EOQ Calculator: Economic Order Quantity, Free Online Tool

What economic order quantity is and why it saves money

Economic order quantity answers the most basic question in inventory management: how much should you buy or make in a single order? The answer matters because every order carries two opposing costs. Each time you place an order you incur a fixed ordering cost, the paperwork, receiving, inspection, and setup that happen no matter how large the order is.

And every unit you hold in stock carries a holding cost, the capital tied up plus storage, insurance, and the risk of obsolescence. Order in big batches and you place fewer orders, so ordering cost falls, but average inventory climbs and holding cost rises. Order in small batches and holding cost drops while ordering cost climbs.

EOQ is the order size where those two costs balance and their sum is at its lowest.

That balance point is not a guess. It follows directly from the math: total annual cost is the ordering cost times the number of orders plus the holding cost times the average inventory, and the order size that minimizes this sum is the square root of two times annual demand times ordering cost, divided by the annual holding cost per unit. The result is the quantity that neither over-orders, burying cash in stock, nor under-orders, wasting money on too many orders. Getting it right turns inventory from a guess into a controlled, minimized cost.

This calculator turns that logic into an immediate answer and shows the reasoning behind it. Enter your annual demand, the cost to place one order, and the cost to hold one unit for a year, and it returns the economic order quantity along with the numbers that matter: the total annual cost, how that splits between ordering and holding, how many orders a year that implies, the days between orders, and the average and maximum inventory. It also charts the ordering, holding, and total cost curves so you can see the total cost bottom out exactly at the EOQ, and it handles quantity discounts and production batches for the cases the textbook formula does not.

How this calculator works, step by step

Start with annual demand: enter how many units you use or sell in a year. Then enter the ordering cost, the fixed cost of placing one order, including administration, receiving, and inspection, or for in-house production, the setup or changeover cost. Finally enter the holding cost. You can type it directly as an amount per unit per year, or switch the holding-cost input to a percentage of unit cost, which is how most businesses actually think about carrying cost; the calculator then multiplies your unit cost by that percentage to get the holding cost per unit.

With those three inputs the calculator computes the economic order quantity and the full cost picture instantly, updating as you type. The large figure is the order quantity. Below it, the total annual cost and its split into ordering and holding cost show you exactly what the order size costs and why. The orders-per-year and days-between-orders figures translate the quantity into an ordering rhythm you can check against your suppliers and receiving capacity, and the average and maximum inventory show how much stock the policy carries. If you enter your current order size, the calculator also reports how much you would save per year by moving to the EOQ.

Two optional models handle the common real-world cases. Switch the model to production batch to size an economic production quantity when items are made gradually rather than delivered all at once, and enter your annual production rate. Switch it to quantity discounts and enter your supplier price breaks, one per line as a minimum quantity and its price, to find the order size with the lowest total cost including the purchase price. The chart updates for every case, and you can download a PDF or CSV or share the result. Everything runs in your browser and nothing you enter is stored.

The four inputs: demand, ordering cost, holding cost, and model

Annual demand is how many units you expect to use or sell in a year. It should reflect a representative full year, not a single busy or slow month, because EOQ assumes a steady pull. For seasonal items, an annual total still works for setting the order size; the timing of orders is handled separately by the reorder point.

Ordering cost is the fixed cost of placing one order, independent of its size. For purchased goods it is the administrative cost of raising a purchase order, receiving, inspecting, and paying for a shipment. For manufactured items it is the setup or changeover cost of a production run. Because it is charged once per order, a higher ordering cost pushes the EOQ up, favoring fewer, larger orders.

Holding cost is the cost of keeping one unit in stock for a year, covering the cost of capital, storage, insurance, shrinkage, and obsolescence. It is the force pulling the EOQ down: the more expensive it is to hold stock, the smaller and more frequent your orders should be. Entering it as a percentage of unit cost, commonly 15 to 30 percent, is often easier than estimating an absolute figure, and this calculator supports both.

The model selector chooses which version of the calculation to run. Standard EOQ assumes orders arrive all at once with no discounts. The production-batch model relaxes the instant-arrival assumption for items you make gradually, and the quantity-discount model relaxes the single-price assumption when suppliers reward larger orders. Each is explained in its own section below.

Five worked examples you can follow

Example 1: a standard purchased part

A distributor sells 12,000 units a year of a part. Placing an order costs $25, and holding one unit for a year costs $3. EOQ is the square root of two times 12,000 times 25 divided by 3, which is the square root of 200,000, about 447 units. At that size the firm places 12,000 divided by 447, roughly 27 orders a year, one about every 14 days. Annual ordering cost is 27 times $25, about $671, and annual holding cost is 447 divided by 2 times $3, also about $671. The two are equal, which is the signature of the EOQ, and the total is about $1,342.

