The EOQ formula gives the order size that minimises the combined yearly cost of placing orders and holding stock. Economic order quantity equals the square root of (2 x annual demand x cost per order / holding cost per unit per year). It assumes steady demand and a fixed cost for each order.
What is the EOQ formula?
EOQ balances two costs that move in opposite directions: ordering more often raises ordering cost, while ordering larger lots raises holding cost. The formula finds the point where the total is lowest.
EOQ = square root of ( 2 x D x S / H )
- D: annual demand in units.
- S: the cost of placing and receiving one order, excluding the price of the goods.
- H: holding cost per unit per year, here unit cost x holding rate.
Related results follow directly: orders per year = D / EOQ, days between orders = 365 / orders per year, and annual ordering plus holding cost = (D / EOQ) x S + (EOQ / 2) x H. The purchase price is excluded because in this model it does not change with order size. The EOQ calculator applies the same definitions.
Worked example
This is an illustration. Annual demand is 4,500 units, each order costs $50 to place, the unit cost is $20 and the holding rate is 25% a year, so H = $5.
- EOQ = square root of (2 x 4,500 x 50 / 5) = square root of 90,000 = 300 units.
- Orders per year = 4,500 / 300 = 15.
- Days between orders = 365 / 15 = about 24 days.
- Annual cost = 15 x $50 + (300 / 2) x $5 = $750 + $750 = $1,500.
At the optimum, ordering cost and holding cost are equal. That is a useful sanity check on your own calculation: if the two parts differ widely, something is off.
How sensitive is the answer to getting the inputs wrong?
Not very. The total cost curve is flat near the minimum, so ordering a little more or less than EOQ costs only slightly more.
Using the same example, ordering 400 units instead of 300 gives 11.25 orders a year at $50, which is $562.50, plus average stock of 200 x $5 = $1,000. The total is about $1,562, roughly 4% above the minimum, for an order a third larger than ideal. Because the square root dampens errors, a holding rate that is off by a few points will change EOQ only modestly. So do not spend weeks refining the inputs, and round freely to case or pallet sizes.
What goes into ordering cost and holding cost?
Ordering cost is everything that happens per order regardless of size. Holding cost is everything that scales with stock sitting around.
| Cost | Typical components | Common error |
|---|---|---|
| Ordering cost (S) | Buyer time, purchase order processing, receiving, inspection, per-shipment freight and fees | Including the goods price, or counting salaried time that does not change with order count |
| Holding cost (H) | Cost of capital, storage space, handling, insurance, shrinkage, obsolescence | Counting only warehouse rent and ignoring the cost of money tied up |
Holding cost is stated as a percentage of unit cost per year. Ask your finance team for the cost of capital and the warehouse for the cost of space, rather than copying a rule of thumb from another business.
What assumptions does EOQ make?
The classic model assumes constant demand, a fixed ordering cost, no quantity discounts, no stockouts and predictable replenishment. Real operations break several of these.
- Demand varies. Use EOQ for the order size and pair it with safety stock and a reorder point for timing.
- Price breaks exist. A discount can outweigh the extra holding cost. Compare total cost at each price tier, including the purchase price, and choose the lowest.
- Supplier minimums or pack sizes apply. Round up to the nearest allowed quantity.
- Shelf life is limited. Cap the order so it will sell before it expires, even if EOQ is larger.
- Space is tight. A pallet position or cold room may set the limit before cost does.
When should you use something other than EOQ?
EOQ is a good first answer for stable, independent items bought regularly. It is a poor guide where demand is lumpy, tied to production plans, or heavily seasonal.
For items consumed through a bill of materials, requirements planning or lot-for-lot ordering usually fits better. For very low-value items, the effort of calculating may cost more than the savings, and a simple rule such as ordering monthly is enough. When many items share a supplier or a truck, ordering them together on a schedule can cut ordering cost for the whole group, which the single-item model cannot see. Optimisation software can handle discounts, constraints and many items at once, but it still relies on the same cost inputs, so the quality of those numbers matters more than the sophistication of the tool.
How does EOQ fit into a replenishment rule?
EOQ answers how much to order. A reorder point answers when. Use the two together: when inventory position falls to the reorder point, order the EOQ.
The reorder point itself depends on lead time and safety stock, covered in the guides on the reorder point formula and the reorder point calculator. Revisit EOQ whenever demand, costs or supplier terms change materially. For related methods, see the inventory and warehousing guides.
Common questions
What does EOQ stand for and what does it tell you?
EOQ stands for economic order quantity. It tells you the order size that minimises the sum of yearly ordering and holding costs, given steady demand. It is a planning guide for how much to buy per order, not a guarantee of the lowest total spend.
What costs go into the holding cost?
Holding cost includes the cost of money tied up in stock, storage space, handling, insurance, shrinkage and obsolescence. It is expressed as a percentage of unit cost per year. Use your finance team’s figures instead of a generic rate.
Why are ordering cost and holding cost equal at EOQ?
At the minimum of the total cost curve, the rising holding cost and the falling ordering cost balance exactly. In the standard model this means yearly ordering cost equals yearly holding cost, which gives you a quick way to check the result.
Can EOQ be used with quantity discounts?
Not directly. The basic formula ignores price breaks. Calculate total annual cost, including purchase price, at each discount tier, using the EOQ or the minimum quantity for that tier, then pick the tier with the lowest total.