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Inventory & supply chain

EOQ calculator — economic order quantity and total cost

Calculate economic order quantity from annual demand, order cost and holding cost. See the total cost curve against your current order quantity.

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Short answer

EOQ is the square root of (2 × annual demand × cost per order ÷ annual holding cost per unit). At 48,000 units a year, $180 per order and $3.00 to hold a unit for a year, EOQ is 2,400 units — 20 orders a year, with ordering and holding cost both $3,600.

Every order size is a trade. Order in large batches and you pay to hold stock you will not touch for months. Order in small ones and you pay the buyer, the carrier and the receiving dock over and over. EOQ is the batch size where those two costs are lowest in total.

Enter annual demand, what one purchase order really costs you, and the cost of holding a unit for a year. The calculator returns EOQ, the resulting order frequency, and the full cost curve so you can see how much your current order quantity is costing.

Your numbers

units

Forecast units for the next 12 months. Annualise a recent 13-week run rate if last year is not representative.

$

Buyer time, approvals, per-delivery freight, receiving and inspection. Not the price of the goods.

$

Landed cost per unit. Used for holding cost and average stock value.

Holding cost basis
%

Cost of capital, space, insurance, shrink and obsolescence. Most policies land between 18% and 30%.

units

What you order today, so the cost comparison is against reality.

Result

Economic order quantity
2,400 units

20.0 orders a year, about every 18.3 days

Holding cost per unit per year$3.00
Average cycle stock at EOQ1,200 units · $15,000
Annual ordering cost at EOQ$3,600
Annual holding cost at EOQ$3,600
Total relevant cost at EOQ$7,200
Total at your 4,000 units$8,160
H = $12.50 × 24% = $3.00 per unit per year
2 × D × S = 2 × 48,000 × $180 = 17,280,000
÷ H = 17,280,000 ÷ $3.00 = 5,760,000
EOQ = √5,760,000 = 2,400 units
Check: ordering $3,600 = holding $3,600 at EOQ
Total relevant cost at EOQ (2,400 units)$7,200
Total relevant cost at your 4,000 units$8,160
Moving from 4,000 to 2,400 units per order changes total ordering plus holding cost by $960 a year (11.8%) and releases 800 units of average stock, worth $10,000. Check case packs and supplier minimums before you change the policy.
The cost curve. Purchase cost is excluded because it does not change with order size — only ordering and holding do.
Order quantityOrders/yrOrderingHoldingTotal
1,200 (½ × EOQ)40.0$7,200$1,800$9,000
1,800 (¾ × EOQ)26.7$4,800$2,700$7,500
2,400 (EOQ)20.0$3,600$3,600$7,200
3,600 (1½ × EOQ)13.3$2,400$5,400$7,800
4,000 (yours)12.0$2,160$6,000$8,160
4,800 (2 × EOQ)10.0$1,800$7,200$9,000

Everything is computed in your browser. Nothing you type is sent anywhere or stored.

The formula

EOQ = √(2 × D × S ÷ H)
D
Annual demand in units. Use forecast demand for the next 12 months, not last year's shipments, if the two differ.
S
Cost to place and receive one order: buyer time, approvals, inbound freight per delivery, receiving and inspection. Not the price of the goods.
H
Cost to hold one unit for one year. Either entered directly, or unit cost × annual carrying rate (capital, storage, insurance, shrink, obsolescence).
Total relevant cost
(D ÷ Q) × S + (Q ÷ 2) × H. Purchase cost D × unit price is excluded because it does not change with order size.

EOQ is the quantity where annual ordering cost and annual holding cost are equal — that equality is a consequence of the formula, and a fast way to check your arithmetic. It assumes constant demand, a fixed order cost and no quantity breaks.

Worked example

Annual demand
48,000 units
Cost per purchase order
$180
Unit cost
$12.50
Annual carrying rate
24%
Your current order quantity
4,000 units
Result
EOQ = 2,400 units · $7,200 total relevant cost · $960 a year saved

Holding cost is $12.50 × 24% = $3.00 per unit per year. EOQ = √(2 × 48,000 × 180 ÷ 3) = √5,760,000 = 2,400 units, which is 20 orders a year at $3,600 of ordering cost and $3,600 of holding cost. Ordering 4,000 at a time instead costs $2,160 + $6,000 = $8,160, so the smaller, more frequent order saves $960 a year and releases $10,000 of average stock value.