Example 2: a higher ordering cost means larger orders

Take the same part but suppose each order now costs $100 to place, perhaps because of a long approval process. EOQ becomes the square root of two times 12,000 times 100 divided by 3, the square root of 800,000, about 894 units, exactly double the first example. The number of orders halves to about 13 a year. This shows the pull of ordering cost: when placing an order is expensive, the model batches more into each one to spread that fixed cost over more units.

Example 3: a higher holding cost means smaller orders

Now return to the $25 ordering cost but raise holding cost to $12 per unit per year, as it would be for a bulky or fast-obsolescing item. EOQ becomes the square root of two times 12,000 times 25 divided by 12, the square root of 50,000, about 224 units, half the first example. Orders rise to about 54 a year. Expensive stock pushes the model toward small, frequent orders so that little inventory sits idle, the mirror image of Example 2.

Example 4: holding cost as a percentage

Suppose the item costs $15 each and your carrying rate is 20 percent a year, so holding cost is $3 per unit, and annual demand and ordering cost are 12,000 and $25 as before. The EOQ is the same 447 units as Example 1, because the holding cost per unit is identical. Entering holding cost as a percentage simply lets you work from the unit price and a carrying rate rather than estimating an absolute figure, which is how most cost accountants build the number.

Example 5: a quantity discount changes the answer

A supplier charges $15 per unit, or $14.50 for orders of 500 or more, or $14.00 for 1,000 or more, with holding cost at 20 percent of the unit price. The basic EOQ at $15 is about 447 units, but that misses the purchase savings of buying more. Evaluating each tier, the total cost including purchase price is lowest at 1,000 units and the $14.00 price, because the drop in purchase cost outweighs the extra holding cost. The discount mode makes this comparison automatically and reports 1,000 units as the best order size, an answer the plain formula would never reach.

Three expert tips for using an order-quantity model

The EOQ formula, term by term

The formula is EOQ equals the square root of 2DS/H, and each term earns its place. D is annual demand and S is the ordering cost per order; their product with the number of orders drives the annual ordering cost, which falls as the order size grows because you place fewer orders. H is the annual holding cost per unit; multiplied by the average inventory, which is half the order size, it gives the annual holding cost, which rises as the order size grows. Total cost is the sum of those two.

The minimum of that sum is found where the two costs are equal, and solving that equality for the order quantity yields the square root expression. The two in the numerator and the division by H reflect that average inventory is half the order size, so holding cost is charged on Q/2 rather than Q. Read as a whole, the formula says: take twice the annual demand, weight it by how expensive each order is, and temper it by how expensive it is to hold a unit, then take the square root to land on the balancing quantity. The square root is why doubling the ordering cost multiplies the EOQ by about 1.4 rather than 2, a diminishing response that keeps order sizes stable against input errors.

Ordering cost versus holding cost: the trade-off at the heart of it

Every order-sizing decision is a tug-of-war between two costs that move in opposite directions as the order size changes. Ordering cost per year is the fixed cost per order times the number of orders, and since more units per order means fewer orders, this cost falls as the order size grows, following a curve that drops steeply at first and then flattens. Holding cost per year is the cost per unit times the average inventory, and since average inventory is half the order size, this cost rises in a straight line as the order size grows. One falls, the other rises.

Add the two and you get a U-shaped total-cost curve, and the bottom of that U is the EOQ. To the left of it, orders are too small and too frequent, so ordering cost dominates and total cost is high. To the right, orders are too large, so holding cost dominates and total cost is high again. Only at the EOQ, where the falling ordering-cost curve and the rising holding-cost line cross, is the sum minimized. This calculator draws all three curves so you can see the crossing point and the U-shaped total, which makes the trade-off concrete rather than abstract.

Entering holding cost two ways

Holding cost is the input people most often estimate loosely, and the calculator supports the two ways it is normally expressed. The direct method is an absolute amount per unit per year: if you know it costs $3 to keep one unit in stock for a year, enter that. The percentage method starts from the item unit cost and a carrying rate: enter the unit cost and a rate such as 20 percent, and the calculator computes the holding cost per unit as unit cost times rate. The two are equivalent, and which you use is a matter of what information you have.

The percentage method is usually the more honest one, because holding cost is dominated by the cost of capital tied up in the item, which is naturally a percentage of its value. A carrying rate bundles that cost of capital with storage, insurance, shrinkage, and obsolescence into a single figure, commonly 15 to 30 percent a year, that you can apply consistently across items. It also matters for quantity discounts: when a discount lowers the unit price, the percentage method automatically lowers the holding cost too, since holding a cheaper unit ties up less capital, which the discount comparison needs to be correct.

