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Economic Order Quantity Calculator

Enter annual demand, cost per order, and annual holding cost per unit to find the EOQ.

How it is calculated

The tool finds the order size at which yearly ordering cost and yearly holding cost are equal, which is also where their sum is lowest. With annual demand D (units), cost per order S and holding cost per unit per year H, EOQ = √(2 × D × S ÷ H). It then calculates orders per year = D ÷ EOQ and total cost = orders × S + (EOQ ÷ 2) × H. The EOQ ÷ 2 is the average stock held, because stock falls from a full order to zero between deliveries. The total covers only ordering and holding cost, not the purchase price of the goods. An EOQ of 10 or more is shown as a whole number; a smaller one keeps a couple of decimals so it does not print as 0. The later figures use the unrounded EOQ. All three inputs must be above zero, otherwise there is no result. The model assumes steady demand and a constant cost per order.

Worked example

A shop sells 5,000 units a year. Each order costs $40 to place and holding one unit for a year costs $2.50. Then EOQ = √(2 × 5,000 × 40 ÷ 2.5) = √160,000 = 400 units. Orders per year are 5,000 ÷ 400 = 12.50. The ordering cost is 12.5 × 40 = $500 and the holding cost is (400 ÷ 2) × 2.5 = $500, so the total is $1,000.00. Ordering in lots of 200 would cost 25 × 40 + 100 × 2.5 = $1,250, which is higher.

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Common mistakes

  • Entering the holding cost as a percentage of price. The field wants a money amount per unit per year, so a unit that costs $20 with a 25% holding rate is entered as 5.
  • Using the holding cost per month or the demand per month. Demand and holding cost must both be annual.
  • Putting the purchase price into the cost per order. S is the fixed cost of placing and receiving one order, such as admin and freight, not the price of the goods.
  • Reading the total cost as the full cost of the stock. It leaves out the price of the units; add D × unit price to compare with your real spend.
  • Ignoring practical limits. Supplier minimums, pack sizes and discounts for large lots can make a different quantity cheaper than the EOQ.

Sources

About this calculator

The Economic Order Quantity (EOQ) is the classic inventory-management formula for the order size that minimizes total inventory cost — the balance point between ordering too often (racking up ordering costs) and ordering too much at once (racking up holding costs). It comes from the Wilson formula, EOQ = sqrt(2DS/H), where D is annual demand in units, S is the fixed cost to place one order, and H is the annual holding cost per unit.

Below the EOQ, a business pays too much in repeated ordering, shipping, and processing costs; above it, capital gets tied up in warehouse space, insurance, spoilage, and obsolescence risk. Retailers, manufacturers, and distributors use EOQ to set reorder quantities and estimate how many orders per year they'll place. Annual demand, the cost of placing an order and the yearly holding cost per unit go into √(2DS/H) to give the economic order quantity and how many orders a year that means.

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