Economic Order Quantity Calculator - Optimize Inventory Costs

What Is Economic Order Quantity?

The Economic Order Quantity (EOQ) model is one of the earliest and most widely used formulas in inventory management. Developed more than a century ago, it provides a simple method for balancing the trade-off between ordering costs and holding costs. When a business places a new order, it incurs a fixed setup cost that includes paperwork, transportation and time spent handling the shipment. Holding goods in storage also carries a cost—warehousing, insurance and the opportunity cost of capital. The EOQ seeks the order size that minimizes the combined expense of replenishing inventory and keeping it on hand.

The EOQ Formula

The classic EOQ formula is elegantly short:

Q^* = \sqrt{\frac{2 D S}{H}}

Here $D$ is the total demand in units over the planning horizon—typically one year—$S$ is the fixed cost to place a single order and $H$ is the cost to hold one unit for the same period. The square root reveals diminishing returns: as you order more at once, the incremental savings in setup cost shrink, while holding cost grows. The EOQ represents the sweet spot where these costs are balanced.

Interpreting the Variables

Annual demand is often estimated from sales forecasts or historical data. Order setup cost may include purchasing department labor, supplier minimum charges and inbound shipping fees. Holding cost covers warehousing, insurance, depreciation and the capital tied up in stock. Many firms express holding cost as a percentage of the unit price—for instance, carrying inventory might cost 20 % of the item's value each year. Accurate estimates of these parameters are crucial for meaningful results.

Example Calculation

Suppose a retailer sells 10,000 units of a particular product each year. Placing an order costs $50 in administrative expense and inbound shipping. Holding one unit in stock for a year costs $2. Plugging these numbers into the equation gives:

Q^* = \sqrt{\frac{2 \times 10000 \times 50}{2}} = 707

The optimal order size is about 707 units. The business would place roughly 14 orders per year (D/Q*) and keep half the order, or about 354 units, on average in storage. This approach minimizes the total annual cost of ordering and holding inventory.

Cost Breakdown

The EOQ yields a total cost that is the sum of the annual ordering and holding expenses. The ordering cost equals $ D/Q^* \times S $. The holding cost equals $ Q^* / 2 \times H $. The table below shows how these costs compare for various order sizes around the optimal value from the previous example:

Order Quantity	Orders per Year	Ordering Cost	Holding Cost
500	20	$1,000	$500
707	14	$707	$707
900	11	$550	$900

The total cost is minimized near the middle row where ordering and holding expenses are equal. Ordering significantly more or less than the EOQ increases the combined cost of inventory.

Assumptions and Limitations

The EOQ model relies on several simplifying assumptions: demand is steady throughout the year, orders arrive all at once, and holding cost is proportional to the average inventory level. In reality, demand may fluctuate and suppliers might provide partial shipments. The model also assumes that stockouts never happen, so it's best applied when lead times are short and reliable. Nevertheless, the EOQ offers valuable insight into the trade-offs between large orders that tie up capital and small orders that require frequent replenishment.

Beyond the Basic Formula

Businesses often adapt the EOQ to account for quantity discounts, uncertain demand and other real-world factors. For instance, the total cost may include a per-unit purchase cost that decreases for larger orders, shifting the optimal quantity upward. Some organizations incorporate shortage costs or variable lead times. Advanced models still rely on the core EOQ concept but tweak the cost terms to fit specific circumstances.

Using the Calculator

Enter your estimated annual demand, the fixed cost of placing an order and the holding cost per unit per year. The calculator computes the EOQ, the expected number of orders, and the total cost assuming the basic model. Results appear instantly without any network connection, so you can iterate quickly and test different what-if scenarios. Use the Copy button to save the figures for your reports or spreadsheets.

Practical Tips

Updating your EOQ whenever costs or demand change can keep your inventory strategy on target. Many companies review it annually or quarterly. Watch for trends in customer orders or supplier pricing that might warrant a new calculation. Even if the exact assumptions are not met, EOQ still highlights the approximate scale of orders that minimize expenses. Combine this insight with your own business knowledge to set purchase quantities that balance risk, cash flow and storage space.

Conclusion

The Economic Order Quantity formula remains a foundational tool in operations management because of its simplicity and clear logic. By carefully estimating annual demand, ordering cost and holding cost, any business can use the EOQ to explore how different purchasing strategies affect total inventory expense. This calculator makes the math accessible in just a few clicks, offering a launching point for more sophisticated analysis if needed. With a grasp of EOQ, you can move one step closer to a leaner, more efficient supply chain.