EOQ Formula: How to Calculate Economic Order Quantity (With Examples)

The Economic Order Quantity (EOQ) formula answers a question every purchasing and inventory manager faces: how much should we order at a time? Order too much and you’re tying up capital in excess stock, paying for storage, and risking obsolescence. Order too little and you’re placing orders constantly, paying higher per-unit costs, and risking stockouts.

EOQ calculates the order quantity that minimizes the sum of ordering costs and holding costs — the sweet spot where total inventory cost is lowest.

The EOQ Formula

The classic EOQ formula is:

EOQ = √(2DS / H)

Where:

• D = Annual demand (units per year)
• S = Ordering cost per order (fixed cost to place one order)
• H = Holding cost per unit per year (storage, insurance, opportunity cost, obsolescence)

The result is the quantity to order each time you place a replenishment order that minimizes your total annual inventory cost.

Step-by-Step Calculation

Example: A distributor sells 12,000 units per year of a product. Each purchase order costs $100 to process (staff time, shipping coordination, admin). The holding cost is $5 per unit per year (warehouse space, insurance, capital tied up).

Plugging in:

• D = 12,000 units
• S = $100
• H = $5

EOQ = √(2 × 12,000 × 100 / 5) EOQ = √(2,400,000 / 5) EOQ = √480,000 EOQ = 693 units

This means placing orders of approximately 693 units minimizes total inventory cost. With annual demand of 12,000 units, you’d place roughly 17-18 orders per year (12,000 / 693 ≈ 17.3).

Order Cycle Time and Reorder Frequency

Once you have the EOQ, you can calculate:

Number of orders per year = D / EOQ = 12,000 / 693 ≈ 17 orders

Order cycle time = EOQ / D × 365 = 693 / 12,000 × 365 ≈ 21 days

So in this example, you’d place an order every 21 days on average to maintain the optimal order size.

How to Determine Each Input

Annual demand (D): Use historical sales data, adjusted for seasonality and expected growth. For new products, use market estimates or comparable product data. Demand should reflect actual consumption, not purchase orders placed (which may include safety stock top-ups that distort the calculation).

Ordering cost (S): This is the total fixed cost to place a single order, regardless of quantity. Include: staff time to process the PO (hours × hourly cost), shipping coordination cost, receiving and inspection cost, and any fixed supplier setup fees. Do not include variable costs that scale with quantity — those are captured in the holding cost. Many companies underestimate ordering cost because they exclude staff time.

Holding cost (H): The annual cost to store one unit. Components:

• Capital cost: If inventory is financed, use the interest rate applied to the unit cost. If self-funded, use your weighted average cost of capital (WACC) applied to unit cost — typically 10-20%.
• Storage cost: Warehouse space cost per square foot / cubic foot, allocated per unit stored.
• Insurance: Annual insurance premium allocated per unit.
• Obsolescence/spoilage risk: For perishables or fast-moving consumer goods, the estimated percentage of inventory that goes bad or obsolete, applied as an annual rate.
• Shrinkage: Theft, damage, and administrative error rate, applied as a cost.

Holding cost is often expressed as a percentage of unit cost (e.g., 20-30% of unit purchase price per year) to make it easier to apply across a product catalog with varying unit prices.

EOQ with Quantity Discounts

The standard EOQ formula assumes a constant unit cost. When suppliers offer quantity discounts — lower per-unit price for larger order quantities — you need to evaluate whether the discount justifies ordering more than the EOQ suggests.

Process:

1. Calculate EOQ using the base price
2. For each discount tier, calculate the total annual cost at that order quantity (ordering cost + holding cost + purchase cost)
3. Choose the order quantity with the lowest total annual cost

In some cases, a quantity discount is substantial enough that ordering more than the EOQ — and accepting higher holding costs — reduces total annual cost due to purchase price savings. This analysis is straightforward to run in a spreadsheet.

EOQ Assumptions and When They Break Down

The EOQ formula rests on several assumptions that frequently don’t hold in real supply chains:

Constant demand. EOQ assumes steady, uniform demand throughout the year. Seasonal businesses, promotional spikes, and event-driven demand make this assumption fail. If your product has significant demand variability, EOQ gives you a reasonable starting point but not an accurate optimal — safety stock calculations account for the variability EOQ ignores.

Constant ordering cost. EOQ assumes each order costs the same to place. In practice, ordering from multiple suppliers, coordinating complex freight arrangements, or managing import documentation creates variable ordering costs that the formula doesn’t capture.

Instantaneous replenishment. EOQ assumes inventory arrives all at once. When inventory arrives continuously (production runs, daily deliveries), the Economic Production Quantity (EPQ) model is more appropriate.

No stockouts permitted. The classical EOQ model treats stockouts as unacceptable. If your business tolerates planned stockouts (backorders, lost sales accepted), modified EOQ models exist that incorporate stockout costs.

Single product. EOQ optimizes one SKU in isolation. When you’re ordering multiple products from the same supplier, ordering frequency constraints, minimum order values, and joint ordering economics affect optimal order quantities in ways EOQ doesn’t address.