Quantity discounts: when buying more is genuinely cheaper

The basic EOQ ignores the purchase price of the goods because it assumes the price is fixed, so buying more never changes the per-unit cost. Quantity discounts break that assumption: suppliers often drop the unit price at higher order volumes, and then the purchase cost itself becomes part of the decision. Buying a larger quantity to reach a lower price raises holding cost but can cut the far larger purchase cost, so the cheapest order size may be well above the plain EOQ.

The method the calculator uses is the standard price-break procedure. For each price tier it computes the EOQ at that price, then checks whether that quantity actually falls in the range that earns the price; if the EOQ is below the tier minimum, it is raised to that minimum, the smallest quantity that unlocks the price.

It then computes the full annual cost, purchase plus ordering plus holding, for each candidate and picks the lowest. Because holding cost is often a percentage of the unit price, a lower price also lowers holding cost, which the calculator accounts for.

Enter your price breaks in discount mode and it reports the true lowest-cost order quantity and the price it earns, a comparison that is tedious by hand and easy to get wrong.

The production batch model (EPQ)

Standard EOQ assumes an order arrives all at once, so the moment it lands, inventory jumps by the full order quantity. That fits purchased goods delivered in one shipment, but not items you produce in-house, where units are made a few at a time and some are consumed even as production continues. For that case the economic production quantity, or EPQ, adjusts the model: because stock builds gradually rather than instantly, the maximum inventory is lower than the batch size, and the optimal batch is correspondingly larger.

EPQ multiplies the basic EOQ by a factor based on the ratio of the production rate to the difference between the production and demand rates. When production is much faster than demand, the factor approaches one and EPQ nears EOQ; when production only slightly outpaces demand, the factor grows and the optimal batch is much larger. The maximum inventory is the batch size times one minus the ratio of demand to production, which is why EPQ carries less peak stock than EOQ for the same batch. Switch the model to production batch and enter your annual production rate to size a run this way; the calculator reports the optimal batch and the lower maximum inventory it produces.

Why the total cost curve is forgiving

One of the most useful and least appreciated properties of EOQ is that its total-cost curve is flat near the bottom. Because the curve is shaped like a shallow bowl around the optimum, ordering a quantity somewhat above or below the exact EOQ raises total cost only slightly. Ordering 20 percent more or less than the EOQ typically raises the combined ordering and holding cost by only about 2 percent. This robustness is what makes EOQ practical despite its strong assumptions.

The flat curve has two important consequences. First, small errors in the inputs, an ordering cost that is a bit off or a holding rate that is an estimate, barely move the resulting cost, so you do not need perfect data to get most of the benefit. Second, you can round the EOQ to a convenient lot size, a full pallet, a case pack, or a supplier minimum, without meaningfully increasing cost. Compute the EOQ for the target, then round to whatever the real world orders in; the model expects you to. This is why EOQ has survived as the anchor of inventory policy for over a century even though real demand is never perfectly steady.

EOQ assumptions and their limits

The classic model rests on a set of simplifying assumptions, and knowing them tells you when to trust it and when to reach for a variant. It assumes demand is known and steady, that ordering cost and holding cost per unit are constant, that the whole order arrives at once after a known lead time, that no stockouts occur, and that there are no quantity discounts. Real inventory rarely satisfies all of these at once, which is why the raw formula is a starting point rather than the last word.

The variants exist precisely to relax the assumptions that bite. When orders earn volume discounts, the discount model adds the purchase price to the decision. When items are produced gradually rather than delivered at once, the EPQ model adjusts for the build-up rate. When demand varies, EOQ still sets a sensible order size from average demand, and safety stock and a reorder point handle the variability separately. The one assumption that no variant removes is that some steady average demand exists to plan around; for truly erratic or one-off demand, EOQ is the wrong tool, and a project or make-to-order approach fits better.

A century-old idea that still holds

The order-quantity model is one of the oldest quantitative tools in management, and its longevity is a testament to how well the underlying trade-off captures reality. Ford W. Harris, an engineer at Westinghouse, derived it in 1913, reasoning that the most economical lot to manufacture balanced the setup cost of a run against the interest and storage cost of the resulting stock. The consultant R. H. Wilson later popularized it for purchasing, which is why the formula is sometimes called the Wilson formula or the Wilson EOQ. More than a century later, the same square-root expression sits inside virtually every inventory and enterprise-planning system in use.

It endures for two reasons. The trade-off it models, fixed cost per order against cost per unit held, is genuinely universal: it applies whether the order is a purchase, a production run, or a cash transfer, which is why the same math reappears in finance as the cash-management model. And its forgiving cost curve means the model delivers most of its benefit even when the inputs are rough and the assumptions imperfect, so it remains useful in messy real operations rather than only in theory. Understanding where it came from also makes its assumptions explicit, which is the key to knowing when to trust the plain formula and when to reach for a variant.

Common mistakes when applying EOQ

A handful of errors cause most EOQ results to mislead. Watch for these before acting on a number.

