Inventory EOQ (Economic Order Quantity) Calculator
Calculate the optimal order quantity that minimizes total ordering and holding costs. Estimate number of orders per year, cycle time, and reorder points using the classic EOQ formula.
Calculate an Optimal Economic Order Quantity
Enter demand, order cost, and holding cost to estimate the EOQ that balances ordering and carrying cost. You can also add lead time and safety stock for a simple reorder point calculation.
Tip: Start with annual demand and basic costs. You can add lead time and safety stock later to calculate when to reorder.
What the Economic Order Quantity Answers About Your Purchasing
Your warehouse manager orders 500 units every time stock runs low. But why 500? EOQ answers that question mathematically: it is the order quantity that minimises the sum of ordering costs and holding costs over a year. Order too often and you burn money on purchase orders, freight, and receiving labour. Order too rarely and you tie up cash in excess inventory that sits on shelves costing you storage, insurance, and obsolescence risk. The common mistake is setting order quantity by gut feel or supplier minimums without calculating whether those quantities actually minimise total cost.
The EOQ formula balances two forces: ordering cost per order (fixed, regardless of quantity) and holding cost per unit per year (proportional to how much you store). The sweet spot — the EOQ — is where the marginal cost of placing one more order equals the marginal cost of holding slightly more inventory.
Inputs That Change Total Inventory Cost
Annual demand (D). If demand doubles, EOQ increases — but only by a factor of √2 (about 41%), not 2×. The square-root relationship means EOQ grows slower than demand, which is why high-volume products do not need proportionally larger orders.
Ordering cost (S). This is the per-order fixed cost: purchase-order processing, freight, inspection, and receiving. If you automate purchasing (EDI, API-based reordering), S drops and EOQ drops with it, meaning you should order more frequently in smaller batches. Many companies ignore this lever entirely and keep ordering in large lots even after they have eliminated the manual cost of placing an order.
Holding cost (H). This includes warehouse rent, insurance, capital tied up, and expected shrinkage or obsolescence. H is often expressed as a percentage of unit cost (typically 15–30% per year). Under-estimating H leads to bloated EOQ and excess inventory; over-estimating it leads to too-frequent orders and higher freight spend.
EOQ, Cycle Time, and Reorder Frequency at a Glance
EOQ produces more than just a number of units. It implies a cycle time — how many days of demand each order covers — and a reorder frequency — how many orders you place per year.
If the cycle time is shorter than your supplier lead time, you need to place the next order before the current batch runs out. That is where the reorder point comes in — a separate calculation that accounts for lead-time demand.
Assumptions That Make EOQ Wrong in Practice
Constant demand. EOQ assumes demand is uniform across the year. If your product is seasonal (holiday gifts, winter coats), the model over-orders in the off-season and under-orders in the peak. Use period-specific EOQ or adjust D to the demand rate for each planning window.
No quantity discounts. If the supplier offers 10% off at 1,000 units and your EOQ says 600, the discount may more than offset the extra holding cost. Compare total cost at EOQ vs total cost at the discount break to see which wins. This is the most common reason EOQ is overridden in practice.
Instantaneous replenishment. The basic model assumes the entire order arrives at once. If you receive a production run gradually (as in a manufacturing environment), use the production order quantity (POQ) variant, which accounts for the production rate relative to the demand rate.
Edge Cases: Zero Ordering Cost, Perishables, and Lumpy Demand
Near-zero ordering cost. If S approaches zero (fully automated reordering with no freight cost per shipment), EOQ approaches zero too — meaning you should order as frequently as possible in tiny batches. This is the logic behind just-in-time (JIT) systems. In practice, there is always some minimum order cost, so the model produces a very small but nonzero EOQ.
Perishable goods. If the product expires in 30 days and EOQ says order 45 days’ worth, you will throw away unsold inventory. Cap EOQ at the shelf-life equivalent in units and accept that total cost will be higher than the theoretical minimum.
Lumpy or project-based demand. If demand comes in large, infrequent bursts (construction materials for specific jobs), EOQ’s smooth-demand assumption breaks down. Use lot-for-lot ordering or MRP-based planning instead of EOQ for these SKUs.
EOQ and Total Inventory Cost Equations
The core formulas for economic order quantity and associated costs:
Auto Parts Distributor EOQ: Full Worked Example
Scenario: A distributor sells 10,000 brake pads per year. Each purchase order costs $75 to process and ship. Unit cost is $12, and the holding cost rate is 25% of unit cost per year (H = $3.00/unit/year).
EOQ: √(2 × 10,000 × $75 / $3.00) = √500,000 = 707 units. Round to 710 for pallet compatibility.
Orders per year: 10,000 / 710 ≈ 14 orders. Cycle time: 710 / (10,000/365) ≈ 26 days between orders. Average inventory: 355 units at $12 = $4,260 in average stock.
