EOQ Calculator - Economic Order Quantity
Enter your annual demand, cost per order, and annual holding cost per unit to find the Economic Order Quantity that minimizes your total inventory costs. The calculator also shows how many orders to place per year, the time between orders, your average inventory level, the full cost breakdown, and the reorder point for any lead time you supply. Results update instantly as you type.
What is Economic Order Quantity?
Economic Order Quantity (EOQ) is the ideal number of units you should purchase in a single order to minimize the combined cost of ordering and storing inventory over the course of a year. The concept was introduced by Ford W. Harris in 1913 and later popularized by R.H. Wilson, which is why the formula is sometimes called the Wilson EOQ model. The core insight is that ordering costs and holding costs move in opposite directions as order size changes: larger orders mean fewer orders per year (lower ordering cost) but more stock sitting in the warehouse at any time (higher holding cost). EOQ finds the exact quantity where these two costs are equal and their sum is at its lowest point.
The EOQ formula explained
The standard EOQ formula is: EOQ = sqrt(2 x D x S / H), where D is annual demand in units, S is the fixed cost incurred each time an order is placed (also called the setup or ordering cost), and H is the annual cost of holding one unit in inventory for a full year. At the EOQ, annual ordering cost (D / EOQ x S) and annual holding cost (EOQ / 2 x H) are exactly equal. This mathematical property means that if your order quantity is above EOQ your holding costs dominate, and if it is below EOQ your ordering costs dominate. The number of orders per year is D / EOQ, and the average cycle time between orders is 365 / (D / EOQ) days. Average on-hand inventory between orders (assuming no safety stock) is EOQ / 2.
How to use the Reorder Point alongside EOQ
EOQ tells you how much to order; the Reorder Point (ROP) tells you when. The basic ROP formula is: ROP = average daily demand x lead time in days. Average daily demand is your annual demand divided by 365. For example, if you sell 24,000 units per year (about 65.8 units per day) and your supplier takes 10 days to deliver, you should place a new order when your stock level drops to 658 units. In practice, demand and lead times both vary, so most businesses add a safety stock buffer: ROP = (daily demand x lead time) + safety stock. A common safety stock formula is z x sigma x sqrt(L), where z is the service-level z-score (1.645 for 95 %, 2.33 for 99 %), sigma is the standard deviation of daily demand, and L is lead time in days.
When EOQ works best and when to adjust it
EOQ performs best for stable, year-round products with predictable supplier lead times and no quantity discounts. It is widely used in manufacturing, wholesale distribution, retail replenishment, and raw-material procurement. You should adjust your approach in several situations. If your supplier offers price breaks above a certain quantity, compare the total landed cost (purchase cost plus ordering cost plus holding cost) at both the EOQ quantity and at each price-break threshold, then choose whichever gives the lowest total. If demand is highly seasonal, recalculate EOQ separately for the peak and off-peak periods rather than using a single annual average. If your products have short shelf lives or high spoilage rates, add those costs to H. If you manufacture your own stock rather than buying it, use the Economic Production Quantity (EPQ) variant, which accounts for inventory building up gradually during a production run rather than arriving all at once.
EOQ model assumptions and real-world adjustments
| Assumption | What it means | Practical adjustment when violated |
|---|---|---|
| Constant demand | Sales rate does not vary by season or trend | Use a rolling 12-month average; recalculate EOQ for peak and off-peak seasons |
| Constant lead time | Supplier always delivers in the same number of days | Add safety stock: z x (demand std dev) x sqrt(lead time) |
| Constant unit price | No quantity discounts apply | Compare total cost at each price-break quantity and choose the cheapest option |
| Instantaneous replenishment | Entire order arrives at once | Use the Economic Production Quantity (EPQ) model if goods arrive gradually over time |
| No stockouts allowed | You never run out between deliveries | Add a safety stock buffer on top of the ROP to achieve your desired service level |
| Only two variable costs | Only ordering and holding costs matter | Include shortage costs, spoilage, or insurance if they are significant |
The classic EOQ model rests on simplifying assumptions. Knowing when each breaks down helps you decide when to add safety stock or recalculate.
Frequently asked questions
What is the EOQ formula?
EOQ = sqrt(2 x D x S / H), where D is annual demand in units, S is the fixed cost to place one order, and H is the annual cost of holding one unit in inventory. The result is the order quantity that minimizes the sum of annual ordering and holding costs.
What does EOQ tell you in practice?
EOQ tells you the batch size that produces the lowest possible total inventory cost for the year. It implies a specific number of orders per year (annual demand divided by EOQ) and a specific order cycle (365 days divided by orders per year). Ordering more than the EOQ raises holding costs; ordering less raises ordering costs.
How do I calculate the Reorder Point (ROP)?
The basic Reorder Point is: ROP = (annual demand / 365) x lead time in days. This tells you the stock level at which to trigger the next order so it arrives just as you run out. Add safety stock on top to account for demand variability and late deliveries.
What is holding cost and how do I estimate it?
Holding cost (also called carrying cost) is the total annual cost of keeping one unit in stock. It includes warehouse rent, insurance, obsolescence risk, spoilage, and the opportunity cost of capital tied up in inventory. A common rule of thumb is to estimate holding cost as 20-30 percent of the unit purchase price per year, though it varies significantly by product type and industry.
What happens to EOQ if demand doubles?
If annual demand doubles, EOQ increases by a factor of sqrt(2), roughly 41 percent. This is because EOQ is proportional to the square root of demand. So a twofold increase in demand does not require twice as large an order - the optimal batch size grows more slowly than demand does.
Can I use EOQ when there are quantity discounts?
The basic EOQ model assumes a constant unit price. When discounts apply, calculate EOQ normally, then also calculate total annual cost (ordering cost plus holding cost plus purchase cost) at each price-break quantity. Choose whichever option gives the lowest total cost overall - sometimes the discount saves more than the extra holding cost incurred by buying a larger batch.
What is the difference between EOQ and EPQ?
EOQ assumes the entire order arrives as a single batch. The Economic Production Quantity (EPQ) model applies when goods arrive or are produced gradually over time - for example, a manufacturer receiving parts from a production line rather than a warehouse. EPQ accounts for inventory building up during the production run rather than all at once, which generally results in a larger optimal batch size than EOQ.