The economic order quantity is the order size that makes total inventory cost as low as possible, by balancing two costs that pull in opposite directions: order more often and you pay more in ordering costs, order in bigger batches and you pay more to hold the stock. EOQ is the point where those two meet.
This calculator returns the EOQ itself plus everything a brief normally asks for alongside it — orders per year, the length of an order cycle, ordering and holding costs separately, total annual cost, and the reorder point if you supply a lead time. It shows the substitution line by line, because in supply chain assignments the working carries the marks.
EOQ = sqrt(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 arrives because you are minimising the sum of two costs — one that falls as order size rises (D/Q × S) and one that rises with it (Q/2 × H). Setting the derivative of that sum to zero and solving for Q gives the expression above.
A useful consequence: at the EOQ, annual ordering cost and annual holding cost are exactly equal. If your calculated figures differ by more than rounding, something is wrong in the inputs — and checking that equality is a fast way to verify an answer before you submit it.
The Q/2 in the holding cost is average inventory, and it assumes stock is drawn down at a steady rate from Q to zero before the next delivery arrives. That assumption is why the basic model needs no safety stock: demand and lead time are both taken as certain.
Holding cost is where most EOQ answers go wrong, because briefs express it two different ways. Sometimes it is given directly as a cost per unit per year. More often it is given as a percentage — "holding costs are 25% of unit value" — in which case H is 25% of the purchase cost per unit, and you must do that multiplication before using the formula.
Watch the time period too. H is a cost per unit per year, matched to an annual demand figure. If a question gives monthly demand and an annual holding rate, one of the two has to be converted, and mixing them produces an EOQ that is wrong by a factor of twelve or by its square root.
Holding cost properly includes capital tied up in stock, storage, insurance, obsolescence and shrinkage. Most assignment briefs simplify this to a single figure, but if yours asks you to justify the rate, those are the components to name.
Basic EOQ assumes constant, known demand, a fixed lead time, no quantity discounts, no stockouts, and instantaneous replenishment of the whole batch. Real supply chains satisfy none of these exactly. Many rubrics award marks specifically for identifying the assumptions and discussing what breaks when they fail, so calculating the number and stopping is leaving marks on the table.
Where a brief adds quantity discounts, the method changes: calculate the EOQ at each price break, discard any quantity that is not feasible in its price band, then compare total cost — purchase cost included — at each candidate quantity. The lowest total cost wins, and it is frequently not the EOQ.
Where production is gradual rather than instantaneous, the economic production quantity model replaces EOQ, adding a term for the production rate. If your question mentions a daily production rate alongside a usage rate, that is the model being asked for.
EOQ = sqrt(2DS / H) — D is annual demand in units, S is the cost of placing one order, H is the cost of holding one unit for a year. The calculator shows the substitution as well as the result.
Multiply the percentage by the unit purchase cost. A unit costing 40 with a holding rate of 25% gives H = 10 per unit per year. Do this before entering the figure.
They should be. That equality is a property of the EOQ, and it is the quickest check that your answer is right. A visible difference means an input is wrong.
No. The reorder point here is demand during lead time only, which assumes demand and lead time are certain. For variability, use the safety stock calculator — it is linked below.
Use it to find the EOQ at each price level, then compare total costs including purchase cost across the feasible quantities. The calculator gives you each EOQ; the comparison is the part your brief is assessing.
Usually yes, since you cannot order a fraction of a unit — but round at the end, not partway, and state that you have rounded. Some markers want the unrounded figure shown first.