Economic order quantity: how much to order at once

Economic order quantity is the order size where the cost of placing orders and the cost of holding stock add up to the least money, and it is the square root of 2DS ÷ H. For a line selling 4,800 units a year, costing £45 every time an order is placed and £2.60 a unit a year to hold, EOQ is 408 units at a total cost of £1,059.81 a year. Ordering 1,200 at a time instead — which feels efficient, because it is fewer orders — costs £1,740, or £680 a year more. This page works the formula, shows why being roughly right is good enough, and tests a supplier discount properly.

The formula, and what the three letters mean

Every order size is a trade between two costs that pull in opposite directions. Order in small batches and you place a lot of orders, each with its own cost. Order in big batches and you place few, but you are paying to hold a warehouse of stock that is not selling yet. EOQ is the bottom of that curve.

EOQ = √(2DS ÷ H)

S is the figure most people have never calculated, and it is usually larger than they expect, because it is almost entirely their own time. If raising a purchase order, chasing the supplier, booking the delivery, checking the goods in and reconciling the invoice takes two hours, and you price your hours at £18, then S is £36 before any bank charge or freight fee. Guessing S at £5 because “it is just an email” is how shops end up ordering far too often.

H comes from the unit cost and a holding rate. The build-up of a holding rate — cost of money, storage, insurance and shrinkage, obsolescence — is worked through in inventory turnover. Use your own rate; the one below is illustrative.

A worked order quantity

Marlow and Pike is an invented homewares shop. One line, a stoneware mug, sells steadily.

Put them through the formula one step at a time:

2 × 4,800 × £45.00 = 432,000
432,000 ÷ £2.60 = 166,153.85
√166,153.85 = 407.62

So the economic order quantity is 408 units, which at 4,800 a year means ordering about 11.8 times a year, or roughly every four and a half weeks. The annual cost of running the line that way:

The holding cost uses half the order quantity because stock arrives full and runs down to nothing, so the average held across the cycle is about half a delivery.

Notice that the two costs came out almost identical, £529.41 against £530.40. That is not a coincidence: at the exact EOQ the ordering cost and the holding cost are equal, and the pennies between them here are only rounding 407.62 up to a whole 408 units. It is a free check on your arithmetic — if your two columns are far apart, the quantity is not the EOQ.

Why the curve is flat, and why that is the useful part

EOQ produces a precise-looking number, and the precision is the least valuable thing about it. Run a range of order sizes for the same mug:

Two things fall out of that table, and the second is the one worth keeping.

First, the popular instinct is expensive. Ordering 1,200 at a time means only four orders a year and a very satisfying £180 of ordering cost — and it costs £680 a year more than the EOQ, because £1,560 of holding cost swallows the saving whole. Fewer orders is not the same as cheaper.

Second, the bottom of the curve is remarkably flat. Anywhere between 300 and 600 units the total cost stays within £81 of the optimum, on a line turning over £55,200 a year. That is the practically useful finding: you do not need the exact number. You need to know that 408 is the right neighbourhood, so that rounding to a 400-unit pallet or a 500-unit carton costs you almost nothing, while ordering 1,200 because the supplier offered a nicer price per unit might cost a great deal.

The flatness also means EOQ tolerates the shakiness of its own inputs. If S is really £55 rather than £45, EOQ moves to 451 units and the total cost at 408 is barely different. The formula is far more robust than its square root makes it look.

Testing a supplier discount properly

This is where EOQ actually earns its keep, because it turns “shall I take the bulk price?” into a subtraction.

Marlow and Pike’s supplier offers 4% off the £11.50 unit cost for orders of 1,200 or more. The instinct is to take it. Test it instead.

Take the discount. The point is not the answer, which depends entirely on the numbers; it is that the answer was not obvious. A 4% discount on a £55,200 spend is worth £2,208 and the extra stock costs £680, so the deal wins comfortably. Change one input and it flips: had the discount been 1%, the saving would be £552 against the same £680 of extra cost, and taking it would have lost £128 a year while feeling like a win.

There is a small refinement worth naming rather than hiding. If the unit cost falls to £11.04, the holding cost per unit falls with it, to about £2.50, which slightly reduces the £1,560 holding figure. It moves the answer in the direction the discount was already going, so it does not change the decision here, but on a marginal call it is worth redoing H at the discounted cost.

Two things the subtraction does not cover, and both can outweigh it. Money spent on 1,200 units is money not available for anything else for three months, and if cash is tight that matters more than £1,527. And 1,200 units of a product that might be discontinued, reformulated or simply go out of fashion is a much bigger bet than 408. The arithmetic says take it; the cash position and the shelf life get a vote.

