Accounting Economic Order Quantity Formula
Learn how the economic order quantity formula estimates an order size that balances annual ordering and holding costs.
The Economic Order Quantity (EOQ) model estimates a replenishment quantity that minimizes the combined annual cost of placing orders and holding inventory. It is useful for building a baseline inventory plan when demand, ordering cost, and holding cost are reasonably stable.
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Economic Order Quantity
Where:
Multiply annual demand by the cost per order and by 2, divide by the annual holding cost per unit, then take the square root. The result is the estimated order quantity that balances ordering and holding costs.
Variables Explained
| Variable | What It Means | Unit |
|---|---|---|
| EOQ - Economic order quantity | Estimated number of units to order in each replenishment order. | units |
| D - Annual demand | Expected number of units used or sold during one year. | units |
| S - Cost per order | Cost incurred each time an order is placed, processed, received, and handled. | currency |
| H - Annual holding cost per unit | Estimated annual cost of holding one unit of inventory. | currency |
| C - Unit purchase cost | Purchase or production cost of one unit, used when estimating total annual inventory cost. | currency |
Step-by-Step Calculation
Estimate annual demand
Use the expected number of units required over a full year.
D = annualDemand
Identify the cost of one order
Include order-specific administration, receiving, processing, and delivery costs where applicable.
S = orderingCost
Identify the annual holding cost
Use the yearly cost of carrying one unit in stock, including relevant storage and capital-related costs.
H = annualHoldingCost
Calculate the economic order quantity
This calculates the order size that balances estimated annual ordering cost with annual holding cost.
economicOrderQuantity = sqrt((2 * annualDemand * orderingCost) / annualHoldingCost)
Calculate order frequency
Divide annual demand by the EOQ to estimate the number of replenishment orders per year.
ordersPerYear = annualDemand / economicOrderQuantity
Calculate relevant inventory cost
Relevant inventory cost is the combined annual ordering and holding cost, excluding purchase cost.
relevantInventoryCost = (ordersPerYear * orderingCost) + ((economicOrderQuantity / 2) * annualHoldingCost)
Calculate total annual inventory cost
Add annual purchase cost to ordering and holding cost to show the estimated total inventory-related cost.
totalAnnualInventoryCost = (annualDemand * unitPurchaseCost) + relevantInventoryCost
EOQ calculation for a regularly used product
Calculate EOQ
√((2 × 10,000 × 50) / 2)
707.11 units
Calculate orders per year
10,000 / 707.11
14.14 orders
Calculate average inventory
707.11 / 2
353.55 units
Calculate annual ordering cost
14.14 × $50
$707.11
Calculate annual holding cost
353.55 × $2
$707.11
Calculate total annual inventory cost
(10,000 × $20) + $707.11 + $707.11
$201,414.21
Final Result
The EOQ is about 707 units per order. Estimated annual ordering and holding costs are $1,414.21, and total annual inventory cost is $201,414.21.
Assumptions
- ✓Annual demand is steady and known for the period being analyzed.
- ✓Each replenishment order arrives in full when needed, without stockouts or delivery delays.
- ✓Ordering cost and annual holding cost per unit remain constant.
- ✓The unit purchase cost does not change with order quantity.
- ✓Inventory declines evenly from the order quantity to zero between deliveries.
Limitations
- !Demand may be seasonal, uncertain, or affected by changing customer behavior.
- !The standard EOQ model does not calculate safety stock or reorder points.
- !Supplier minimums, capacity limits, delivery schedules, and storage constraints can make the calculated quantity impractical.
- !Quantity discounts and changing unit prices require a separate comparison of total costs.
- !Results are planning estimates, not accounting, financial, or business advice.
Common Mistakes to Avoid
Entering monthly demand instead of annual demand without converting it to a yearly figure.
Using the full shipping cost when only part of it changes per order.
Leaving out storage, insurance, obsolescence, or capital costs from the holding-cost estimate.
Treating EOQ as a reorder point; EOQ is an order size, while a reorder point also depends on lead time and safety stock.
Rounding the EOQ without checking supplier pack sizes, minimum order quantities, and available storage.
Assuming the calculated quantity accounts for quantity discounts when unit prices vary by order size.
Related Formulas
Frequently Asked Questions
What is the EOQ formula?
The standard EOQ formula is EOQ = √((2 × annual demand × cost per order) / annual holding cost per unit).
Why do ordering and holding costs match at EOQ?
The formula identifies the balance point where the estimated annual cost of frequent ordering equals the estimated annual cost of carrying larger average inventory.
Does unit purchase cost affect the basic EOQ result?
No. When the unit price is constant, it does not change the basic EOQ. It is included to estimate total annual inventory cost.
How do I calculate orders per year from EOQ?
Divide annual demand by the calculated economic order quantity.
Can EOQ be rounded to a whole number?
Yes. Orders normally use whole units, pack sizes, or supplier minimums, so the calculated result can be rounded and then reviewed against practical constraints.
What is the difference between EOQ and average inventory?
EOQ is the quantity ordered each time. Average inventory under the basic model is EOQ divided by 2.
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