EOQ(Economic Order Quantity) Calculator

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Economic order quantity (EOQ)

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Table of Contents

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What is EOQ Calculator?

Economic order quantity, usually shortened to EOQ, estimates the replenishment size that balances two recurring inventory costs: the cost of placing orders and the cost of holding units. Ordering in small batches creates more orders; ordering in large batches raises average inventory. The classic EOQ is the point where their combined annual cost is lowest under the model’s assumptions.

This page uses annual demand, cost per order and annual holding cost per unit. It returns units per order. It does not choose a reorder date, safety stock, supplier or service level, and it does not model quantity discounts.

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How to Use This Calculator

  1. Estimate yearly demand in units for the same item and planning horizon.
  2. Enter the administrative and receiving cost caused by one replenishment order. Avoid including the purchase price per unit unless it genuinely changes per order.
  3. Enter annual holding cost for one unit. This can combine storage, insurance, shrinkage, obsolescence and the opportunity cost of tied-up capital when those components are measured consistently.
  4. Select the same currency for order cost and holding cost. The currency cancels in the ratio, but the two costs still must use one currency.
  5. Calculate, then round the theoretical quantity to a feasible pack, pallet or supplier minimum. Compare nearby practical quantities because the cost curve is often fairly flat around EOQ.

All time bases must agree. If demand covers one year, holding cost must also be per unit per year. For a monthly model, both should be placed on a monthly basis; the label on this form is specifically yearly.

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Formula Used

EOQ = √(2DS / H)

D is demand per year, S is ordering cost per order and H is annual holding cost per unit. Under the basic model, annual ordering cost is (D/Q)S and annual holding cost is (Q/2)H, where Q is the chosen order quantity. At EOQ these two variable cost components are equal.

Unit purchase cost is absent because, when it is constant for every quantity, annual purchase cost does not change the minimizing order size. If suppliers offer quantity discounts, the basic square-root result is only a candidate and total cost should be checked at the relevant price-break quantities.

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Variables Explained

Symbol or resultMeaning and unit
DExpected yearly demand, in units per year.
SIncremental ordering or setup cost for one order, in the selected currency per order.
HHolding cost for one unit for one year, in the same currency per unit-year.
QOrder quantity being considered, in units per order.
EOQThe model’s cost-balancing order quantity, in units per order.
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Worked Example

A part has expected annual demand of 10,000 units. Processing one purchase order costs $25, and carrying one unit for a year costs $2. Enter D = 10,000, S = 25 and H = 2:

EOQ = √((2 × 10,000 × 25) / 2) = √250,000 = 500 units. At that quantity, the model implies 10,000 / 500 = 20 orders per year. Average cycle inventory is 500 / 2 = 250 units.

Annual ordering cost is 20 × $25 = $500. Annual cycle-stock holding cost is 250 × $2 = $500. Their equality is a useful check. If cartons contain 24 units, practical candidates might be 480 or 504. Evaluate the real ordering and holding costs at both rather than assuming the unrounded answer can be purchased.

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Why Use This Calculator?

EOQ is a planning benchmark, not an instruction to order immediately. The reorder point answers a different question: when to replenish given demand during lead time and any safety stock. A business can use EOQ for order size and a separate reorder-point calculation for timing.

The classic result assumes stable, known demand; constant lead time; replenishment arriving as a batch; no stockouts; and costs that stay constant. Seasonal demand, uncertain lead times, perishability and warehouse constraints weaken those assumptions. Review the quantity whenever demand, freight, labor, interest rates or storage costs change materially.

A fractional output is a mathematical optimum. Physical items may need a whole number, case quantity or truckload. Because total relevant cost changes slowly near its minimum, a convenient nearby quantity can be sensible. Document the operational reason for rounding and check capacity and shelf life.

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Common Mistakes

    • Entering total annual holding cost: H must be the annual cost for one unit.
    • Using purchase price as order cost: S is the incremental cost of placing one order.
    • Mixing monthly and annual inputs: demand and the holding-cost period must match.
    • Mixing currencies: the page requires matching order-cost and holding-cost selectors and performs no exchange conversion.
    • Confusing EOQ with reorder point: quantity and timing solve separate decisions.
    • Ignoring price breaks or constraints: supplier minimums, storage limits and discounts require a broader total-cost comparison.
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Frequently Asked Questions

Does EOQ include safety stock?

No. The basic formula balances cycle-stock ordering and holding costs. Add safety stock through an inventory policy suited to demand and lead-time uncertainty.

Is EOQ the same as a reorder point?

No. EOQ estimates how much to order. A reorder point estimates the inventory position at which an order should be released.

Why must holding cost be per unit per year?

The formula pairs annual demand with annual holding cost for one unit. A total warehouse cost or a monthly rate has a different dimension and changes the answer.

Can I round the EOQ?

Yes. Compare feasible quantities around the result, such as full cartons or pallets. The lowest practical total cost may be close to the theoretical quantity.

What if the supplier offers quantity discounts?

Calculate total purchase, ordering and holding cost at the feasible price breaks. The standard EOQ alone does not optimize a tiered price schedule.

How often should EOQ be updated?

Recalculate when expected demand, ordering cost, holding cost, pack size or supply conditions change enough to affect the inventory decision.

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Sources & References

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