Economic order quantity is the order size that costs you the least overall. It balances two costs that move in opposite directions: ordering frequently costs more in the effort and expense of each order, whilst ordering in large quantities costs more in holding the stock that results.
EOQ finds the point where those two costs are lowest combined. It answers how much to buy each time — a different question from when to buy, which is what a reorder point tells you.
EOQ in plain English
Imagine you use 1,200 units a year of something.
Order all 1,200 at once and you place one order a year. Ordering costs are tiny. But you hold an average of 600 units all year, tying up cash and space, and paying to store, insure and handle them.
Order 100 units a month and you hold an average of 50 units. Holding costs collapse. But now you place twelve orders a year, each with its administration, its delivery charge and its receiving work.
Somewhere between those extremes is an order size where the two costs added together are as low as they get. That is the economic order quantity.
The useful insight is that the total cost curve is quite flat around its minimum. Being 20% away from the exact EOQ typically costs only a few percent more than being exactly on it. That is why EOQ is best treated as a sense-check rather than an instruction — it is very good at telling you when your current order size is wildly wrong, and not worth agonising over to the nearest unit.
The EOQ formula
EOQ = square root of ( (2 × D × S) ÷ H )
Or, in the notation you will see elsewhere: EOQ = √(2DS/H)
D — annual demand. The number of units you use or sell in a year. Take it from actual sales history rather than a target, and exclude any period the product was out of stock, because sales during a stockout record availability rather than demand.
S — cost per order. What it costs you to place and receive one order, regardless of its size. This is the input people get wrong most often. It includes the purchasing time to raise and chase the order, the delivery or freight charge where it is fixed rather than per unit, the goods-in labour to receive, check and put away, and the invoice processing. It does not include the cost of the goods themselves.
H — annual holding cost per unit. What it costs to hold one unit for a year. Usually calculated as a percentage of unit cost — commonly 20–30% once capital, storage, insurance, handling, shrinkage and obsolescence are included. So a $20 item at a 25% holding rate gives H = $5. There is a full breakdown in carrying cost of inventory.
Note what is missing from the formula: the purchase price of the goods. It does not appear because, in the model’s world, you buy the same annual quantity whatever your order size, so the purchase cost is identical across every option and cannot influence the answer. It does appear indirectly, through H.
A fully worked example
A business sells a storage box. The figures:
- It sells 2,400 units a year
- Each purchase order costs about $75 to place and receive — roughly an hour of purchasing time, a fixed $40 delivery charge, and the goods-in labour
- Each box costs $12 to buy, and the business uses a 25% annual holding rate
Step one — establish D. Annual demand = 2,400 units.
Step two — establish S. Cost per order = $75.
Step three — calculate H. Holding cost per unit per year = $12 × 25% = $3.00.
Step four — put them into the formula.
EOQ = √( (2 × 2,400 × 75) ÷ 3.00 ) EOQ = √( 360,000 ÷ 3.00 ) EOQ = √120,000 EOQ = 346 units
Step five — work out what that means in practice.
- Orders per year = 2,400 ÷ 346 = 6.9, so roughly every 7–8 weeks
- Average stock held = 346 ÷ 2 = 173 units, or $2,076 of stock
- Annual ordering cost = 6.9 × $75 = $518
- Annual holding cost = 173 × $3.00 = $519
Notice that the two costs come out almost identical. That is not a coincidence — at the EOQ they are always equal, which is a useful way to check your arithmetic.
Total relevant cost = $1,037 a year.