EOQ in Practice: What Actually Matters

Running the EOQ formula gives you a number. Using it effectively requires judgment:

Round to supplier minimums and standard pack sizes. If EOQ says 693 units but your supplier’s minimum order is 500 and they sell in cases of 50, your practical order quantity is the nearest standard size — probably 700 (14 cases of 50) or 650 (13 cases of 50).

Recalculate when inputs change. EOQ is not a set-it-and-forget-it number. When demand changes significantly, when freight costs spike (as they did repeatedly post-2020), or when warehouse costs change, the optimal order quantity changes. Build EOQ recalculation into your quarterly inventory review.

Combine with reorder point calculations. EOQ tells you how much to order. The reorder point formula tells you when to order. Running both together gives you a complete replenishment policy: reorder when inventory falls to the reorder point, in the EOQ quantity.

EOQ is a starting point, not an answer. For ABC inventory classification, EOQ makes most sense for B and C items — high-volume, consistent movers where optimization delivers consistent savings. For A items with high variability and high cost, more sophisticated demand-driven planning is warranted.

EOQ vs. Other Inventory Policies

EOQ vs. Fixed period ordering: EOQ orders a fixed quantity at variable intervals. Fixed period ordering orders variable quantities at fixed intervals (e.g., every Monday). EOQ typically performs better when ordering costs are high and demand is stable. Fixed period ordering is simpler to manage when supplier lead times require regular scheduling.

EOQ vs. Min-max: Min-max sets minimum and maximum stock levels and orders up to the max when stock hits the min. It’s simpler to set up than EOQ but less mathematically optimal. For operations with limited analytical resources, min-max is often the pragmatic choice.

EOQ vs. demand-driven MRP: For complex manufacturing environments with dependent demand (component parts driven by finished goods demand), demand-driven MRP is more appropriate than EOQ. EOQ is best suited for independent demand items — finished goods or direct materials purchased for resale.

Calculating Total Inventory Cost

The total annual inventory cost at EOQ is:

Total cost = (D/Q × S) + (Q/2 × H)

Where Q is the order quantity. At EOQ, ordering cost and holding cost are equal — that’s the mathematical property that defines the minimum.

Using our example (D=12,000, S=$100, H=$5, EOQ=693):

• Ordering cost: 12,000 / 693 × $100 = $1,732
• Holding cost: 693 / 2 × $5 = $1,733
• Total: ~$3,465/year

Compare this to ordering 1,000 units at a time:

• Ordering cost: 12,000 / 1,000 × $100 = $1,200
• Holding cost: 1,000 / 2 × $5 = $2,500
• Total: $3,700/year — 7% higher than EOQ

The difference grows with larger deviations from EOQ. The model is relatively robust to small deviations (orders 10-15% off EOQ cost less than 1% more than optimal), which is why rounding to practical order sizes rarely causes significant cost impact.

EOQ in Excel

EOQ is straightforward to implement in a spreadsheet:

=SQRT(2*D2*S2/H2)

Where D2, S2, and H2 are your demand, ordering cost, and holding cost inputs. Adding a table with multiple order quantity scenarios and calculating total cost for each makes it easy to visualize the cost curve around EOQ.

For multi-SKU applications, run EOQ for each SKU with its specific demand, ordering cost, and holding cost inputs. The holding cost (H) can be expressed as a percentage of unit cost to simplify multi-SKU calculations — if holding cost is 25% of unit cost per year, H = 0.25 × unit cost.

EOQ for Perishables and Products with Short Shelf Life

The standard EOQ model assumes inventory has no time-dependent expiration. For perishables — food, pharmaceuticals, certain chemicals — the holding cost calculation must include the cost of spoilage or obsolescence at the actual rate your product experiences.

If 3% of inventory spoils per month before use, that spoilage cost is a real component of holding cost:

• Annual spoilage rate: 3% × 12 = 36%
• Applied to a unit cost of $10: spoilage cost = $3.60/unit/year added to H

This materially increases holding cost, which decreases EOQ — smaller, more frequent orders that minimize spoilage risk. For high-spoilage products, the mathematical EOQ may point toward order frequencies (daily or weekly) that align with natural replenishment cadences.

EOQ and Supplier Lead Time

The EOQ formula tells you how much to order but says nothing about when to order. That’s the reorder point, which accounts for supplier lead time and demand during that lead time.

The two decisions — order quantity (EOQ) and reorder timing (reorder point) — work together to define a complete replenishment policy:

• Reorder when: Inventory falls to the reorder point (average demand × lead time + safety stock)
• Order how much: EOQ quantity

This policy is called a (Q, R) inventory model — order quantity Q when inventory hits reorder point R. It’s the practical implementation of EOQ in a real supply chain with non-zero lead times.

Bottom Line

EOQ is one of the most practical formulas in inventory management — simple to calculate, intuitive in concept, and directly actionable. It works best for products with relatively stable, predictable demand where the inputs (ordering cost, holding cost) can be reasonably estimated.

Its limitations are real: it doesn’t handle demand variability (use safety stock calculations for that), quantity discounts require modified analysis, and supplier constraints often override the mathematical optimum.

For most B and C inventory items, running EOQ once, validating the inputs, and reviewing quarterly gives you significantly better replenishment economics than intuition-based ordering — without the complexity of enterprise planning systems. For A items with high value and high variability, pair EOQ with safety stock analysis and monitor closely.