Economic Order Quantity Calculator
Determine the ideal purchase quantity that minimizes total inventory ordering and holding costs. Use it when negotiating supplier order sizes or setting purchasing policies.
About this calculator
Economic Order Quantity (EOQ) is the order size that minimizes the sum of ordering costs (administrative and shipping costs per order) and holding costs (storage, insurance, and capital tied up per unit per year). Ordering too frequently drives up ordering costs; ordering too rarely inflates holding costs. EOQ finds the sweet spot. The formula is: EOQ = √(2 × Annual Demand × Ordering Cost / Holding Cost per Unit). This derives from setting the marginal ordering cost equal to the marginal holding cost and solving for quantity. Annual demand is in units, ordering cost is the fixed cost each time an order is placed (in dollars), and holding cost is the annual cost to store one unit (in dollars). The model assumes constant demand, fixed costs, and instantaneous replenishment — a useful baseline even when real conditions vary.
How to use
A retailer sells 1,200 units per year, pays $50 per order placed, and incurs $3 per unit per year in holding costs. Step 1 — Multiply: 2 × 1,200 × 50 = 120,000. Step 2 — Divide by holding cost: 120,000 / 3 = 40,000. Step 3 — Take the square root: √40,000 ≈ 200 units. The retailer should order 200 units at a time. With 1,200 units needed annually, that means placing 6 orders per year (1,200 / 200). This balances the $50 ordering cost against the $3 annual holding cost per unit optimally.
Frequently asked questions
What assumptions does the Economic Order Quantity model make?
The EOQ model assumes that demand is constant and known, ordering and holding costs are fixed and known, and each order arrives in full instantaneously (no lead time or partial deliveries). It also assumes no quantity discounts and that the product is a single item managed independently. In reality, demand fluctuates, suppliers offer volume discounts, and lead times vary — so EOQ is best used as a starting benchmark rather than a rigid rule. More advanced models like the EOQ with reorder point or quantity discount EOQ address some of these limitations.
How do I calculate the holding cost per unit for the EOQ formula?
Holding cost per unit typically includes warehousing space, insurance, spoilage or obsolescence, and the opportunity cost of capital tied up in stock. A common approximation is to take 20–30% of the unit purchase cost as the annual holding cost rate and multiply it by the unit cost. For example, if a unit costs $10 and your holding rate is 25%, the annual holding cost is $2.50 per unit. Be sure to use a per-unit, per-year figure so it matches the units of the EOQ formula. Using an inaccurate holding cost is one of the most common sources of error in EOQ calculations.
Why does ordering a larger quantity not always reduce total inventory costs?
Ordering a larger quantity reduces how often you order, which lowers total ordering costs. However, larger order quantities mean you hold more inventory on average (roughly half the order quantity), which increases holding costs proportionally. These two forces move in opposite directions as order size changes. EOQ finds the exact quantity where the marginal reduction in ordering cost from ordering one more unit equals the marginal increase in holding cost — the mathematical minimum of their combined total. Ordering more than EOQ actually increases total costs, even though the per-order cost is spread over more units.