Economic Order Quantity (EOQ) Calculator

Ordering stock involves two costs that pull in opposite directions. Each order costs something to place and receive, so many small orders add up. Each unit held in the stockroom also costs something, in storage, insurance and the money it ties up, so a few large orders add up too. The economic order quantity is the size at which the two balance and the total is smallest. It dates from 1913 and remains a standard exercise in operations management.

The formula

EOQ = √(2 × D × S ÷ H), where D is the yearly demand in units, S the cost of placing one order and H the cost of holding one unit for a year. The page also shows orders per year, which is D ÷ EOQ, and the days between orders, which is the number of days you operate divided by that. At the EOQ the yearly ordering cost D ÷ Q × S and the yearly holding cost Q ÷ 2 × H come out equal.

Entering the holding cost

You can type an amount per unit per year, or choose a percentage of the unit cost and type the cost. With 20% and a unit cost of 18, the holding cost is 3.60. If you also enter the unit cost in the amount mode, the page shows the yearly cost of the goods themselves, which does not change with the order size under this model. Optionally, enter the order size you use now to see how much it costs against the EOQ.

A worked example

The default is a product with a yearly demand of 12,000 units, an order cost of 50 and a holding cost of 2.40 a unit. EOQ is 707 units (707.11 before rounding), or 16.97 orders a year, one every 21.5 days. Ordering costs 848.53 a year and holding costs 848.53, so the total is 1,697.06. The table shows how flat the curve is: at 530 units, three-quarters of the EOQ, the total is 1,767.77; at 354, half, it is 2,121.32; and at 1,414, double, it is also 2,121.32. The second sample has a demand of 4,800, an order cost of 85 and a holding cost of 20% of an 18 unit cost. The EOQ is 476 units, 10.08 orders a year and 36.2 days apart, for a total of 1,713.94, with goods costing 86,400. If you ordered 1,000 at a time instead, the cost would be 2,208.00, which is 494.06 more.

Why the answer is forgiving

Because of the square root, an order size 20% away from the EOQ raises the total by only a couple of percent, while doubling or halving it raises it by about a quarter. That is good news in practice: you can round to a full pallet, a case size or a supplier’s minimum without losing much, and you can use rough estimates for S and H.

Edge cases

Yearly demand and the holding cost must be above zero, and the order cost zero or more. With a zero order cost the EOQ is zero, which just means that ordering is free and you should order as often as you like. In percentage mode the unit cost must be above zero. The days in the year can be changed from 365 if you trade fewer days.

Limits

The model assumes steady demand, instant replenishment, a fixed cost per order, a constant holding cost, and no quantity discounts, shortages or price changes. Suppliers who give a lower price for larger orders can make a bigger order cheaper overall, and you would compare the totals, goods included, at each price break. Shelf life, storage space and cash flow can also override the formula.

Related tools

• Inventory Reorder Point and Safety Stock Calculator says when to order, where this page says how much.
• Inventory Turnover and Sell-Through Rate Calculator measures how quickly the stock turns over once you order in the right size.
• Bill of Materials (BOM) Cost Calculator works out the unit cost that feeds the holding percentage.
• Wholesale vs Retail Tiered Pricing Calculator shows how a supplier’s quantity breaks affect the price you pay.