The economic order quantity is the quantity per order at which ordering and holding costs together are lowest.
It is calculated with the EOQ formula from four inputs: annual demand, cost per order, unit value and holding cost rate.
At the optimum, total ordering costs and total holding costs are exactly equal.
The formula assumes constant demand, fixed prices and no quantity discounts, conditions that rarely all hold in practice.
First step: gather these four values for your most important item and run the formula once.
Order quantities too small and you pay for it: every order costs time, handling and goods receipt. Order quantities too large and you pay for it too: capital sits on the shelf, ties up storage space and drives holding costs.
Between these two opposing cost types there is exactly one point where their sum is lowest. That quantity is the economic order quantity, and it can be calculated precisely. This article shows the formula, a worked example, the table method, and the points where the model breaks in practice.
What is the economic order quantity?
The economic order quantity is the order quantity per purchase at which the sum of ordering costs and holding costs is lowest. It resolves a conflict: both cost types move in opposite directions.
The larger the order quantity, the less often you order. Total ordering costs fall, but inventory and therefore holding costs rise.
The smaller the order quantity, the lower the inventory. Holding costs fall, but you order more often, and ordering costs rise.
The optimum is the point where both effects balance out. The classic method for finding it is the EOQ formula, first derived by Ford W. Harris in 1913 and known in German-speaking countries as the Andler formula (Kurt Andler, 1929).
The EOQ formula: how it is built
The economic order quantity follows from four inputs: annual demand, cost per order, unit value and holding cost rate.
EOQ formula
economic order quantity = √( (2 × annual demand × cost per order) / (unit value × holding cost rate) )
The individual terms:
Annual demand: the total quantity of this item you consume per year.
Cost per order: the fixed cost per order, independent of quantity (handling, shipping, goods receipt, inspection).
Unit value: the purchase price per unit.
Holding cost rate: the share of the unit value spent per year on holding, from tied-up capital and physical storage. The guide to warehouse costs shows how to determine it.
There is no version of the formula without a square root. The root follows directly from setting the derivative of the total cost function to zero at the minimum. There is only one notation variant: if you enter the holding cost rate as a percentage instead of a decimal, you use 200 instead of 2 in the numerator.
Variant with percentage
economic order quantity = √( (200 × annual demand × cost per order) / (unit value × holding cost rate in %) )
The 200 converts the percentage automatically. The result is the same.
Calculating the economic order quantity: a worked example
The formula is clearest with a concrete item that almost every business orders: shipping boxes.
Beispiel
An online retailer uses 12,000 standard boxes per year. Each order costs 50 euros in handling and goods receipt, a box costs 1.50 euros to buy, and the holding cost rate is 20 percent.
So the economic order quantity is 2,000 boxes. Two further values follow directly.
order frequency = annual demand / economic order quantity = 12,000 / 2,000 = 6 orders per year
average inventory = economic order quantity / 2 = 2,000 / 2 = 1,000 boxes
The average inventory is half the order quantity, because stock falls steadily from full to empty before the next delivery arrives. In this example, total ordering costs (6 × 50 = 300 euros) are exactly equal to holding costs (1,000 × 1.50 × 0.20 = 300 euros). This balance is what defines the optimum.
Determining the economic order quantity with a table
If you do not want to apply the formula, or need to see the curve first, a table gets you to the result too. You work through several order quantities and look for the lowest total cost row. The same example, four quantities compared:
Order quantity (boxes)
Orders / year
Ordering costs (€)
Holding costs (€)
Total costs (€)
1,000
12
600
150
750
2,000
6
300
300
600
3,000
4
200
450
650
4,000
3
150
600
750
The row with 2,000 boxes has the lowest sum (600 euros) and confirms the formula result. Note: that is exactly where ordering costs and holding costs are equal. Below that quantity ordering costs dominate, above it holding costs do.
Graphical representation: where the curves cross
Plot the cost types in a chart and three curves emerge. Order quantity is on the horizontal axis, cost on the vertical.
The ordering cost curve falls: the larger the quantity, the less often you order.
The holding cost curve rises: the larger the quantity, the more stock and tied-up capital.
The total cost curve is the sum of both and has the shape of a U.
The lowest point of the total cost curve sits exactly above the intersection of the ordering and holding cost curves. That point is the economic order quantity. In the table above it is the row where ordering costs and holding costs have the same value.
Economic order quantity or economic lot size?
Both terms use the same math but apply to different situations.
Economic order quantity: the quantity you order per purchase from an external supplier. External procurement.
Economic lot size: the quantity a manufacturing business produces in one run. In-house production.
The only difference is the fixed cost per event: for the order quantity it is the ordering cost, for the lot size it is the machine setup cost. The EOQ formula stays identical in both cases.
The 5 assumptions behind the EOQ formula
The formula delivers a clean result because it simplifies reality heavily. It assumes five conditions:
Annual demand is known and evenly spread across the year.
Cost per order is constant, independent of quantity.
The unit value is constant, with no quantity discounts.
The holding cost rate is constant.
The full order quantity is delivered at once, with no lead-time effects and no stockouts.
When these conditions hold, the EOQ formula is exact. In a real business, usually more than one of them is violated.
What the formula does not capture
The economic order quantity is a starting value, not a finished ordering recipe. Three effects shift the result noticeably in practice.
Quantity discounts. When suppliers offer tiered pricing, the unit value drops sharply above a certain quantity. It can then be cheaper to order up to the next discount tier, even if that is above the calculated economic order quantity. The formula does not know about this jump.
Pack sizes and units. Many items come only in fixed units: cartons of 500, pallets of 1,200. An economic order quantity of 2,000 then has to be rounded to the nearest whole pack. The same applies to supplier minimum order values.
Variable demand. The formula assumes even annual demand. As soon as demand fluctuates seasonally or by project, that assumption no longer holds. You then need an extra buffer that the economic order quantity alone does not provide.
How much and when: economic order quantity meets reorder point
The economic order quantity answers only one of two questions. It tells you how much you order per purchase. It does not tell you when to order.
The reorder point answers that second question: the stock level that triggers an order. It includes consumption during the lead time plus a minimum stock as a buffer against fluctuations, exactly the safety that the EOQ formula leaves out.
Together they form a complete ordering rule: when stock reaches the reorder point, you order the economic order quantity. Both values also define the maximum stock as an upper limit (minimum stock plus economic order quantity). The guide to min-max inventory management shows how these thresholds work together as a closed system.
In practice the calculation per item only pays off if something keeps it current: demand, prices and lead times change. Inventory software handles this, stores the values per item and triggers the reorder automatically. repleno uses this logic for demand notifications.
Conclusion
The economic order quantity is the quantity per order at which ordering and holding costs together are lowest, calculated with the EOQ formula or with a cost table. At the optimum both cost types are equal.
Treat the result as a guide value, not a fixed rule: quantity discounts, pack sizes and variable demand shift it. The first concrete step: take your most important item, gather annual demand, cost per order, unit value and holding cost rate, and run the formula once.
Frequently asked questions about the economic order quantity
With the EOQ formula: economic order quantity = square root of (2 × annual demand × cost per order) divided by (unit value × annual holding cost rate). Example: 12,000 units annual demand, 50 euros per order, 1.50 euros unit value, 20 percent holding cost rate → square root of (2 × 12,000 × 50) / (1.50 × 0.20) = 2,000 units.
