An EOQ calculator answers one question: how much should you order at a time? Order in small batches and you pay the fixed cost of placing an order many times a year. Order in large batches and you tie up cash in stock that sits on a shelf accruing storage, insurance and the risk of never selling. The economic order quantity is the batch size where the sum of those two costs is at its lowest.
That is deliberately a different question from when to order. The live reorder point calculator already answers the timing question — it takes demand, lead time and a service level and tells you the stock level that should trigger a purchase, including the safety stock buffer. This page never touches lead time or service level. Use the reorder point tool to decide the trigger, and this one to decide the quantity that gets ordered when the trigger fires. Arb Digital publishes both in the free tool library at arbsbuy.com so the two decisions stay separate, because conflating them is how businesses end up ordering the right amount at the wrong moment.
What This EOQ Calculator Does
Enter annual demand for one item, the fixed cost of placing an order, the unit purchase cost and an annual holding cost rate. The calculator derives the holding cost per unit per year, solves for the order quantity that minimises total relevant cost, and reports it as the headline.
The supporting figures translate that quantity into an operating rhythm. Orders per year and days between orders tell you what the answer means for the purchasing team. The annual ordering cost and annual holding cost tiles show the two components being balanced — at the economic quantity they are equal, which is a useful self-check that the arithmetic behind the page is behaving.
The optional current-order-quantity field is where most of the practical value sits. Very few businesses are ordering at the economic quantity, and the interesting number is rarely the theoretical optimum. It is the annual cost penalty of the quantity you use today, which is what turns this from an academic exercise into a purchasing decision.
How to Use It
- Work one SKU at a time. EOQ is a per-item calculation. Aggregating a category and dividing produces a number that is optimal for nothing.
- Build the ordering cost from fixed components only. Anything that scales with the number of units belongs in the unit cost, not here, or the model double-counts it.
- Construct your own holding rate. Add the cost of capital tied up, warehouse space, insurance, handling, shrinkage and obsolescence risk for that specific item. A slow-moving fashion line and a staple component do not share a rate.
- Enter your current order size and read the penalty. If it is small, the current practice is fine and you have better problems to solve.
- Sanity-check the answer against reality — pallet quantities, minimum order quantities, shelf life and supplier break points all constrain what you can actually order.
The Formula / How It's Calculated
The economic order quantity is EOQ = √(2DS ÷ H), where D is annual demand in units, S is the fixed cost of placing one order, and H is the cost of holding one unit for one year. Here H is derived as unit cost × holding rate.
The formula comes from adding two costs and finding the minimum. Annual ordering cost is (D ÷ Q) × S — the number of orders times the cost of each. Annual holding cost is (Q ÷ 2) × H, because average inventory under a steady draw-down from Q to zero is Q divided by two. The first falls as Q rises, the second rises as Q rises, and the total is at its minimum where they are equal. Setting them equal and solving for Q gives the square root formula directly.
Work the defaults. Annual demand is 24,000 units, ordering cost 180 per order, unit cost 15 and holding rate 22 percent, so H = 15 × 0.22 = 3.30 per unit per year. EOQ = √(2 × 24,000 × 180 ÷ 3.30) = √(8,640,000 ÷ 3.30) = √2,618,181.82 = 1,618.08 units.
Check the two costs at that quantity. Orders per year = 24,000 ÷ 1,618.08 = 14.83, so annual ordering cost is 14.83 × 180 = 2,669.8. Average inventory is 1,618.08 ÷ 2 = 809.04 units, so annual holding cost is 809.04 × 3.30 = 2,669.8. They match, as the derivation requires, and total relevant cost is 5,339.6. Days between orders is 365 ÷ 14.83 = 24.6.
Now compare the default current quantity of 3,000. Ordering cost becomes 24,000 ÷ 3,000 × 180 = 1,440, holding cost becomes 1,500 × 3.30 = 4,950, and the total is 6,390 — a penalty of 1,050 a year, or 19.7 percent above the optimum, on a single SKU.
The Cost Curve Is Flat Near the Bottom
This is the single most useful and least discussed property of the model, and it changes how the answer should be used. The total cost curve is very shallow around the optimum, so being somewhat wrong about the order quantity costs remarkably little.
Order 20 percent above the economic quantity and total relevant cost rises by about 1.7 percent. Order 50 percent above it and the penalty is around 8 percent. You have to be roughly double or half the optimum before the cost penalty reaches 25 percent. The default comparison above illustrates it: 3,000 units is 85 percent above the economic quantity of 1,618, and even that produces only a 19.7 percent penalty.
Two practical consequences follow. First, precision in the inputs matters much less than people assume — if you are unsure whether your holding rate is 18 or 26 percent, calculate both and you will usually find the recommended quantities are close enough that the difference is immaterial. Second, rounding to a practical quantity is nearly free. Rounding 1,618 up to a full pallet of 1,800 or down to 1,500 costs a fraction of a percent, so operational convenience should win over arithmetic purity almost every time.
Building an Honest Holding Rate
The holding rate is the input that decides the answer, and it is the one most often taken from a textbook rather than from the business. It has five components and they are all specific to your operation and to the item.
The cost of capital comes first: money in inventory is money not available elsewhere, and the right rate is your actual cost of funds rather than a nominal figure. Storage is second — the space, racking, heating or refrigeration the item occupies. Insurance and handling follow. Shrinkage covers damage and loss in handling. Obsolescence is last and is usually the largest and most variable component: a staple fastener has almost none, while a seasonal or perishable line can carry a very high effective rate because unsold stock loses most of its value at a known date.