Total cost at EOQ: Ordering = 14 × $75 = $1,050. Holding = 355 × $3.00 = $1,065. Total = $2,115/year. Compare to the current practice of ordering 2,000 at a time: ordering = 5 × $75 = $375, holding = 1,000 × $3.00 = $3,000, total = $3,375. Switching to EOQ saves $1,260/year on this single SKU.
Sources
Investopedia — Economic Order Quantity (EOQ): EOQ formula derivation, assumptions, and limitations for inventory management.
MIT OCW — Operations Management: EOQ model, production order quantity variant, and quantity discount extensions.
APICS — The ABCs of Inventory Management: Holding cost estimation, ABC classification, and practical EOQ implementation.
Harvard Business Review — Managing Inventories: Trade-offs between ordering frequency, holding cost, and service level in supply chain operations.
Frequently Asked Questions
What assumptions does the EOQ formula make?
The classic EOQ formula assumes: (1) Demand is constant and known, (2) Lead time is constant and known, (3) Replenishment is instantaneous (the entire order arrives at once), (4) There are no quantity discounts, (5) Only one product is considered, and (6) No shortages/stockouts are allowed. These assumptions simplify the math but may not reflect real-world complexity. Understanding these assumptions helps you see when EOQ is appropriate and when more sophisticated models are needed.
What happens if my demand is seasonal or uncertain?
If demand varies seasonally or is uncertain, the basic EOQ provides only a rough guideline. You might calculate EOQ using average demand as a starting point, but real inventory policy should account for demand variability through safety stock, periodic review systems, or more advanced models like (s, Q) or (R, S) policies that explicitly handle demand uncertainty. Understanding this helps you see when EOQ is sufficient and when advanced methods are required.
Should I always order exactly the EOQ?
Not necessarily. EOQ is a theoretical optimum under specific assumptions. In practice, you might adjust order quantities for: supplier minimum order quantities, package/pallet sizes, transportation constraints, cash flow timing, or quantity discounts. The total cost curve is relatively flat near the EOQ, so moderate deviations don't dramatically increase costs. Understanding this helps you see that EOQ is a guideline, not a rigid rule.
How do lead time and safety stock affect the reorder point?
Lead time determines how much inventory you consume while waiting for an order to arrive. Longer lead times require higher reorder points. Safety stock adds a buffer against uncertainty in demand or lead time. The simple formula is: ROP = (Daily Demand × Lead Time) + Safety Stock. This calculator uses a deterministic ROP; service-level-based safety stock calculations require knowing demand variability. Understanding this helps you see how to calculate reorder points and when to use safety stock.
Can I use this tool for multiple products or warehouses?
This calculator handles one product at a time. For multiple products, you would calculate EOQ for each item separately. However, real multi-item inventory systems may coordinate orders to reduce shipping costs or share setup costs. Multi-echelon (multiple warehouses) inventory is even more complex and requires specialized models. Understanding this helps you see when single-item EOQ is appropriate and when multi-item coordination is needed.
What if my supplier offers quantity discounts?
Quantity discounts change the optimization problem. You need to compare the total annual cost (ordering + holding + purchasing) at each price break quantity and at the EOQ calculated for each price level. The optimal order quantity might be at a discount break point even if it's not the classic EOQ. This calculator doesn't model quantity discounts. Understanding this helps you see when quantity discounts affect order quantity decisions and why EOQ alone may not be optimal.
How do I estimate holding cost if I don't know it directly?
A common approach is to estimate holding cost as a percentage of the unit cost (carrying rate). Typical annual carrying rates range from 15% to 35% of unit cost, including: cost of capital (opportunity cost of money tied up in inventory), storage space costs, insurance, taxes, obsolescence risk, and handling costs. This calculator supports both direct holding cost input and the percentage-of-unit-cost method. Understanding this helps you estimate holding cost when direct values aren't available.
Why does ordering cost plus holding cost equal total cost at EOQ?
At the EOQ, annual ordering cost exactly equals annual holding cost. This is a mathematical property of the EOQ formula. The total cost curve is U-shaped: below EOQ, ordering cost dominates (too many small orders); above EOQ, holding cost dominates (too much inventory). The minimum occurs where these two costs are balanced. Understanding this helps you see why EOQ minimizes total cost and why the cost curve has this shape.
Is EOQ still relevant in modern supply chains?
Yes, but with caveats. EOQ provides foundational intuition about inventory trade-offs and is still taught in operations courses. Modern supply chains often use more sophisticated methods that account for demand forecasting, variability, service levels, and integrated planning. However, EOQ remains a useful starting point and sanity check for inventory decisions. Understanding this helps you see when EOQ is appropriate and when advanced methods are needed.
How sensitive is EOQ to input errors?
EOQ is moderately robust to input errors because the square root function dampens the effect of errors. For example, if you overestimate demand by 50%, EOQ increases by only about 22%. Similarly, errors in cost estimates have a dampened effect. This means rough estimates are often good enough for practical EOQ calculations. Understanding this helps you see that EOQ is forgiving of estimation errors and why it's practical for real-world use.
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