Find the order size that minimizes total ordering and holding costs. All calculations run locally in your browser.
Total units consumed or sold per year.
Fixed cost each time you place an order: purchasing labor, shipping, receiving, paperwork.
Warehousing, insurance, capital, and obsolescence cost per unit per year.
Purchase price per unit. Used for extended cost analysis.
Economic Order Quantity
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Optimal units per order
Orders per Year
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Order Cycle
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Formula: EOQ = √(2DS / H)
Every time you place a purchase order, you pay a fixed cost: someone reviews stock levels, contacts the supplier, processes the PO, receives the shipment, and updates the system. That cost is the same whether you order 10 units or 10,000. Ordering more frequently means paying that fixed cost more often.
On the other hand, ordering in bulk means carrying more inventory. Inventory sitting in your warehouse ties up capital, takes up space, requires insurance, and risks going obsolete. The longer it sits, the more it costs.
EOQ finds the order size where these two forces balance out. At the EOQ, your total annual ordering cost equals your total annual holding cost. Any other order size - larger or smaller - results in a higher combined cost.
The classic Wilson EOQ formula is:
EOQ = √(2 × D × S / H)
Where:
The formula was developed by Ford W. Harris in 1913 and refined by R.H. Wilson in 1934. It remains one of the most widely used inventory models because of its simplicity and the insight it provides into cost trade-offs.
Consider an item with 10,000 units of annual demand, $50 per order, and $5 per unit per year in holding costs. The EOQ is √(2 × 10,000 × 50 / 5) = 447 units.
At 447 units per order, you place about 22 orders per year. Annual ordering cost is 22 × $50 = $1,118. Annual holding cost is (447/2) × $5 = $1,118. They match - that is the hallmark of an optimal EOQ solution. Total inventory cost: $2,236 per year.
If you ordered 200 units instead, you would place 50 orders ($2,500 ordering) but hold less stock ($500 holding) for a total of $3,000. If you ordered 1,000 units, you would place 10 orders ($500 ordering) but hold more ($2,500 holding) for the same $3,000. Both alternatives cost $764 more per year.
EOQ assumes constant demand, fixed costs, and no quantity discounts. Real supply chains rarely meet all three conditions. Here is when to adjust:
The holding cost per unit is often the hardest input to estimate. It typically runs 20-30% of item value per year. Major components:
If you are unsure of your exact holding cost, our carrying cost calculator breaks it down component by component.
EOQ answers "how much to order." The reorder point answers "when to order." Together they form a complete (Q, R) inventory policy: order Q units whenever on-hand stock drops to R units.
Use our reorder point calculator to determine the trigger level based on your lead time and demand variability. The safety stock calculator provides additional methods for setting buffer levels.
Economic Order Quantity (EOQ) is the order size that minimizes total inventory costs by balancing ordering costs against holding costs. Ordering more frequently means higher ordering costs but lower holding costs. Ordering less frequently means lower ordering costs but higher holding costs. EOQ finds the crossover point.
The classic EOQ formula assumes constant and known demand, fixed ordering cost, fixed holding cost per unit, instantaneous replenishment (no lead time stockouts), and no quantity discounts. Real operations rarely meet all these conditions perfectly, but EOQ still provides a useful starting point.
Quantity discounts reduce the unit cost at higher order quantities, which lowers the annual holding cost per unit. To evaluate discounts, calculate the total cost (ordering + holding + purchase) at the EOQ and at each discount break quantity, then pick the lowest total. The optimal order may jump to a discount break.
EOQ works best with relatively stable demand. For seasonal products, recalculate EOQ each season using that period's demand rate. Some operations use a weighted annual demand that emphasizes recent months, then recalculate quarterly.
EOQ tells you how much to order. The reorder point tells you when to order. Together they form a complete replenishment policy: place an order of EOQ units whenever inventory drops to the reorder point. Use our reorder point calculator to find the trigger level.
The basic EOQ formula does not consider warehouse capacity. If your EOQ exceeds available storage space, you may need to order less than the calculated amount and accept somewhat higher total costs. Factor storage constraints into the holding cost rate for a more realistic result.
Recalculate when input costs change materially - a new supplier contract, a warehouse move, or a significant demand shift. Most operations review EOQ quarterly or when ordering costs or holding costs change by more than 10%.
Inventory Pro calculates reorder points and generates purchase orders based on demand history, supplier lead times, and min/max levels. We have been developing inventory solutions since 1996.
Learn more about Inventory Pro and our capabilities. From small business to industrial warehousing, our software can scale and adapt to various industries.