• Understating ordering cost. Counting only the purchase-order fee and ignoring receiving, inspection, and setup makes the model order too little too often. Capture the full fixed cost of an order.
• Guessing holding cost too low. Leaving out the cost of capital, the largest component, understates holding cost and inflates the EOQ. Build it from a realistic carrying rate.
• Mismatched time units. Demand must be annual and holding cost must be per year for the formula to balance. Mixing a monthly demand with an annual holding cost gives a nonsense answer.
• Ignoring quantity discounts. Running plain EOQ when the supplier offers price breaks can miss a cheaper order size. Use the discount mode whenever price depends on volume.
• Using EOQ for erratic demand. EOQ assumes steady demand. For spiky or one-off items it gives a misleading order size; plan those differently.
• Treating EOQ as the reorder trigger. EOQ says how much to order, not when. Pair it with a reorder point, or you will order the right quantity at the wrong time.
• Refusing to round. Insisting on the exact EOQ instead of a practical lot ignores the flat cost curve and creates awkward orders for no real saving.

How EOQ connects to reorder point and safety stock

EOQ is one piece of a complete inventory policy, and it works alongside two others. EOQ answers how much to order in one batch. The reorder point answers when to place that order: it is the on-hand level, equal to expected demand during the lead time plus a safety buffer, at which replenishment should be triggered. Safety stock answers how large that buffer should be to absorb variability in demand and lead time. Together they form a policy: order EOQ units whenever stock falls to the reorder point, and hold safety stock to cover the uncertainty in between.

Seeing the three together clarifies what each does and does not do. EOQ minimizes the cost of ordering and holding under steady demand but says nothing about timing or uncertainty. The reorder point and safety stock handle timing and uncertainty but say nothing about the economical order size. A firm that computes only EOQ will order the right amount at unpredictable times; one that sets only a reorder point will order at the right time but perhaps in an uneconomical quantity. This calculator sizes the order; pair it with a reorder point and safety stock, both launching soon in this hub, to build the full policy.

Reading this calculator’s results panel

The panel is built to be read as a policy decision, not just a single number. The large figure is the economic order quantity, the headline answer for how much to order at once. Directly below, the total annual cost and its split into ordering and holding cost show what that order size costs and confirm the balance: at the EOQ, ordering and holding cost are equal, so if they are far apart the inputs or the model may not fit. The orders-per-year and days-between-orders lines translate the quantity into an ordering rhythm you can sanity-check against your suppliers.

The average and maximum inventory lines show how much stock the policy carries, which is what the holding cost is paid on, and the holding-cost-per-unit line confirms the figure the model actually used, useful when you entered it as a percentage. In discount mode, extra lines report the best order quantity and the unit price it earns; in production-batch mode, the maximum inventory reflects the gradual build-up. If you entered a current order size, the savings line shows the annual cost difference of moving to the EOQ. The chart ties it together, plotting ordering, holding, and total cost against order quantity so the minimum sits visibly at the EOQ.

Read in sequence, the panel walks you from decision to consequence. First the order quantity itself, then what it costs and how that cost divides, then how often you will order and how much stock you will carry as a result.

That order matters because the best order size is rarely obvious from the demand and cost figures alone; the value of the model is in exposing the hidden holding cost that grows with every extra unit ordered and the hidden ordering cost that grows with every extra order placed.

Seeing both, and their sum, on one screen turns an inventory rule of thumb into a defensible number you can put in front of a supplier or a finance team, and the export buttons let you carry exactly that evidence out of the browser as a PDF or CSV.

Units and quick reference

Keep demand annual and holding cost per year; everything else follows. Demand is units per year, ordering cost is currency per order, holding cost is currency per unit per year (or a percentage of unit cost), and the EOQ comes back in units. Orders per year is demand divided by EOQ, and days between orders is 365 divided by that. The reference below shows how a few input combinations size out, so you can sanity-check your own case. Notice how doubling the ordering cost multiplies the EOQ by about 1.4, not 2, and how raising the holding cost shrinks it, the square-root response that keeps order sizes stable.

Economic order quantity frequently asked questions

Sources, disclaimer, and editorial transparency

The EOQ formula, the quantity-discount procedure, and the production-batch (EPQ) variant used here follow recognized operations-management sources, including Ford W. Harris’s original 1913 derivation, the APICS/ASCM body of knowledge, and standard inventory-management texts. This calculator and guide are built and reviewed by the OpsCalculators team; see our Editorial Policy for how each tool is researched, built, and tested.

Results are accurate estimates for planning and education, not certified engineering or financial advice. Validate outputs against your own measured demand, cost data, and supplier terms before changing inventory policy or committing capital. See our full Disclaimer. OpsCalculators.com is operated by MAFHH INTERNATIONAL LTD. Your inputs are processed in your browser and are never stored; see our Privacy Policy.