Economic Order Quantity (EOQ): Formula, Examples & Calculator

The economic order quantity (EOQ) is one of the most practical formulas in manufacturing inventory management. EOQ calculates the optimal order quantity that minimizes the total cost of ordering and holding inventory — answering the fundamental purchasing question: "How much should we order at a time?" Despite being over 100 years old, the EOQ formula remains relevant because the trade-off it solves — balancing setup costs against carrying costs — is still real in every manufacturing operation.

This guide covers the EOQ formula, step-by-step calculation examples, real-world applications, and honest guidance on when EOQ works well and when you should use alternative approaches. If you are configuring MRP lot sizing methods, EOQ is one of the most important options to understand.

The EOQ Formula Explained

The economic order quantity formula was developed by Ford W. Harris in 1913 and refined by R.H. Wilson in 1934. The formula is:

EOQ = sqrt(2DS / H)

Where:

• D = Annual demand (units per year)
• S = Ordering cost per order (also called setup cost)
• H = Annual holding cost per unit

The formula finds the order quantity where the total annual cost of ordering plus the total annual cost of holding inventory is minimized.

Why the Formula Works

The insight behind EOQ is that ordering cost and holding cost move in opposite directions as order quantity changes:

• Ordering cost decreases as order quantity increases — fewer orders means fewer order processing costs per year
• Holding cost increases as order quantity increases — larger orders mean more average inventory sitting in the warehouse

At some point, these two costs cross. The EOQ is the quantity where total cost is at its minimum — the sweet spot where you are not ordering too frequently (high ordering cost) or carrying too much inventory (high holding cost).

Total Cost Formula

The total annual inventory cost at any order quantity Q is:

Total Cost = (D/Q) x S + (Q/2) x H

Where:

• (D/Q) x S = Annual ordering cost (number of orders per year times cost per order)
• (Q/2) x H = Annual holding cost (average inventory times holding cost per unit)

At the EOQ, these two components are equal. This is a useful check — if your annual ordering cost and annual holding cost are roughly equal, you are ordering near the optimal quantity.

Step-by-Step EOQ Calculation Examples

Example 1: Purchased Component

A manufacturer purchases steel brackets from a supplier. Here are the parameters:

• Annual demand (D): 12,000 brackets per year
• Ordering cost (S): $75 per purchase order (includes PO processing, receiving, inspection, and AP processing)
• Unit cost: $8.50 per bracket
• Annual holding rate: 25% of unit cost
• Holding cost (H): $8.50 x 0.25 = $2.125 per bracket per year

EOQ = sqrt(2 x 12,000 x $75 / $2.125)

EOQ = sqrt(1,800,000 / 2.125)

EOQ = sqrt(847,059)

EOQ = 920 brackets

This means the manufacturer should order approximately 920 brackets at a time.

Verification: At Q = 920:

• Number of orders per year: 12,000 / 920 = 13.0 orders
• Annual ordering cost: 13.0 x $75 = $978
• Average inventory: 920 / 2 = 460 units
• Annual holding cost: 460 x $2.125 = $978
• Total cost: $978 + $978 = $1,956 per year

Notice that ordering cost equals holding cost — confirming we are at the EOQ.

Example 2: Manufactured Item

A job shop produces custom gear housings. The setup cost for the CNC lathe is significant:

• Annual demand (D): 2,400 units per year
• Setup cost (S): $450 per changeover (includes setup labor, test pieces, and lost production time)
• Unit manufacturing cost: $65 per unit
• Annual holding rate: 22%
• Holding cost (H): $65 x 0.22 = $14.30 per unit per year

EOQ = sqrt(2 x 2,400 x $450 / $14.30)

EOQ = sqrt(2,160,000 / 14.30)

EOQ = sqrt(151,049)

EOQ = 389 units

With an EOQ of 389 units, the manufacturer would run this part approximately 6 times per year (2,400 / 389 = 6.2 production runs).

Comparison with current practice: If the manufacturer currently runs batches of 200 units (12 runs per year):

• Current total cost: (12 x $450) + (100 x $14.30) = $5,400 + $1,430 = $6,830
• EOQ total cost: (6.2 x $450) + (194.5 x $14.30) = $2,790 + $2,781 = $5,571
• Annual savings: $1,259 by switching to EOQ-based batch sizing

This is the practical value of EOQ — quantifying how much money suboptimal batch sizes cost. Understanding changeover time reduction helps reduce the setup cost component, which in turn reduces the EOQ and enables smaller batches.

