Economic Order Quantity (EOQ): The Formula and Its Limits
The classic formula for how much to order at once — the EOQ equation, the two costs it balances, a worked example, and the assumptions that make it lie in the real world.
Economic Order Quantity (EOQ) answers one question: given that you have to reorder, how much should you buy each time? Order too little and you pay the fixed cost of ordering over and over — placing POs, receiving, paperwork. Order too much and you pay to hold it — capital tied up, storage, insurance, obsolescence. EOQ is the quantity where those two costs are equal, which is also where their sum is lowest.
The formula
EOQ = √( (2 × D × S) / H ), where D is annual demand in units, S is the fixed cost per order, and H is the cost to hold one unit for a year. The square root is what makes EOQ counter-intuitive: doubling your demand does not double your order size — it raises it by only about 40%. Ordering cost and holding cost pull in opposite directions, and the formula finds their balance point.
| Cost | What it includes | Which way it pushes order size |
|---|---|---|
| Ordering cost (S) | PO processing, receiving, inspection, admin per order | Higher S → larger, less frequent orders |
| Holding cost (H) | Cost of capital, storage, insurance, spoilage, obsolescence | Higher H → smaller, more frequent orders |
| Total cost | Ordering + holding across the year | Minimised at the EOQ |
A worked example
Suppose you sell 3,600 units of an item a year (D). Each order costs 500 to place and receive (S). Holding one unit for a year costs 20 (H). Then EOQ = √((2 × 3,600 × 500) / 20) = √180,000 ≈ 424 units per order. At that size you place roughly 8–9 orders a year, and the money spent ordering almost exactly equals the money spent holding. Order 1,000 at a time instead and holding cost balloons; order 100 at a time and ordering cost does. The 424 is the floor of the total-cost curve.
EOQ tells you how much; the reorder point tells you when
These are the two halves of replenishment and they are constantly confused. EOQ sizes the order; the reorder point times it. You can have a perfect EOQ and still stock out because the trigger fired too late, or never stock out while drowning in the wrong order size. Calculate both, per item.
Where EOQ quietly lies
The formula assumes a tidy world that inventory rarely inhabits. Knowing where the assumptions break is the difference between using EOQ as a guide and trusting it as gospel.
- It assumes constant, known demand. Real demand is seasonal and spiky; EOQ computed on a flat annual average will over-order in the quiet months and under-order in the peak.
- It ignores quantity discounts. If the supplier prices in breaks — cheaper per unit at 500 than at 424 — the true optimum may be a discount tier, not the raw EOQ. Compare the EOQ total cost against each price break.
- It assumes a fixed unit cost. Landed cost — freight, duty, clearing — often changes with order size and shipment mode, which shifts H and sometimes the whole calculation.
- It ignores capital and shelf-life limits. EOQ may say order 424; your cash, your storage, or the product’s expiry may say you cannot. The constraint wins.
- It assumes ordering cost is fixed. Automating procurement drives S down — and a lower S means smaller, more frequent orders become optimal, which is precisely why digitised buyers can afford to hold less.
How to use it in practice
Treat EOQ as a starting point, not a mandate. Compute it for your high-volume, stable-demand items where the assumptions roughly hold, sanity-check it against supplier price breaks and your cash position, and round to a sensible pack or pallet size. For erratic or slow-moving items, EOQ matters less than simply not over-buying. And because the biggest lever in the formula is ordering cost, the highest-return move is often not a better EOQ — it is cheaper ordering, which procurement automation delivers by turning a reorder suggestion into an approved PO in seconds.
Order the right quantity, automatically
AWRA OpsHub raises sized replenishment suggestions from live demand and lead times, so buyers order the economical quantity without running the math by hand.
See procurement automationFrequently asked questions
What does EOQ actually minimise?
The total of ordering cost plus holding cost across a year. Ordering more often lowers holding cost but raises ordering cost; ordering in big batches does the reverse. EOQ is the single order size where the two are balanced and their sum is at its minimum.
Why is there a square root in the EOQ formula?
Because the total cost curve is a balance between a term that rises with order size (holding) and one that falls with it (ordering). Minimising that sum mathematically produces a square root, which has a practical consequence: order size grows much more slowly than demand — quadruple your sales and the economical order size only doubles.
Is EOQ still useful with modern software?
Yes, but its inputs shift. Software drives ordering cost (S) down sharply, which lowers the EOQ and favours smaller, more frequent orders — exactly the lean-inventory pattern good systems enable. The formula is less a fixed answer than a lens for seeing how cheaper ordering lets you hold less stock.
Should I use EOQ for every item?
No. It works best for high-volume items with reasonably steady demand and stable costs. For seasonal, erratic, perishable, or slow-moving stock, the assumptions break down and simpler rules — do not over-buy, respect shelf life, watch cash — serve better than a formula that assumes a flat, predictable year.
