Economic Order Quantity (EOQ): The Formula, the Trade-Off, and When It Breaks Down

The trade-off EOQ solves

Every replenishment decision involves two costs that move in opposite directions. Ordering cost is incurred each time you place a replenishment order, purchase order processing, supplier communication, receiving labor, inspection, and freight per shipment. If you order frequently in small quantities, you incur this cost many times per year. If you order infrequently in large quantities, you incur it rarely.

Carrying cost is the annual cost of owning inventory, capital tied up in stock, warehouse space, insurance, obsolescence risk, and shrinkage. See the inventory carrying cost post for how to build this number. If you order in large quantities, average inventory is high and carrying cost is high. If you order in small quantities, average inventory is low and carrying cost is low.

Total cost is the sum of these two components. As order quantity increases, ordering cost falls (fewer orders per year) and carrying cost rises (more average inventory). As order quantity decreases, ordering cost rises and carrying cost falls. The total cost curve has a minimum, and the order quantity at that minimum is the EOQ.

The EOQ formula

EOQ = √(2 × D × S ÷ H)

Where:

• D = Annual demand (units per year)
• S = Ordering cost per order (cost per purchase order placed)
• H = Carrying cost per unit per year (unit value × carrying cost rate)

Worked example. A distributor sells 12,000 units of a component per year. Each purchase order costs 150 USD to process (ordering cost). The component is valued at 25 USD per unit and the carrying cost rate is 24 percent per year, making the carrying cost per unit per year 25 × 0.24 = 6 USD. EOQ = √(2 × 12,000 × 150 ÷ 6) = √(3,600,000 ÷ 6) = √600,000 = 775 units.

At this order quantity, the company places 12,000 ÷ 775 = 15.5 orders per year (approximately every 3.4 weeks). Average inventory is 775 ÷ 2 = 387.5 units. Annual ordering cost: 15.5 × 150 = 2,325 USD. Annual carrying cost: 387.5 × 6 = 2,325 USD. The two costs are equal at the EOQ, this is a useful check.

Use the EOQ Calculator to find the optimal order quantity for your own inputs without working through the arithmetic manually.

What the EOQ assumes, and why it matters

The EOQ formula makes several simplifying assumptions. Understanding them tells you when the formula is reliable and when to adjust the result.

Constant, known demand. The formula assumes demand is stable and predictable. For a product with steady sales, this is a reasonable approximation. For a seasonal or highly variable product, the EOQ gives a result that fits the average but may be wrong at the extremes. In those cases, you need separate replenishment logic for peak and off-peak periods, or a dynamic EOQ that updates as the demand rate changes.

Instantaneous replenishment. The formula assumes the full order quantity arrives at once. When there is a non-trivial production or delivery lead time, you need to layer a reorder point calculation on top of the EOQ. The EOQ tells you how much to order; the reorder point tells you when to order. See the Reorder Point Calculator and the reorder point post.

No quantity discounts. The formula assumes unit price is constant regardless of order quantity. When suppliers offer volume discounts for larger orders, the optimal order quantity may be at a discount threshold rather than at the EOQ. The total cost at each discount breakpoint, unit cost times annual demand, plus ordering cost, plus carrying cost, must be compared to the EOQ total cost to find the true optimum.

Fixed ordering cost. The formula assumes each order costs the same to place. If order complexity, supplier setup time, or freight cost varies by order size, the fixed ordering cost assumption breaks down. Use an average or build a cost model that reflects actual ordering cost behavior.

EOQ and the reorder point

EOQ and reorder point are two separate but complementary calculations. EOQ answers: how many units should I order each time? Reorder point answers: at what inventory level should I place the next order?

The reorder point is set to cover demand during the replenishment lead time plus a safety stock buffer for variability. Without a correct reorder point, even a perfectly sized EOQ will generate stockouts if the order is triggered too late, or excess inventory if triggered too early.

