Economic order quantity (EOQ): formula, calculator and worked example
EOQ finds the order size that minimises ordering plus holding cost. See the formula, a worked example, when it works, when it does not, and how to round to MOQs and cases.
Stokrio Team · · 6 min read
Economic order quantity, or EOQ, is the order size that gives the lowest total of two costs that pull in opposite directions: the cost of placing orders and the cost of holding stock. Order small and often, and you pay for lots of orders. Order big and rarely, and you pay to store and tie up cash in stock.
Key takeaways
- EOQ = √(2 × annual demand × cost per order ÷ holding cost per unit per year).
- At the EOQ, annual ordering cost equals annual holding cost.
- It assumes steady demand and a fixed price, so treat it as a guide, not an order.
- Round the answer to your supplier's MOQ and case pack.
The formula
EOQ = √( 2 × D × S ÷ H )- D is annual demand in units.
- S is the cost to place one order (admin, freight booking, receiving).
- H is the holding cost per unit per year, often 15–30% of unit cost.
Worked example
Annual demand is 12,000 units. Placing an order costs $90. Unit cost is $12 and holding cost is 20% of that, so H = $2.40.
- EOQ = √(2 × 12,000 × 90 ÷ 2.40) = √900,000 ≈ 949 units
- Orders per year: 12,000 ÷ 949 ≈ 12.6, or one every 29 days
- Ordering cost: 12.6 × $90 ≈ $1,138. Holding cost: 949 ÷ 2 × $2.40 ≈ $1,139
The two costs match, as they should. Change the inputs in the EOQ calculator.
Why the answer is forgiving
Total cost is flat near the minimum, so ordering 800 or 1,100 units costs little more than 949. That is useful because real orders must be rounded to a case pack, a pallet or a container, and to the supplier's MOQ.
When EOQ does not fit
- Seasonal or trending demand. The formula assumes a steady rate. Plan by period from a forecast instead.
- Volume discounts. A price break can justify ordering above EOQ; compare total cost including the discount.
- Perishable or dated stock. Shelf life caps how much you can safely hold.
- Cash constraints. If cash is the limit, open-to-buy decides, not EOQ.
- Long lead times. EOQ says how much, not when. You still need a reorder point.
Getting the inputs right
Include in the order cost only what changes with the number of orders. Include in holding cost only what changes with the stock level. Mixing in fixed warehouse rent makes the holding cost too high and the EOQ too small.
How Stokrio handles it
Stokrio suggests order quantities from the forecast, cover to the next delivery and your supplier terms, rounded to MOQ and case packs, and drafts the purchase order. See replenishment and purchase orders.