Step six — compare it with the alternatives. This is where the exercise earns its keep.
| Order size | Orders per year | Ordering cost | Average stock | Holding cost | Total |
|---|---|---|---|---|---|
| 100 | 24.0 | $1,800 | 50 | $150 | $1,950 |
| 200 | 12.0 | $900 | 100 | $300 | $1,200 |
| 346 (EOQ) | 6.9 | $518 | 173 | $519 | $1,037 |
| 600 | 4.0 | $300 | 300 | $900 | $1,200 |
| 1,200 | 2.0 | $150 | 600 | $1,800 | $1,950 |
Two things stand out. The EOQ genuinely is the cheapest. And the curve is flat around it — ordering 200 or 600 instead of 346 costs $163 more a year, which on a business of this size is close to noise. If your supplier’s case quantity is 250, or their minimum is 500, take it and stop worrying.
An EOQ calculator
Work through this for any product. The arithmetic takes a minute; establishing S and H honestly is the real work.
| Step | What to find | Your figure |
|---|---|---|
| 1 | D — units sold or used in the last twelve months | |
| 2 | Purchasing time, fixed freight, goods-in labour and invoice processing per order | |
| 3 | S — total cost per order (the sum of step 2) | |
| 4 | Unit cost of the item | |
| 5 | Your annual holding rate (20–30% is typical) | |
| 6 | H — step 4 × step 5 | |
| 7 | 2 × D × S | |
| 8 | Step 7 ÷ H | |
| 9 | EOQ — the square root of step 8 |
The worked row, for reference: D = 2,400, S = $75, H = $3.00. (2 × 2,400 × 75) = 360,000. 360,000 ÷ 3 = 120,000. √120,000 = 346 units.
Then sanity-check the answer against reality:
- Does it fall between your supplier’s minimum order quantity and something you have space for?
- Does it round sensibly to a case, layer or pallet quantity? Round to the nearest practical unit — the flat cost curve means you lose almost nothing.
- How many orders a year does it imply? If the answer is 40, ask whether S is understated. If it is 0.8, ask whether H is.
- Would a volume discount at a larger quantity beat the extra holding cost? The basic formula cannot see discounts, so check this separately.
What EOQ tells you, and why it matters
It quantifies a trade-off people usually resolve by instinct. Most order quantities are set by habit, by the supplier’s case size, or by whoever placed the first order years ago. EOQ puts a number against the alternative.
It exposes an understated cost of ordering. Businesses that order very frequently often have not counted what each order actually costs in purchasing and goods-in time. Calculating S is frequently more revealing than the EOQ itself.
It exposes an understated cost of holding. Equally, businesses that buy in bulk to capture unit discounts rarely price the year of storage that follows. Working out H at 25% of unit cost tends to change minds about volume deals.
It gives you a defensible answer to a supplier’s discount offer. “Buy double and save 4%” can be tested rather than accepted. If the extra holding cost exceeds the discount, the deal is not a saving.
It is the input to your ordering rhythm. EOQ divided into annual demand gives orders per year, which in turn tells you how often purchasing should be reviewing that line.
Assumptions and limitations
The model is nearly a century old and rests on assumptions that are rarely fully true. Knowing where it breaks is what separates using it from being misled by it.
It assumes constant, known demand. Real demand is seasonal, trending and uncertain. For a product with a sharp seasonal peak, a single annual EOQ is close to meaningless — calculate separately by season, or do not bother.
It assumes a fixed cost per order regardless of size. In reality freight often scales with volume, and consolidating several products into one delivery changes the per-order cost entirely.
It assumes constant holding cost per unit. Holding cost jumps in steps rather than smoothly — a quantity that needs an extra pallet location, or tips you into renting more space, costs far more than the linear model suggests.
It ignores volume discounts. The basic formula assumes one purchase price. Where discount breaks exist, you have to compare the total cost at each break point against the EOQ answer separately. This is the most common practical gap.
It assumes instant replenishment and no stockouts. No lead time, no variability, no possibility of running out. Safety stock and reorder points exist precisely because those assumptions are false, and they sit outside the EOQ calculation.
It ignores perishability and obsolescence beyond whatever you built into H. For short-dated or fast-moving-fashion goods, the real constraint is shelf life rather than cost.