Reorder point = (Average daily demand × Lead time in days) + Safety stock

The safety stock component is sized using demand and lead time variability, not by EOQ. The two calculations are independent. You can use the EOQ to set your order quantity and the safety stock calculator to set your reorder point, running both calculations separately against the same SKU data.

EOQ and MOQ

The EOQ is the financially optimal order quantity. The supplier’s minimum order quantity is the floor below which the supplier will not accept orders. When MOQ is greater than EOQ, you are forced to order more than optimal, carrying extra inventory and incurring carrying cost above the minimum. When MOQ is less than EOQ, you can order at the EOQ and the MOQ is not a binding constraint.

The MOQ post covers this in detail, but the operational question is: how much does the MOQ constraint cost you annually? The answer is the carrying cost of the forced excess inventory:

Annual MOQ penalty = (MOQ − EOQ) ÷ 2 × Unit value × Carrying cost rate

Dividing by 2 converts the forced excess from peak to average inventory. This figure is the financial basis for MOQ negotiation, it represents the annual cost to your business of the supplier’s minimum quantity requirement.

EOQ with quantity discounts

When a supplier offers a lower unit price for orders above a certain quantity, you must compare the total annual cost at each option: the EOQ total cost at the standard price, and the total annual cost at each discount breakpoint.

Total annual cost at any order quantity Q:

Total cost = (D ÷ Q) × S + (Q ÷ 2) × H + D × unit price

The third term, D × unit price, is usually omitted in the basic EOQ because unit price is constant and does not affect the optimal quantity. When price varies by quantity, it must be included.

Example: continuing the earlier example, the supplier offers a 5 percent discount (unit price 23.75 USD, carrying cost 5.70 USD/unit/year) for orders of 1,000 or more. At Q = 1,000: ordering cost = (12,000 ÷ 1,000) × 150 = 1,800 USD; carrying cost = (1,000 ÷ 2) × 5.70 = 2,850 USD; material cost = 12,000 × 23.75 = 285,000 USD. Total: 289,650 USD. Compare to EOQ: ordering + carrying = 4,650 USD plus material cost = 12,000 × 25 = 300,000 USD. Total: 304,650 USD. The discount option saves approximately 15,000 USD per year, the volume discount outweighs the additional carrying cost in this case.

EOQ in practice: how to apply it

The EOQ model works best as a systematic baseline across a large SKU portfolio, not as a precise answer for any individual SKU. Use it to:

Set a starting order quantity for new SKUs, then refine based on observed demand patterns after the first few replenishment cycles.

Identify SKUs where current order quantities are significantly above or below EOQ, these are the highest-priority targets for carrying cost reduction or ordering frequency reduction.

Evaluate supplier MOQ proposals: calculate the EOQ first, then compare it to the proposed MOQ to quantify the annual penalty before entering negotiations.

Prioritize purchasing process improvement. A key lever that reduces the EOQ is the ordering cost S. If you invest in purchase order automation or EDI, S falls, which means the optimal order quantity falls, you carry less average inventory, and carrying cost drops. Quantify this trade-off before approving purchasing system investments.

Sensitivity of EOQ to input changes

Because EOQ is a square root function, it is less sensitive to input changes than you might expect. If demand doubles, EOQ increases by only 41 percent, not by 100 percent. If carrying cost doubles, EOQ falls by only 29 percent. This means imprecise inputs still produce useful order quantities. You do not need exact values for S and H; reasonable estimates produce good results.

The practical implication: do not let imprecision in your ordering cost or carrying cost estimate stop you from applying the model. A 20 percent error in carrying cost changes the EOQ by about 10 percent, a change that matters less than the gap between your current order quantity and the EOQ in most cases where the model has not been applied before.

