Annual Economic Order Quantity Formula
Learn how annual economic order quantity is calculated from demand, order cost, and annual holding cost per unit.
The annual economic order quantity, or EOQ, estimates an order size that balances the cost of placing orders against the cost of carrying cycle inventory. It helps create a consistent starting point for inventory replenishment planning.
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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 units to order each time.
Variables Explained
| Variable | What It Means | Unit |
|---|---|---|
| EOQ - Economic order quantity | Estimated cost-balancing quantity to buy or replenish in each order. | units per order |
| D - Annual demand | Expected total number of units used or sold during one year. | units |
| S - Cost per order | Cost incurred whenever an order is placed, processed, received, and handled. | currency |
| H - Annual holding cost per unit | Annual cost of holding one unit in inventory. | currency |
Step-by-Step Calculation
Estimate annual demand
Use the expected number of units needed over the full year.
D = annualDemand
Identify the ordering cost
Include costs that arise each time an order is placed, such as processing, receiving, and delivery administration.
S = orderCost
Identify the unit holding cost
Use the annual carrying cost of one unit, not the total holding cost for all inventory.
H = annualHoldingCost
Calculate economic order quantity
This gives the order size where annual ordering and cycle-stock holding costs are equal under the basic EOQ model.
EOQ = sqrt((2 * D * S) / H)
Calculate order frequency
Divide annual demand by EOQ to estimate how many replenishment orders are needed per year.
ordersPerYear = D / EOQ
Calculate relevant annual cost
Add annual ordering cost and annual holding cost. Purchase cost is not included.
totalRelevantCost = (ordersPerYear * S) + ((EOQ / 2) * H)
Annual EOQ calculation for a stocked component
Calculate the EOQ expression
(2 × 10,000 × 50) ÷ 2
500,000
Calculate EOQ
sqrt(500,000)
707.11 units per order
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 per year
Calculate total relevant cost
$707.11 + (353.55 × $2)
$1,414.21 per year
Final Result
The estimated EOQ is 707 units per order, requiring about 14.14 orders per year and creating total relevant annual ordering and holding costs of about $1,414.21.
Assumptions
- ✓Annual demand is known, steady, and spread evenly through the year.
- ✓Orders arrive in full when needed, with no planned stockouts.
- ✓The cost per order stays constant regardless of order size.
- ✓The annual holding cost per unit remains constant.
- ✓Supplier unit prices do not change with order quantity.
Limitations
- !The calculation does not include safety stock, shortages, lead-time uncertainty, or seasonal demand.
- !Supplier minimum quantities, delivery schedules, storage limits, and pack sizes can make the exact EOQ impractical.
- !Quantity discounts can change the preferred order size because the standard formula excludes purchase cost.
- !Results depend on the quality of demand, ordering-cost, and holding-cost estimates.
Common Mistakes to Avoid
Entering monthly demand instead of annual demand without converting it to a yearly total.
Using the purchase price as the cost per order rather than the cost of placing and receiving one order.
Entering total annual warehouse cost instead of the annual holding cost for one unit.
Treating average inventory as EOQ rather than EOQ divided by 2.
Assuming EOQ is a reorder point; the reorder point also depends on demand during lead time and safety stock.
Related Formulas
Frequently Asked Questions
What is the annual EOQ formula?
The basic annual EOQ formula is EOQ = √((2 × annual demand × cost per order) ÷ annual holding cost per unit).
Why are ordering and holding costs equal at EOQ?
In the basic EOQ model, the minimum combined relevant cost occurs where annual ordering cost equals annual cycle-stock holding cost.
Does the EOQ formula include the inventory purchase price?
No. Standard EOQ excludes purchase price when the unit price is unchanged at every order quantity.
How is average inventory calculated from EOQ?
Average cycle inventory is EOQ ÷ 2 because stock is assumed to decline evenly from the received quantity to zero.
How do I calculate orders per year from EOQ?
Divide annual demand by the calculated EOQ.
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