The trade-off, and why the curve is flat

Total relevant cost is (D ÷ Q) × S for ordering plus (Q ÷ 2) × H for holding. At the example numbers, ordering 1,800 units instead of the 2,400-unit EOQ costs $7,500 against $7,200 — 4.2% more for being 25% off. Ordering 3,600 costs $7,800, or 8.3% more.

That flatness is the practical point of the economic order quantity: you do not need the exact answer. You need to know whether you are near the bottom of the curve or at 4,000 units where the penalty is $960 a year on one SKU. Round EOQ to a pallet, a case pack or a supplier minimum without guilt.

Order quantity vs EOQTotal relevant costPenalty
½ × EOQ (1,200)$9,000+25.0%
¾ × EOQ (1,800)$7,500+4.2%
EOQ (2,400)$7,200—
1½ × EOQ (3,600)$7,800+8.3%
2 × EOQ (4,800)$9,000+25.0%
At D = 48,000 units, S = $180, H = $3.00. Small batches are punished harder than large ones.

Where the EOQ assumptions break

EOQ is a 1913 model and it shows. It is still the right starting point for a stable, purchased item, and the wrong tool the moment one of these holds:

AssumptionWhat actually happensWhat to do
Demand is constant and knownDemand is seasonal or lumpy, so a year-average EOQ over-buys in the trough.Recompute per season, or use the recent 13-week run rate annualised.
Unit price is independent of quantitySuppliers offer price breaks at 5,000 units.Compare total cost including purchase price at each break point, not EOQ alone.
Any quantity can be orderedCase packs, pallet quantities and supplier minimums exist.Round to the nearest legal quantity — the curve is flat, so the penalty is small.
Order cost is fixed per orderThe real cost is mostly buyer time, which falls to near zero on an automated blanket release.Recalculate S honestly; a low S drives many small orders, which is the point of vendor-managed replenishment.
Replenishment is instant, no stockoutsLead time exists and demand varies during it.EOQ sets how much; safety stock and the reorder point set when.
Holding cost is knownThe carrying rate is a policy assumption, often 18–30%, and the answer moves with it.Build it from components with the inventory carrying cost calculator.

Getting D, S and H out of your ERP

Annual demand is a query. Ordering cost is an internal costing exercise — total purchasing department cost divided by purchase order lines is a defensible first pass. Holding cost is a policy number your CFO should sign, because it decides how much stock the whole business carries.

Ask for "units received and order line count by item for the last 12 months, top 50 items by value" and you have D and the order frequency you are actually running, with the SuiteQL shown so you can check what counted as a receipt.

Frequently asked questions

What is the EOQ formula?

EOQ = √(2DS ÷ 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. With D = 48,000, S = $180 and H = $3.00, EOQ is √(17,280,000 ÷ 3) = √5,760,000 = 2,400 units.

Why does EOQ ignore the purchase price of the goods?

Because buying 48,000 units a year costs the same whether you take them in four deliveries or forty. Purchase cost is constant with respect to order size, so it drops out of the optimisation. It comes back the moment a supplier offers a quantity discount, which EOQ alone cannot evaluate.

How do you calculate holding cost per unit?

Multiply unit cost by an annual carrying rate. The rate adds cost of capital, warehouse space and handling, insurance and tax, plus shrink and obsolescence. Most rates land between 18% and 30%. At $12.50 unit cost and 24%, holding cost is $3.00 per unit per year.

What is the difference between EOQ and reorder point?

EOQ answers how much to order; the reorder point answers when. EOQ comes from ordering and holding costs. The reorder point comes from demand during lead time plus safety stock. You need both, and changing one does not change the other.

Is EOQ still useful with quantity discounts?

Yes, as the first step. Calculate EOQ, then compare total annual cost — purchase plus ordering plus holding — at EOQ against each price-break quantity. A discount that forces four months of stock often loses to a smaller order once holding cost is charged honestly.

How often should EOQ be recalculated?

When demand shifts by more than about 20%, when unit cost changes, or when your carrying rate is revised. Because EOQ moves with the square root of demand, doubling demand raises the order quantity only 41%, so small forecast changes rarely justify a new purchase policy.

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