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 shortening the path from a low-stock flag to an approved PO.
If you want to run the numbers rather than read about them, the EOQ calculator does this arithmetic, and the reorder point and safety stock calculators handle the other half of the replenishment question.
What AWRA OpsHub does today
- A reorder point and safety stock figure per item, held on the item record alongside a lead time in days.
- A Low Stock report that lists every item at or below its reorder point, so the trigger is visible rather than remembered.
- Actual supplier lead times derived from purchase order history, so the input to your own calculation is evidence rather than a guess.
- An automatic replenishment rule, if you build one: a low-stock trigger can raise a procurement request for the item without anyone watching a report.
- A public EOQ calculator, free and outside the product, for the arithmetic itself.
More we can add to your workspace
- An EOQ engine inside the product, computing and storing an economical order quantity per item.
- Intelligent sizing on the automatic rule. It orders a fixed quantity you configure, or the distance back up to the reorder point; neither is an EOQ, and computing one is the build.
- A price-break optimisation. Supplier discount tiers are not compared against an EOQ anywhere.
- A demand forecast feeding an order size. Forecasting exists, but it is a blended velocity projection, not a replenishment quantity.
This is a build rather than a deliberate design line, and worth saying plainly: EOQ computed for you per item is something to commission. What ships today makes the inputs — real lead times, real consumption, a visible trigger — reliable enough that the calculation is worth running.
Anything above that you need, we can build for you
Everything listed above as something we can add describes what ships in the standard product today — it is a starting point, not a limit on what AWRA OpsHub can do for your organisation. Kenya's eTIMS integration and its maintained payroll engine are both in the product because clients needed them and commissioned them; neither appeared by itself, and the same door is open for whatever you just read about. One qualification so this is worth what it claims: a small number of things on this blog we deliberately leave to a specialist rather than build — a statutory ledger we will not sign our name to, a rule that would decide a tax question for you, a clinical or member-funds record that belongs in a regulated system — and where that is true the post says so in those words. Everything else is a scope, a timeline and a price.
The operational work, which is what most commissions actually are
An extra approval stage in a chain that does not match the standard one, a custom field set on employees or assets that only your sector needs, an expiry that has to block an order rather than send an email, a report your board asks for in a shape nothing produces, or a scanner or weighbridge feeding the goods-in door. These are the commissions we are asked for most often and the smallest ones we quote — and unlike a revenue-authority pipeline, none of them waits on a regulator.
The module-shaped additions, which are the ones readers ask for most often
A price list with real discount authority, a customer-facing quotation that expires, a bill of materials or recipe costing, a staff advance that is issued, acquitted and chased, a member or unit ledger, a matching rule that holds a payment. Each of these is a build rather than a setting, and each has been quoted before — a bigger piece of work than a custom field, with a written spec and a date instead of a roadmap slide.
The report, document or pack nothing currently produces
The board pack in the shape your board actually asks for, a donor or funder layout, an invoice or receipt template carrying what your regulator or your customer expects, a dataset the report builder cannot reach yet. Usually the fastest thing on this list to deliver, because the data is already in the system.
Systems, rails and hardware you already run
The accounting package, CRM, online store, core banking or custom database you intend to keep — connected through our API so a fact is entered once and appears everywhere it is needed. Plus the physical edge: a scanner, a scale, a weighbridge or a till peripheral feeding the door it belongs to.
How it works: you describe the requirement, we return a written scope, timeline and cost, and once agreed it is built into your environment and maintained as part of the product. Nothing here waits on a regulator or a published specification, which is why operational builds are the ones we quote fastest. Tell us the requirement that would otherwise rule us out — that is a better first conversation than a demo.
Tell us what your operation needsOrder sizing sits inside a wider set of stock controls — stock control in Kenya covers the ones that matter more than the formula.
Get the inputs right first
Reorder points, [safety stock](/glossary/safety-stock) and real supplier lead times per item — the evidence an order-size decision actually rests on.
Explore inventory managementFrequently 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.