Common mistakes

• Applying EOQ to individual SKUs one at a time. The EOQ model generates real value when applied systematically across the portfolio, especially to identify outliers where current quantities are far from optimal. Applying it to one or two SKUs manually adds administrative cost without proportional benefit.
• Ignoring the reorder point. EOQ tells you how much to order, not when. Without a correctly set reorder point, even the right order quantity will generate stockouts or excess inventory depending on when the order is triggered. The two calculations must be used together.
• Using a carrying cost rate that is too low. The most common source of EOQ error. Underestimating carrying cost makes the EOQ too large, you order more than optimal and carry more inventory than necessary. Calculate your actual carrying cost rate as described in the carrying cost post.
• Not updating EOQ when demand rates change. EOQ is calculated from annual demand. If demand for a SKU has changed significantly, a new customer, a lost account, a seasonal shift, recalculate the EOQ. Running on a stale EOQ is running the replenishment system on wrong parameters.
• Treating EOQ as an exact answer. The EOQ model produces a continuous optimum in a model world. Real-world constraints, truck or pallet sizes, standard packaging, supplier lead time variability, round the practical order quantity. Use the EOQ as the center of a range, not as a precise target.

Frequently asked questions

What is Economic Order Quantity (EOQ)?

EOQ is the order quantity that minimizes the total cost of replenishment, defined as the sum of annual ordering cost and annual carrying cost. It is derived from the EOQ formula: √(2 × annual demand × ordering cost per order ÷ carrying cost per unit per year). At the EOQ, ordering cost and carrying cost are equal and their combined total is at its minimum. Ordering below the EOQ means placing orders too often (excess ordering cost). Ordering above it means holding too much inventory (excess carrying cost).

What is ordering cost in the EOQ formula?

Ordering cost (S) is the cost incurred each time a replenishment order is placed, independent of order size. It includes purchase order processing (staff time, system cost), supplier communication and confirmation, receiving labor, incoming inspection, and any fixed freight component that applies per shipment rather than per unit. For manual purchase orders in typical manufacturing environments, S commonly runs between 50 and 250 USD per order. Automated procurement (EDI, blanket orders) can reduce S significantly, which shifts the optimal EOQ lower and reduces average inventory.

What is carrying cost in the EOQ formula?

Carrying cost (H) in the EOQ formula is the annual cost to hold one unit of inventory for one year, the unit value multiplied by the carrying cost rate. The carrying cost rate includes capital cost, storage cost, insurance, obsolescence risk, and shrinkage as a percentage of inventory value per year. For most operations, the rate is 20 to 35 percent. A 50 USD item with a 25 percent carrying rate has H = 12.50 USD per unit per year. Using a carrying cost rate that is too low makes the EOQ too large, leading to excess inventory.

How does EOQ relate to reorder point?

EOQ and reorder point are two independent calculations that work together to define the replenishment policy for a SKU. EOQ answers how much to order; the reorder point answers when to order. The reorder point is set to cover average demand during the supplier lead time plus a safety stock buffer for variability. EOQ calculations do not include lead time or demand variability, those inputs go into the reorder point and safety stock calculations separately. Both are needed to run an effective continuous review replenishment system.

When should you not use the EOQ model?

The EOQ model works poorly when demand is highly variable or seasonal (the stable-demand assumption breaks down), when replenishment is made-to-order with no standard ordering cost, when items have a shelf life that limits how much can be ordered at once, or when the supplier is the only source and imposes a MOQ that far exceeds the EOQ. In these cases, the EOQ result still provides a useful reference point, an indication of where total cost is minimized under ideal conditions, but the practical order quantity will differ from the EOQ for identifiable reasons.

How does a volume discount affect the EOQ decision?

When a supplier offers a lower unit price at higher order quantities, the optimal decision may shift to the discount breakpoint even if it is above the EOQ. To evaluate this, calculate total annual cost, ordering cost plus carrying cost plus annual material cost, at the EOQ (standard price) and at each discount breakpoint. If a breakpoint’s total annual cost is lower than the EOQ’s total annual cost, the discounted quantity is the better choice. The discount must save more than the additional carrying cost it generates to be worth taking.