Two items in the same warehouse can therefore justify rates that differ by a factor of three, and applying a single blended rate across a catalogue systematically over-orders the risky items and under-orders the safe ones. Accounting standards give some structure to what is capitalised into inventory rather than expensed — IAS 2 Inventories sets out the measurement basis under IFRS, and the Internal Revenue Service's Publication 538 on accounting periods and methods covers the equivalent US inventory rules — but a holding rate is a management figure, not an accounting one, and building it is your job.
The Assumptions and When They Break
The classical model rests on four assumptions, and knowing which one your situation violates tells you how to adjust the answer.
It assumes demand is constant and known. Real demand varies, which is exactly what safety stock exists to absorb — and safety stock is a timing decision, handled by the reorder point rather than by the order quantity. Because the cost curve is flat, moderate demand variability does not move the economic quantity much, which is why the two decisions can be separated cleanly in the first place.
It assumes the whole order arrives at once. If your supplier delivers gradually while you are consuming the item, the production-order-quantity variant applies and the correct batch is larger, because average inventory never reaches the full order size. It assumes no quantity discounts, which is the assumption most often broken in practice: when a supplier offers a price break, the right method is to calculate total cost including purchase price at the economic quantity and at each break point, then choose the lowest — a comparison this page's total-cost figures let you run manually. It also assumes the fixed ordering cost really is fixed, which fails when freight is charged per container or when a minimum order value applies.
Finally, it says nothing about capital availability. A business that is short of working capital may rationally order below the economic quantity, accepting a small cost penalty to keep cash free. The working capital calculator and the cash conversion cycle calculator are the right places to weigh that trade-off, because inventory is usually the largest single component of both.
Where the Answer Meets the Warehouse
An economic quantity of 1,618 units is a mathematical result, not an order. Several real constraints will reshape it, and because the cost curve is flat, letting them win is usually correct.
Case and pallet quantities come first — ordering a part-pallet often costs more in handling than the model saves. Supplier minimums may set a floor below which the quantity is not available at all. Shelf life sets a ceiling: if 1,618 units represents 24.6 days of stock and the product expires in three weeks, the model's answer is unusable regardless of what it costs. Storage capacity does the same in physical terms.
It is also worth checking the result against how fast stock actually moves. At the economic quantity here, average inventory is 809 units against annual demand of 24,000, implying inventory turns of roughly 29.7 times a year for this item — a figure the inventory turnover calculator puts in context against the rest of your catalogue. The Census Bureau's Manufacturing and Trade Inventories and Sales series publishes aggregate inventory-to-sales ratios for US retail, wholesale and manufacturing, which is a reasonable sanity check on whether your overall stock position is unusual for your sector.
Arb Digital builds long-term online growth programmes for product businesses, so demand rises against the same warehouse and the same holding cost.
Web Growth Services Talk to Arb DigitalCommon Mistakes to Avoid
- Putting variable costs in the ordering cost — anything that scales with units belongs in the unit cost, or the model double-counts it and inflates the order size.
- Using one holding rate for every SKU — obsolescence risk varies enormously by item, and a blended rate over-orders exactly the lines you should hold least of.
- Running EOQ on a category — the formula is per item, and an aggregate answer is optimal for no individual product.
- Ignoring quantity discounts — when a price break exists, compare total cost including purchase price at each break rather than taking the unconstrained EOQ.
- Treating the result as a reorder trigger — this is how much to order, not when. Lead time and service level belong in the reorder point calculation.
Related Free Tools From Arb Digital
Pair this with the reorder point calculator for the timing decision and safety stock, the inventory turnover calculator for how fast stock moves, the FIFO LIFO inventory calculator for valuing what is on hand, the COGS calculator for the cost that flows to the income statement, the working capital calculator for the cash tied up, and the shipping cost per item calculator for inbound freight. The full free online tools hub lists everything else.
Frequently Asked Questions
EOQ is the square root of two times annual demand times the fixed cost per order, divided by the annual holding cost per unit. It is the quantity at which annual ordering cost and annual holding cost are equal.
EOQ answers how much to order and depends on demand, ordering cost and holding cost. The reorder point answers when to order and depends on lead time, demand during that lead time and the safety stock you choose to hold.
Add the cost of capital tied up in stock, storage, insurance, handling, shrinkage and obsolescence risk for that specific item, then express the total as a percentage of unit cost per year. It should differ between fast staples and slow or perishable lines.
Less than most people expect, because the total cost curve is flat near its minimum. Ordering twenty percent above the economic quantity raises total relevant cost by under two percent, so rounding to a practical pallet or case size is close to free.
Not directly, because the basic model assumes a constant unit price. The standard approach is to compute total cost including purchase price at the unconstrained EOQ and at each discount break point, then take whichever is lowest.
Per product. Demand, ordering cost and holding cost differ item by item, and averaging them across a category gives an answer that is not optimal for any single line in it.
Because the basic model assumes stock arrives all at once and is drawn down at a steady rate to zero before the next delivery. The average of a straight line from the order quantity to zero is the order quantity divided by two.
This calculator performs arithmetic on figures you supply and is provided for general information only. It is not accounting, tax or purchasing advice, and the classical model rests on assumptions that may not hold in your operation — confirm any figure used in a purchasing commitment or in accounts with a qualified professional.
