Economic Order Quantity (EOQ) Calculator

Understanding the Economic Order Quantity formula

The Economic Order Quantity, commonly abbreviated as EOQ, is the order quantity that minimises the total cost of inventory management by balancing two opposing cost pressures: ordering costs and holding costs. Ordering more frequently reduces average inventory (and therefore holding cost) but increases total ordering cost. Ordering less frequently reduces ordering cost but requires larger batches and higher average inventory. The EOQ formula finds the mathematically optimal point where these two costs are equal and their sum is minimised.

The formula is EOQ equals the square root of (2 times annual demand times ordering cost divided by annual holding cost per unit). Each input has a precise meaning. Annual demand is the total number of units consumed in a year. Ordering cost is the fixed cost incurred each time an order is placed, including purchasing, receiving, and processing costs. Holding cost is the annual cost of storing one unit in inventory, including storage space, insurance, opportunity cost of capital, and the risk of obsolescence or damage. Holding cost is sometimes expressed as a percentage of unit value rather than an absolute amount.

Once the EOQ is calculated, several useful secondary metrics follow automatically. Orders per year is annual demand divided by EOQ. The reorder cycle in days is 365 divided by orders per year: this tells you how often you will be placing orders under the EOQ policy. Annual ordering cost is the cost per order multiplied by orders per year. Annual holding cost is the holding cost per unit multiplied by EOQ divided by 2 (representing the average inventory level of half the order quantity). At the EOQ, these two costs are equal, which is the mathematical property that makes EOQ the minimum-cost solution.

When does EOQ apply?

The classic EOQ model makes several simplifying assumptions that determine when it produces useful results. It assumes that demand is constant and known, that lead time is fixed and known, that the full order arrives at once rather than gradually, and that there are no quantity discounts. In practice, few inventories meet all these conditions perfectly. EOQ is most applicable to high-volume, steady-demand items where demand is reasonably predictable, such as fast-moving consumer goods, manufacturing components with steady production schedules, or office supplies with consistent consumption patterns. For items with highly variable demand, seasonal patterns, or suppliers who offer meaningful volume discounts, the EOQ model requires modification or should be replaced with a more sophisticated approach.

Holding cost estimation

Many businesses struggle to estimate holding cost accurately because it includes several elements that are rarely tracked in a single place. The most significant components are: the cost of capital tied up in inventory (the opportunity cost of not investing that money elsewhere, typically estimated at 10 to 15 percent of unit value per year for a business with normal investment alternatives), storage cost (rent or depreciation of warehouse space per unit per year), insurance (proportional to inventory value), and obsolescence or spoilage risk (the probability that a unit will be unsellable due to age, damage, or obsolescence before it is consumed). When combined, total holding cost typically runs 20 to 30 percent of inventory unit value per year for most product businesses.

EOQ and supplier minimum order quantities

A practical complication in applying EOQ is that suppliers frequently impose minimum order quantities that may be larger than the EOQ. When this happens, you must order at least the supplier minimum. Running the EOQ calculation still has value in this situation because it tells you how far the supplier minimum deviates from optimal and what the associated cost penalty is. If the supplier minimum is significantly above the EOQ, there may be an opportunity to negotiate lower minimums in exchange for a longer-term supply commitment, which could reduce your total inventory cost meaningfully.