Economic order quantity:
formula and worked example

The order size where two costs meet

Every replenishment order carries a fixed cost, such as raising the purchase order, receiving and inspection or freight. Every unit held costs money for as long as it sits there. Large, rare orders save on the first and inflate the second; small, frequent orders do the reverse. Economic order quantity is the order size that minimises the combined annual cost.

It rests on simple assumptions: demand is steady and known, the cost to place an order is the same whatever the size, and holding cost per unit per year is constant. Those conditions are rarely perfect, but the result is a dependable starting point and, as shown below, quite forgiving of small errors.

In practice EOQ is less about hitting an exact number and more about avoiding the two common habits: ordering by gut feel in small, frequent lots, or buying large to feel safe. Both can feel sensible in the moment. Putting the two costs on the same page shows how much money each habit is quietly costing over a year.

Formula and the three inputs

• Annual demand: units used or sold in a year.
• Order cost: fixed cost of placing and receiving one order, in currency per order.
• Holding cost: the cost of keeping one unit in stock for a year, in currency per unit per year.

Units must be consistent. If demand is in units per year, holding cost has to be per unit per year, not per unit per month.

Worked example: 10,000 units a year

A retailer sells 10,000 units a year of one product. Each order costs 300 to place and receive, and holding one unit for a year costs 24.

1. 1Multiply 2 by annual demand and order cost: 2 × 10,000 × 300 = 6,000,000.
2. 2Divide by the holding cost per unit: 6,000,000 ÷ 24 = 250,000.
3. 3Take the square root: √250,000 = 500.
4. 4The economic order quantity is 500 units.

That means 20 orders a year (10,000 ÷ 500), roughly one every 18 days.

Checking that 500 really is the sweet spot

Compare total annual cost at the EOQ with neighbouring order sizes. Ordering cost is orders per year times 300; holding cost is average stock (half the order size) times 24.

• At 500 units: ordering 20 × 300 = 6,000 and holding 250 × 24 = 6,000, total 12,000.
• At 250 units: ordering 40 × 300 = 12,000 and holding 125 × 24 = 3,000, total 15,000.
• At 1,000 units: ordering 10 × 300 = 3,000 and holding 500 × 24 = 12,000, total 15,000.
• The two cost components are equal at the optimum, a quick sanity check on any EOQ result.

Do not forget safety stock. EOQ tells you how much to order each time; it does not say when to order or how much buffer to keep for delays and demand surprises. Reorder point and safety stock are separate calculations that sit alongside it, and a company with long, unreliable lead times needs both.

What growth in demand does to order size

Because demand sits inside a square root, 10% more demand raises the EOQ by only about 4.9%, from 500 to roughly 524 units. Orders per year rise faster, from 20 to about 21. A real world consequence is that growing businesses do not need to order proportionally larger lots; they order a little larger and a little more often.

Ways EOQ results go astray

• Mixing time bases, such as annual demand with a monthly holding cost per unit.
• Treating order cost as the purchase price of goods; it is only the fixed cost of processing an order.
• Ignoring supplier minimum quantities, pack sizes, quantity discounts or shelf life, which can make the theoretical optimum impractical.
• Applying the model to items with very erratic or seasonal demand, where the steady-demand assumption fails.

Quantity discounts break the simple model, because price now changes with order size and purchase cost enters the total. The standard approach is to compute total annual cost at the EOQ and at each discount threshold, including the purchase price, and pick the lowest. A discount that applies at 800 units might beat the EOQ of 500 despite higher holding costs, particularly where the discount is large relative to the cost of carrying the extra stock.

Turning the result into a practical rule

The EOQ is rarely ordered exactly. If the supplier ships in cartons of 120, you might round 500 to 480 or 600. The cost curve is flat near the minimum, so a small departure costs little: at 600 units, ordering is about 16.67 × 300 = 5,000 and holding 300 × 24 = 7,200, total 12,200, only about 1.7% above the minimum. That tolerance makes it safe to adjust for pack sizes and storage space.

Use the EOQ as a baseline when negotiating. If a supplier's minimum order is far above your EOQ, you can estimate the extra holding cost that minimum creates and ask for a better price, or consider consolidating items from the same supplier into a shared order to spread the fixed cost.