Economic Order Quantity Calculator

How it is calculated

Economic order quantity is the order size that minimises the sum of ordering cost and carrying cost: √(2DS ÷ H), where D is annual demand, S is the cost of placing one order, and H is the cost of holding one unit for a year.

The square root is doing the work. It means doubling demand does not double the order quantity. It raises it by about 41%, which is why large businesses order proportionally less often per unit sold than small ones.

The same thing with real figures

Annual demand 2,080 units, ordering cost $85, unit cost $18 with carrying cost at 25% a year, so H = $4.50.

EOQ = √(2 × 2080 × 85 ÷ 4.50) = √78,578 = 280 units. That means 7.4 orders a year, roughly one every seven weeks.

Check the balance: ordering cost is 7.4 × $85 = $631, and carrying cost is (280 ÷ 2) × $4.50 = $630. At the optimum the two are equal, which is the property that makes the formula work and a useful check that the arithmetic is right.

The catch

The cost curve near the optimum is remarkably flat, which is the most useful and least known property of EOQ. Ordering 200 units instead of 280 raises total cost by about 4%; ordering 400 raises it by about 6%. The formula's precision is largely illusory and the practical answer is a range.

It also assumes constant demand, a fixed unit cost regardless of quantity, and no constraints. Volume price breaks, minimum order quantities, container sizes and shelf space all override it, and in practice at least one of them usually does.

Applying it

Use it to sense-check the order quantity you were going to place rather than as the quantity itself. If EOQ says 280 and habit says 1,000, the habit is worth examining; if habit says 250, it is close enough that the difference is not worth an argument.

Then round to something practical: a case quantity, a pallet layer, a container fill. The flat cost curve means the rounding costs almost nothing and the operational simplicity is worth real money.

Getting the two input costs right

Ordering cost is the cost of placing and receiving one order regardless of size: the buyer's time, the paperwork, the inbound freight if it is flat, the goods-in labour, the quality check. For a small business it is typically $50 to $150, and for a business ordering by container it can be far more.

Carrying cost is the annual cost of holding a unit: capital tied up, storage, insurance, shrinkage, obsolescence and the risk of markdown. The conventional range is 20% to 30% of unit cost a year, and for fashion or perishables it is much higher because obsolescence dominates.

Both are usually estimated rather than measured, and the flat cost curve means that is acceptable. An ordering cost estimated at $85 when the truth is $110 changes EOQ from 280 to 318, and the total cost difference between those two order sizes is under 1%. The formula is far more robust to bad inputs than its appearance suggests.