It treats each product independently. In practice you order several lines from one supplier on one delivery, which changes the economics substantially — a shared delivery cost split across ten products makes S much smaller per line.
It assumes unlimited capital and space. Neither is true, and either can cap the answer regardless of what the formula says.
How to use it despite all that. Treat EOQ as a diagnostic rather than an instruction. Run it across your top lines by value. Where the answer is close to what you already order, leave it alone. Where it is several times larger or smaller, investigate — that is the model telling you something is worth a look, which is the most it ever claimed to do.
How EOQ fits with reorder point, safety stock and carrying cost
Four numbers, answering four different questions, and they depend on each other in sequence.
| Question it answers | Feeds into | |
|---|---|---|
| Carrying cost | What does holding one unit for a year cost? | H in the EOQ formula |
| Safety stock | How much buffer against things going wrong? | The reorder point |
| Reorder point | When do I order? | The trigger to act |
| EOQ | How much do I order? | The quantity on the order |
The order of work is: calculate carrying cost first, because EOQ needs it. Size safety stock from your demand and lead time variability. Build the reorder point from lead time demand plus that safety stock. Then use EOQ to set the quantity you order when the point fires.
Get those four in place on your top lines by value and you have the core of a working replenishment system. Extending them across a long tail of slow-moving items rarely repays the effort — simple minimum-maximum levels are usually better there.
Where to go deeper
- What is a reorder point — when to order, as opposed to how much.
- What is safety stock — the buffer EOQ does not account for.
- Carrying cost of inventory — how to calculate H properly.
- Inventory management techniques — where EOQ sits among the alternatives.
- What is overstocking — what happens when order quantities are set by discount alone.
- What is inventory turnover — the measure order quantity most affects.
The one-line takeaway
Economic order quantity is the order size where ordering costs and holding costs are lowest combined, given by the square root of 2DS/H. Its real value is diagnostic: the cost curve is flat around the answer, so use it to find the lines where your current order size is badly wrong rather than to set quantities to the nearest unit.
Frequently asked questions
What is economic order quantity in simple terms? The order size that costs you the least overall, balancing the cost of placing orders against the cost of holding the stock they produce. Order too often and ordering costs mount; order too much and holding costs do.
What is the EOQ formula? EOQ = √(2DS/H), where D is annual demand in units, S is the cost of placing and receiving one order, and H is the cost of holding one unit for a year. The purchase price of the goods does not appear, because it is the same whatever order size you choose.
Can you give an EOQ example? With annual demand of 2,400 units, an ordering cost of $75, and a holding cost of $3.00 per unit per year: (2 × 2,400 × 75) = 360,000; divided by 3 = 120,000; the square root of which is 346 units. That means roughly seven orders a year and an average stock of 173 units.
What are the limitations of EOQ? It assumes constant known demand, a fixed cost per order, a constant holding cost per unit, no volume discounts, instant replenishment and no stockouts. None is fully true. It also treats each product independently, which understates the benefit of consolidating several lines onto one delivery.
What is the difference between EOQ and reorder point? EOQ tells you how much to order; the reorder point tells you when. They are complementary — the reorder point fires, and the EOQ determines the quantity on the purchase order that follows.
Does EOQ account for volume discounts? Not in its basic form. Where a supplier offers price breaks, compare the total annual cost at each break quantity — purchase cost plus ordering cost plus holding cost — against the total at the EOQ, and choose the lowest. Frequently the discount does not survive the extra holding cost.
Is EOQ still relevant? As a diagnostic, yes. Because the total cost curve is flat around the minimum, it is poor at prescribing exact quantities and very good at identifying products where your current order size is several times larger or smaller than it should be. Used that way it still earns its place.
How do I calculate the cost per order? Add the purchasing time to raise and chase the order, any fixed freight or delivery charge, the goods-in labour to receive, check and put away, and the invoice processing. Exclude the cost of the goods themselves, and exclude anything that scales with order size rather than being fixed per order.
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