Economic Order Quantity (EOQ) Calculator
Finds the optimal number of units to order at a time, minimizing combined ordering and inventory-holding costs. Use it when reviewing purchase order policies or evaluating supply chain efficiency.
About this calculator
The Economic Order Quantity (EOQ) formula determines the order size that minimizes the total annual cost of ordering and holding inventory. The formula is: EOQ = √(2 × D × S / H), where D is annual demand in units, S is the cost incurred each time an order is placed, and H is the cost to hold one unit in inventory for one year. Ordering too frequently increases total ordering costs; ordering too rarely increases holding costs. EOQ sits at the sweet spot where the two costs are equal and their total is minimized. Lead time — the gap between placing and receiving an order — does not change the EOQ itself, but it determines the reorder point (ROP = daily demand × lead time). Knowing both EOQ and ROP lets a business maintain continuous stock without overstocking. The model assumes steady, predictable demand and constant costs.
How to use
A warehouse distributes 2,400 units annually (D = 2,400). Each order placed costs $75 (S = $75), and holding one unit costs $4 per year (H = $4). Apply the formula: EOQ = √(2 × 2,400 × 75 / 4) = √(360,000 / 4) = √90,000 = 300 units. The warehouse should order 300 units at a time, placing 2,400 ÷ 300 = 8 orders per year. If lead time is 5 days and demand is uniform, daily demand = 2,400 ÷ 365 ≈ 6.6 units/day, so the reorder point = 6.6 × 5 ≈ 33 units. Place a new order when stock falls to 33 units.
Frequently asked questions
What is Economic Order Quantity and how does it minimize inventory costs?
Economic Order Quantity (EOQ) is the purchase order size that minimizes the total of two competing cost categories: ordering costs and holding costs. Ordering costs are fixed per order (administration, shipping), so they fall as order size grows and frequency decreases. Holding costs (warehousing, insurance, capital tied up) rise as order size — and therefore average inventory — increases. EOQ is derived by setting these two cost functions equal and solving for quantity, yielding EOQ = √(2DS/H). At this quantity, total inventory cost is at its mathematical minimum. Using EOQ means a business neither places unnecessarily small, frequent orders nor accumulates excessive stock.
How does lead time affect when I should place an order using the EOQ model?
Lead time does not change the optimal order quantity (EOQ) but it determines the reorder point — the inventory level at which a new order must be placed so stock arrives before running out. The reorder point is calculated as: ROP = average daily demand × lead time (in days). For example, if daily demand is 10 units and lead time is 7 days, you should reorder when you have 70 units remaining. If demand is variable, a safety stock buffer is added to ROP. EOQ tells you how much to order; the reorder point tells you when.
When does the EOQ model give inaccurate results and how can it be adjusted?
The EOQ model assumes constant, known demand, fixed costs, and no quantity discounts — assumptions that frequently break down in real supply chains. Seasonal or lumpy demand can make the calculated EOQ too large or too small at different times of year. Supplier volume discounts may make it cheaper to order more than EOQ suggests. Lead time variability creates stockout risk that EOQ does not address on its own. To adapt, practitioners combine EOQ with safety stock formulas, periodic review policies, and quantity-discount analysis. Despite its simplicity, EOQ remains the best starting point for inventory policy because it grounds decisions in the cost trade-off that all inventory management must balance.