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EOQ Calculator (Economic Order Quantity)

Calculate economic order quantity from annual demand, order cost, and yearly holding cost, with orders per year, days between orders, and relevant inventory costs.

Published

Optimal order size
Economic order quantity
1,581.14 units
Orders per year
316.23
Days between orders
1.15 days
Annual ordering cost
$3,162.28
Annual holding cost
$3,162.28
Total relevant cost
$6,324.56

Order about 1,581 units at a time to balance $10.00 order costs with $4.00 yearly carrying cost per unit.

Expected units sold or used during one year.
units
Fixed cost to place one purchase or production order.
$
Annual carrying cost for keeping one unit in inventory.
$

Results update as you type.

EOQ Calculator (Economic Order Quantity)

The EOQ calculator finds the economic order quantity for a product, raw material, spare part, or supply item. Enter yearly demand, the fixed cost to place one order, and the yearly holding cost for one unit. The result is the order size that balances ordering cost and inventory carrying cost, plus orders per year, days between orders, annual ordering cost, annual holding cost, and total relevant cost.

Economic order quantity is an inventory-management model. It asks how many units should be ordered each time when demand is reasonably steady and the key trade-off is between ordering too often and holding too much stock. Small orders reduce average inventory but create many purchase orders, setup runs, receiving events, or shipment fees. Large orders reduce order frequency but raise average inventory, storage cost, insurance, shrinkage, obsolescence, and capital tied up in stock. EOQ sits at the point where those two cost pressures are balanced.

Formula

The classic EOQ formula is:

EOQ=2×annual demand×order costyearly holding cost per unit\text{EOQ} = \sqrt{\frac{2 \times \text{annual demand} \times \text{order cost}}{\text{yearly holding cost per unit}}}

Using the common variable names:

EOQ=2DSH\text{EOQ} = \sqrt{\frac{2DS}{H}}

where D is annual demand, S is cost per order, and H is annual holding cost per unit. The calculator also computes:

orders per year=annual demandEOQ\text{orders per year} = \frac{\text{annual demand}}{\text{EOQ}}

days between orders=365orders per year\text{days between orders} = \frac{365}{\text{orders per year}}

annual ordering cost=orders per year×order cost\text{annual ordering cost} = \text{orders per year} \times \text{order cost}

annual holding cost=EOQ2×holding cost per unit\text{annual holding cost} = \frac{\text{EOQ}}{2} \times \text{holding cost per unit}

total relevant cost=annual ordering cost+annual holding cost\text{total relevant cost} = \text{annual ordering cost} + \text{annual holding cost}

All three inputs must be positive. A zero or negative value makes the model invalid because the square-root expression or cost trade-off no longer represents a usable inventory decision.

Worked example using the calculator defaults

The default inputs are 500,000 units of yearly demand, $10 order cost, and $4 yearly holding cost per unit. The calculation determines

EOQ=2×500,000×$10$4\text{EOQ} = \sqrt{\frac{2 \times 500{,}000 \times \$10}{\$4}}

EOQ=2,500,000=1,581.14 units\text{EOQ} = \sqrt{2{,}500{,}000} = 1{,}581.14 \text{ units}

The result panel reports Economic order quantity: 1,581.14 units. It then divides demand by EOQ:

orders per year=500,0001,581.14=316.23\text{orders per year} = \frac{500{,}000}{1{,}581.14} = 316.23

The spacing between orders is:

days between orders=365316.23=1.15 days\text{days between orders} = \frac{365}{316.23} = 1.15 \text{ days}

Annual ordering cost is:

316.23×$10=$3,162.28316.23 \times \$10 = \$3{,}162.28

Annual holding cost is:

1,581.142×$4=$3,162.28\frac{1{,}581.14}{2} \times \$4 = \$3{,}162.28

Total relevant cost is therefore about $6,324.56. The near equality of ordering cost and holding cost is not a coincidence; in the basic EOQ model, the optimum occurs where those two annual costs are balanced.

