EOQ Calculator: Economic Order Quantity Formula
Enter annual demand, the cost of placing one order and the cost of holding one unit for a year to find the order size that minimises total inventory cost. It answers how much to order; the reorder point calculator answers when to order.
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Formula
EOQ = √(2 × D × S ÷ H)Orders per year = D ÷ EOQDays between orders = 365 ÷ orders per yearAnnual cost = S × D ÷ EOQ + H × EOQ ÷ 2
D is annual demand, S the cost per order and H the holding cost per unit per year.
Worked example
D = 1,200, S = 50, H = 6.
- EOQ = √(2 × 1,200 × 50 ÷ 6) = √20,000 = 141.42 units.
- Orders per year = 1,200 ÷ 141.42 = 8.49.
- Days between orders = 365 ÷ 8.49 = 43.02.
- Annual cost = 50 × 1,200 ÷ 141.42 + 6 × 141.42 ÷ 2 = 424.26 + 424.26 = 848.53.
At the EOQ, ordering cost equals holding cost. The purchase price of goods is not included.
Another example
D = 5,000 units a year, S = 40 per order, H = 2.50 per unit per year.
- EOQ = √(2 × 5,000 × 40 ÷ 2.5) = √160,000 = 400 units.
- Orders per year = 5,000 ÷ 400 = 12.5, about every 29.2 days.
- Annual cost = 40 × 5,000 ÷ 400 + 2.5 × 400 ÷ 2 = 500 + 500 = 1,000.
When to use it
Use EOQ for items with steady demand, a stable order cost and a known holding cost, such as packaging, spare parts or staple stock. It is a poor fit for seasonal or one-off products.
Common mistakes
- Mixing time units, for example monthly demand with a yearly holding cost.
- Leaving out the cost of capital in holding cost.
- Rounding to a size the supplier cannot ship, such as full pallets or case packs.
- Treating the result as exact. Total cost is flat near the optimum.
How it differs
EOQ sets the order size. The reorder point calculator sets the stock level that triggers the order, adding safety stock for demand and lead-time variation. Inventory turnover measures the result in the accounts.
Frequently asked questions
What is the EOQ formula?
EOQ = √(2DS ÷ H), where D is annual demand, S is the cost of one order and H is the holding cost per unit per year. For D = 1,200, S = 50 and H = 6, EOQ = √20,000 = 141.4 units.
What is included in holding cost?
Storage space, insurance, capital tied up in stock, handling and the risk of spoilage or obsolescence, stated per unit per year. It is often estimated as a percentage of the unit cost, but here you enter the final amount.
How are orders per year and cycle time found?
Orders per year = D ÷ EOQ, so 1,200 ÷ 141.4 = 8.49. Days between orders = 365 ÷ 8.49 = 43.0 days.
What does the total annual cost cover?
It is ordering cost (S × D ÷ EOQ) plus holding cost (H × EOQ ÷ 2), here 424.26 + 424.26 = 848.53. It does not include the purchase price of the goods. The model assumes steady demand, a fixed order cost and no discounts or stock-outs.
What is the EOQ formula in Excel?
Use =SQRT(2*D*S/H), where D is annual demand, S is cost per order and H is holding cost per unit per year. With D of 5,000, S of 40 and H of 2.5, =SQRT(2*5000*40/2.5) gives 400. Orders per year is =D/EOQ, which is 12.5.
What is the difference between EOQ and the reorder point?
EOQ is how much to order each time; the reorder point is the stock level at which to place the order. With 50 units a day and a 7-day lead time you reorder at 350 units plus safety stock, whatever the order size is. You normally need both.
How accurate is EOQ if I cannot order the exact quantity?
The cost curve is flat near the optimum. Ordering 150 instead of 141.4 in the 1,200 unit example costs 50 × 1,200 ÷ 150 + 6 × 150 ÷ 2 = 400 + 450 = 850, only about 0.2% more than 848.53. EOQ assumes steady demand and no volume discounts.