Where EOQ breaks

EOQ is a model from a tidier world than the one you order stock in. It is still useful, but it is worth knowing exactly which of its assumptions your own situation violates.

• It assumes demand is level. 4,800 a year means 400 a month, every month. A product that sells 150 for ten months and 1,500 in December is not described by this formula, and running it on the annual average will leave you short in the only month that mattered.
• It assumes stock arrives the instant you need it. EOQ answers how much to order and says nothing whatever about when. That is a separate calculation, and it is the reorder point.
• It assumes S and H are constant. In practice freight is often charged per pallet or per container, so the cost per order jumps in steps rather than sliding smoothly, and the real answer is usually the pallet quantity nearest the EOQ.
• It ignores minimum order quantities. If the supplier will not sell fewer than 500, the EOQ of 408 is interesting but not available. Use the flatness of the curve to price the compromise: 500 units costs £1,082 against the optimum £1,060, so the minimum costs about £22 a year. That is worth knowing before negotiating.
• It ignores shelf life and obsolescence beyond the holding rate. For anything perishable or seasonal the real constraint is the date, not the arithmetic.

None of these is a reason to skip the calculation. They are reasons to treat the output as a strong opening position that gets adjusted by the pallet size, the minimum order and the calendar — rather than as an answer.

What economic order quantity cannot tell you

EOQ optimises one thing: the total of ordering and holding costs for one product, assuming steady demand. Everything outside that is outside the formula.

• It cannot tell you whether to stock the product at all. EOQ will happily return a beautifully optimised order quantity for a line that loses money on every unit. Whether the line earns its shelf space is a different sum, worked in inventory turnover.
• It cannot tell you when to place the order. Quantity and timing are separate questions and getting the first right does not help if the stock lands three weeks late.
• It says nothing about cash. The formula minimises cost, not the money you have tied up. A business short of cash is often right to order below EOQ and accept a higher total cost in exchange for not having its bank balance sitting on a shelf. The formula cannot see your bank balance.
• It optimises each product in isolation. Real orders combine several lines with one shared delivery charge, which lowers the effective S for every line in the shipment and pushes all of their quantities down. Treat single-product EOQ as an upper bound when you habitually order in mixed shipments.
• It is only as good as D. Annual demand is taken from history and applied to the future. On a line that is growing or fading, last year’s units are the wrong input, and no amount of precision in the square root repairs it.
• It does not price the risk of being wrong. Ordering 408 of something that stops selling is a £4,692 mistake. The formula weighs costs, not the consequences of a bad forecast, and on a new or untested line the cautious quantity usually beats the optimal one.

Arithmetic and general information only — not financial, tax, legal or investment advice. Your own figures, and your own accountant, decide what any of this means for you.

Frequently asked questions

What is the economic order quantity formula?

EOQ is the square root of (2 × D × S) ÷ H, where D is annual demand in units, S is the cost of placing one order and H is the cost of holding one unit for a year. At 4,800 units a year, £45 an order and £2.60 a unit a year, that is the square root of 166,153.85, which is 408 units.

What should I include in the cost of placing an order?

Mostly your own time, priced at a rate you would accept: raising the order, chasing the supplier, booking the delivery, checking the goods in and reconciling the invoice. Add anything charged per shipment rather than per unit, such as freight handling or a bank transfer fee. Two and a half hours at £18 gives £45, and underestimating this figure is what makes shops order too frequently.

Why does ordering in bulk cost more if the unit price is the same?

Because the stock has to be paid for and held until it sells. In the worked example, ordering 1,200 at a time cuts ordering cost from £529 to £180 a year but raises holding cost from £530 to £1,560, for a total of £1,740 against £1,060 at the economic order quantity — £680 a year worse. Fewer orders is not automatically cheaper.

How exact does the order quantity need to be?

Not very, which is the most useful thing about the formula. In the worked example anything between 300 and 600 units stays within £81 a year of the optimum, so rounding to a pallet or carton quantity near the EOQ costs almost nothing. The number is there to tell you the right neighbourhood, not the exact unit.

How do I decide whether to take a bulk discount?

Compare the saving on goods against the extra ordering and holding cost at the larger quantity. A 4% discount on 4,800 units at £11.50 is worth £2,208 a year, against £680 of extra stock cost, so it wins by £1,528. At a 1% discount the same deal saves £552 and costs £680, losing £128 a year. Also check the cash you would tie up and whether the product could date.

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• How to build a cash flow forecast
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