What EOQ tells an inventory manager

EOQ is a baseline order quantity, not a complete replenishment policy. It tells you how large each order should be under the model’s assumptions. It does not tell you exactly when to order. Timing requires a reorder point based on lead time demand and safety stock. A business might order 1,581 units at a time, but the trigger could be when on-hand inventory falls to five days of expected demand, plus a buffer for supplier delays.

EOQ is most useful when demand is relatively stable, the cost to place an order is known, and holding cost can be estimated. It is common in purchasing, warehouse management, production planning, and small-business inventory reviews. It also helps explain why ordering the largest possible quantity is not always best. Even if a supplier offers free freight above a threshold, excess inventory may sit in storage, expire, become obsolete, or consume working capital that could be used elsewhere.

How to estimate inputs

Annual demand should be measured in the same unit you order: pieces, bottles, cases, kilograms, or components. If demand is seasonal, start with annual demand but test separate EOQ values for high and low seasons. Order cost should include the fixed cost of placing or setting up an order, such as purchasing labor, setup time, receiving, inspection, payment processing, and fixed shipping or handling fees. Do not include costs that change per unit unless they are part of holding cost or a quantity discount analysis.

Holding cost per unit per year should include the annual cost of carrying one unit in inventory. Storage, insurance, shrinkage, damage, obsolescence, spoilage, security, inventory taxes, and capital cost can all matter. If you know holding cost as a percentage of unit value, convert it to dollars per unit per year before using the calculator.

Practical tips

  • Round EOQ to a usable order quantity, then compare the cost impact.
  • Check supplier minimums, case packs, pallet quantities, shelf life, and warehouse capacity.
  • Treat EOQ and reorder point as separate decisions: EOQ is order size, reorder point is timing.
  • Recalculate when demand, order cost, holding cost, or lead-time reliability changes.
  • Use the budget calculator to plan inventory cash needs, the loan calculator to evaluate financing, and the interest calculator to understand the carrying cost of tied-up cash.

For cost-accounting context, EOQ is different from the average fixed cost calculator, average variable cost calculator, and marginal cost calculator. Those tools analyze production costs per unit or per change in output. EOQ analyzes the purchase or production order size that minimizes ordering and holding costs.

Common mistakes to avoid

Do not use monthly demand with annual holding cost unless you convert one of them. Do not confuse unit purchase price with holding cost; holding cost is the annual cost to carry one unit, not the cost to buy it. Do not ignore quantity discounts after calculating EOQ. Do not assume EOQ prevents stockouts; it does not include lead-time uncertainty or safety stock. Finally, do not use EOQ blindly for highly perishable, custom, or rapidly obsolete items.

Sources

  • University of North Georgia, Basic EOQ Model — economic order quantity assumptions, formula, and inventory cost trade-offs.

Frequently asked questions

What does EOQ mean?
EOQ means economic order quantity. It is the order size that balances the fixed cost of placing orders with the annual cost of holding inventory, under assumptions such as steady demand, known costs, and no binding quantity discounts in operations.
What inputs does the EOQ formula need?
The classic formula needs annual demand in units, the fixed cost to place one order, and the yearly holding cost for one unit. The calculator requires all three values to be positive because zero demand, order cost, or holding cost breaks the model.
Is EOQ the same as a reorder point?
No. EOQ is the size of the order to place. A reorder point is the inventory level that triggers the order, and it depends on lead time demand, safety stock, and service-level goals. Many inventory systems use both concepts together.
Should I round the EOQ result?
Usually yes. The formula can return a decimal, but real purchasing uses whole units, cases, pallets, supplier minimums, and truckload constraints. Round to a practical quantity, then compare the ordering and holding cost effect before changing policy for operations today.
When is EOQ less reliable?
EOQ is less reliable when demand is seasonal or uncertain, lead times vary, stockouts are expensive, items expire quickly, storage capacity is tight, or quantity discounts dominate the decision. In those cases, use EOQ as a baseline rather than a final rule.
Does EOQ include the purchase price of inventory?
The basic EOQ model does not include unit purchase price unless it changes with order quantity. If suppliers offer price breaks, compare the total cost at each discount level, including purchase cost, ordering cost, and holding cost together for purchasing decisions.

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