Find the order quantity that minimizes the combined cost of ordering and holding inventory. Enter your annual demand, cost per order, and annual holding cost per unit to compute the EOQ, number of orders per year, total annual cost, and reorder point. Everything recomputes live in your browser.
The Economic Order Quantity (EOQ) model finds the single order size that minimizes the total annual cost of managing an inventory item — the sum of ordering (or setup) cost and inventory holding (carrying) cost. Developed by Ford W. Harris in 1913, it remains one of the most widely used results in operations and supply-chain management. This calculator computes EOQ, orders per year, time between orders, the cost breakdown, and the reorder point, all live in your browser.
EOQ = √(2DS / H), where D is annual demand (units/yr), S is the fixed cost per order or setup ($/order), and H is the cost to hold one unit in inventory for one year ($/unit/yr).
The model balances two opposing costs. Order in large batches and you place fewer orders (low ordering cost) but carry more inventory on average (high holding cost). Order in small batches and you hold less stock but pay the fixed ordering cost more often. The EOQ is the order size where these two curves cross — and at exactly that point the annual ordering cost equals the annual holding cost. The minimized total annual cost works out neatly to √(2DSH).
Holding cost is often the hardest input to pin down. It includes the cost of capital tied up in inventory, warehousing space, insurance, taxes, shrinkage, obsolescence, and spoilage. A common shortcut is to express H as a percentage of the unit cost — typically 15%–30% per year. This calculator lets you enter H directly in dollars per unit per year, or as a percentage of the unit cost (it multiplies unit cost × percentage to get H). For example, a $25 part with a 20% carrying rate has H = $5.00/unit/yr.
EOQ tells you how much to order; the reorder point (ROP) tells you when. With constant demand and a known lead time, ROP = daily demand × lead time, where daily demand = annual demand ÷ working days per year. When inventory on hand falls to the ROP, place an order of size EOQ so that it arrives just as you run out.
Real demand and lead times vary, so in practice you add safety stock to the ROP to buffer against variability: ROP = (daily demand × lead time) + safety stock. The amount of safety stock depends on demand/lead-time variability and your target service level — this calculator computes the deterministic ROP without safety stock.
The classic EOQ model assumes: demand is constant and known, lead time is constant, the entire order arrives at once (instantaneous replenishment), no quantity discounts, and no stockouts. When these break down, use an extended model. Quantity discounts call for comparing the total cost at the EOQ versus at each price-break quantity. Gradual replenishment (you produce while you consume) uses the Economic Production Quantity (EPQ / POQ) model. Variable demand calls for safety stock and a (Q, R) or periodic-review policy. Even so, EOQ is robust: total cost is flat near the optimum, so being within ±20% of the EOQ typically raises total cost by only a few percent.
EOQ is the order quantity that minimizes the total annual inventory cost — the sum of ordering cost and holding cost. It is calculated as the square root of (2 × annual demand × ordering cost ÷ holding cost). At the EOQ, annual ordering cost and annual holding cost are exactly equal.
It falls out of the math. Ordering cost = (D/Q)·S decreases as the order quantity Q grows, while holding cost = (Q/2)·H increases with Q. Setting the derivative of their sum to zero gives Q = √(2DS/H), and at that point (D/Q)·S = (Q/2)·H. This equality is a quick sanity check: if your computed costs are equal, your EOQ is right.
Add up the annual cost of capital, storage, insurance, taxes, and obsolescence per unit. If that is hard, use a carrying-cost percentage of the unit value — commonly 15% to 30% per year — and multiply it by the unit cost. This tool lets you enter H either way.
EOQ answers how much to order; the reorder point (ROP) answers when to order. ROP = daily demand × lead time (plus safety stock in practice). When inventory drops to the ROP, you place an EOQ-sized order so it arrives just as stock runs out.
The basic EOQ ignores discounts. With price breaks, compute the EOQ for each price level, then compare the total annual cost (purchase cost + ordering + holding) at the EOQ and at each discount-break quantity, and pick the lowest. Larger orders can be cheaper overall if the unit-price savings outweigh the extra holding cost.