 units of safety stock = 12,000 ÷ 365 × 7 + 100 ≈ 330 units
- Annual cost = 17.9 × $75 + 671 ÷ 2 × $4 + 100 × $4 ≈ $3,083
At the EOQ, ordering and holding each cost about $1,342 a year; the remaining $400 is the cost of carrying the safety stock.
What goes into holding cost
Holding cost is often underestimated. It includes warehouse space, insurance, property taxes on inventory, shrinkage and damage, obsolescence and, above all, the cost of capital tied up in stock. A rate of 15% to 30% of the item’s value per year is common; fast-moving electronics or perishable goods can run higher.
Limits of the model
The classic EOQ assumes steady demand, a constant lead time, a fixed cost per order and a single price whatever the quantity. In practice:
- Quantity discounts can make a larger order cheaper overall; compare the total cost at each price break.
- Seasonal demand calls for recalculating by season.
- Perishable items and limited storage cap the order size.
- The total cost curve is flat near the optimum: ordering 20% more or less than the EOQ raises costs by only about 2%, so rounding to a full pallet or case is fine.
This calculator gives estimates for education and planning. It is not investment, tax or legal advice; for decisions about your own situation, talk to a qualified financial professional.