Example 3: The Effect of Setup Reduction

Using the same gear housing from Example 2, suppose a SMED initiative reduces setup cost from $450 to $150:

New EOQ = sqrt(2 x 2,400 x $150 / $14.30)

New EOQ = sqrt(720,000 / 14.30)

New EOQ = sqrt(50,350)

New EOQ = 224 units

The setup reduction cut the EOQ from 389 to 224 units — a 42% reduction in batch size. This means:

• More frequent production runs (10.7 per year vs 6.2)
• Lower average inventory (112 units vs 194.5 units)
• Faster response to demand changes
• Less cash tied up in inventory

This example illustrates why lean manufacturing focuses so heavily on setup reduction. Smaller batches are not just a philosophical preference — they are the mathematical result of lower setup costs.

EOQ Input Parameters: Getting the Numbers Right

The EOQ calculation is only as good as its inputs. Here is how to determine each parameter accurately.

Determining Annual Demand (D)

For purchased items, use the past 12 months of actual consumption, adjusted for known demand changes (new products, lost customers, seasonal patterns). For manufactured items, use the past 12 months of production volume for that part number.

Avoid using forecast data unless actual history is unavailable. Forecasts are opinions; consumption history is fact. If demand is growing or declining, use the trailing 12-month figure adjusted for the trend.

Calculating Ordering Cost (S)

For purchased items, ordering cost includes:

• Buyer time to create and manage the purchase order
• Receiving labor to process the shipment
• Incoming inspection cost (if applicable)
• Freight cost per shipment (if fixed per delivery)
• Accounts payable processing cost

A common shortcut: divide your total purchasing department annual cost by the total number of purchase orders processed per year. This gives a reasonable average ordering cost.

For manufactured items, ordering cost is setup cost:

• Setup labor time x labor rate
• Lost production time during changeover
• Test pieces and scrap during startup
• Tooling changeover costs

Calculating Holding Cost (H)

Holding cost is typically expressed as a percentage of the item's unit cost, multiplied by that unit cost. The percentage includes:

Most manufacturers use 20-25% as a default holding rate. Refine this by calculating your actual warehousing, insurance, and obsolescence costs. The opportunity cost of capital — what you could earn by investing the money elsewhere — is often the largest component and varies with interest rates and your company's cost of capital.

When EOQ Works Best

EOQ is most effective when:

• Demand is relatively stable: The annual demand figure is meaningful, not wildly variable month to month
• Ordering and holding costs are known: You have reasonable estimates of both cost components
• Items are not perishable: Shelf life is not a constraint
• Storage space is adequate: You can physically store the EOQ quantity
• Supplier minimums are compatible: The EOQ is above the supplier's minimum order quantity

For items with stable demand that you purchase or produce repeatedly, EOQ provides a solid, mathematically defensible ordering quantity that is better than any rule of thumb.

When to Use Alternatives

EOQ is not the right choice for every item. Consider these alternatives:

Lot-for-Lot

Order exactly what is needed for each period. Best for expensive items with variable demand where holding cost dominates. Common for custom or make-to-order components. Learn more about this and other methods in our MRP lot sizing guide.

Period Order Quantity (POQ)

Combine requirements over a fixed time period. POQ adapts to demand variability better than EOQ because it adjusts order quantity based on actual demand in each period rather than using a fixed quantity.

Quantity Discount Adjustments

When suppliers offer quantity discounts, the standard EOQ calculation may not apply. You need to compare the total cost (ordering + holding + material cost) at each discount break point to find the true optimal quantity. The calculation becomes:

Total Cost = (D/Q) x S + (Q/2) x H + D x C

Where C is the unit cost at each quantity level. Sometimes ordering more than EOQ saves money because the unit price reduction outweighs the extra holding cost.

EOQ in MRP Systems

Within MRP, EOQ functions as a lot sizing rule. When MRP calculates a net requirement for an item configured with EOQ lot sizing, it rounds the requirement up to the nearest EOQ multiple.

For example, if the EOQ is 920 brackets and MRP calculates a net requirement of 200 brackets, it generates a planned order for 920 brackets. If the net requirement is 1,050 brackets, it generates a planned order for 1,840 brackets (2 x 920).

Configure EOQ in your MRP system for purchased items with stable demand and moderate value. Use lot-for-lot for expensive items and items with variable demand. Use fixed order quantity when supplier minimums or packaging constraints dictate the order size. This item-by-item configuration is what makes MRP purchasing effective — the right lot sizing method for each material's characteristics.

FAQ

Optimize Your Inventory with the Right Lot Sizing

EOQ is just one piece of the inventory optimization puzzle. Contact User Solutions to see how RMDB integrates finite capacity scheduling with MRP lot sizing to minimize inventory while protecting production from stockouts.