Economic Order Quantity (Per-Unit) Formula
Learn how to calculate economic order quantity using annual demand, ordering cost, and annual holding cost per unit.
The economic order quantity, or EOQ, estimates an order size that balances the cost of placing orders with the cost of carrying inventory. It helps businesses model a practical replenishment quantity when demand, supplier pricing, and holding costs are reasonably stable.
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Economic Order Quantity
Where:
Multiply annual demand by the cost of placing one order, double that amount, divide by the annual holding cost for one unit, and take the square root.
Variables Explained
| Variable | What It Means | Unit |
|---|---|---|
| EOQ - Economic order quantity | The estimated order quantity that minimizes combined annual ordering and holding costs. | units |
| D - Annual demand | The estimated number of units required during one year. | units |
| S - Ordering cost per order | The total cost of placing, processing, receiving, and managing one order. | currency |
| H - Annual holding cost per unit | The annual cost of carrying one unit in inventory. | currency |
| C - Purchase cost per unit | The supplier price for one unit, used for total annual inventory cost when the unit price is constant. | currency |
| W - Working days per year | The number of working days used to estimate the interval between orders. | days |
Step-by-Step Calculation
Estimate annual demand
Use the number of units expected to be used, sold, or consumed over a full year.
annualDemand = D
Calculate the economic order quantity
This quantity balances the trade-off between ordering more often and holding more stock.
economicOrderQuantity = sqrt((2 * annualDemand * orderingCost) / holdingCostPerUnit)
Estimate orders per year
Divide yearly demand by the suggested order quantity.
ordersPerYear = annualDemand / economicOrderQuantity
Calculate average inventory
Under the basic EOQ model, stock falls evenly from the order quantity to zero, making average inventory half the order quantity.
averageInventory = economicOrderQuantity / 2
Calculate annual ordering and holding costs
These are the relevant costs that EOQ seeks to minimize.
totalRelevantInventoryCost = (ordersPerYear * orderingCost) + (averageInventory * holdingCostPerUnit)
Calculate total annual inventory cost
Add annual purchase cost when a complete annual inventory-cost estimate is needed.
totalAnnualInventoryCost = (annualDemand * unitPurchaseCost) + totalRelevantInventoryCost
Estimate the ordering interval
This estimates the average number of working days between orders when demand is even.
daysBetweenOrders = workingDaysPerYear / ordersPerYear
EOQ example for a regularly used component
Calculate EOQ
√((2 × 10,000 × 50) ÷ 2.50)
632.46 units
Calculate orders per year
10,000 ÷ 632.46
15.81 orders
Calculate average inventory
632.46 ÷ 2
316.23 units
Calculate annual ordering cost
15.81 × $50.00
$790.57
Calculate annual holding cost
316.23 × $2.50
$790.57
Calculate order interval
250 ÷ 15.81
15.81 working days
Calculate total annual inventory cost
(10,000 × $20.00) + $790.57 + $790.57
$201,581.14
Final Result
The estimated EOQ is 632 units. Annual ordering and holding cost is about $1,581.14, excluding purchase cost.
Assumptions
- ✓Annual demand is steady and known for the planning period.
- ✓Each replenishment order arrives in one delivery when inventory is needed.
- ✓The annual holding cost entered applies to each unit held in stock.
- ✓The supplier price per unit is constant, with no quantity discounts.
- ✓Inventory declines at a reasonably even rate between deliveries.
Limitations
- !Actual demand may fluctuate by season, customer order patterns, or production schedules.
- !The model does not include safety stock, stockout costs, uncertain lead times, or service-level targets.
- !Quantity discounts can change the best order quantity because they affect purchase cost.
- !Supplier minimums, pack sizes, storage capacity, and cash constraints may make the exact EOQ impractical.
- !Purchase cost is included in total annual cost but does not change basic EOQ when the unit price is constant.
Common Mistakes to Avoid
Entering a monthly holding cost instead of an annual holding cost per unit.
Using the purchase price as the holding cost without estimating carrying costs separately.
Including annual ordering costs rather than the cost of one order.
Treating the result as an exact required quantity instead of rounding for pack sizes and operating constraints.
Using calendar days when the order interval is intended to be based on working days.
Ignoring quantity discounts or supplier minimum order quantities.
Related Formulas
Frequently Asked Questions
What is the EOQ formula?
The basic EOQ formula is √((2 × annual demand × ordering cost per order) ÷ annual holding cost per unit).
Why are annual ordering and holding costs equal at EOQ?
In the standard EOQ model, the cost-minimizing point occurs where annual ordering cost and annual holding cost are approximately equal.
Does unit purchase cost affect economic order quantity?
Not in the basic model when the price per unit is constant. It affects total annual inventory cost, but not the EOQ calculation itself.
How is average inventory calculated in EOQ?
Average inventory is EOQ divided by two because the model assumes stock falls evenly from the delivery quantity to zero.
Should EOQ be rounded?
Usually, yes. Round to a practical whole-unit quantity that works with supplier pack sizes, storage space, and ordering procedures.
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