EOQ Calculator (Economic Order Quantity)
Economic Order Quantity Calculator
Find the order size that balances annual ordering expense with annual inventory holding expense, then compare nearby purchasing quantities.
Inventory assumptions
Live results
Cost balance at the optimal quantity
How order quantity changes annual inventory cost
Ordering cost falls as batch size rises, while holding cost rises. Their sum reaches its minimum near the EOQ.
Order-quantity comparison
| Quantity vs. EOQ | Order quantity | Orders/year | Ordering cost | Holding cost | Relevant cost | Cost above minimum |
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How to use and interpret the EOQ model
What does this calculator estimate?
Economic order quantity, or EOQ, estimates the replenishment batch size that minimizes two recurring inventory expenses: the fixed cost of placing orders and the annual cost of carrying units in stock. Smaller orders reduce average inventory but create more purchase orders. Larger orders reduce ordering frequency but keep more cash and physical stock tied up. The EOQ is the mathematical balance point between those opposing costs.
The calculator starts with a reference-style example of 500,000 units of yearly demand, a $10 fixed order cost, and a $4 annual holding cost per unit. Those assumptions produce an EOQ of about 1,581 units. Replace them with costs for one specific SKU, component, or raw material. Mixing several products with different demand patterns or carrying costs can make the result misleading.
How should each input be entered?
- Yearly demand is the expected annual number of units consumed or sold. Use a normalized twelve-month forecast, not revenue and not the value of inventory. Higher demand increases EOQ because more units must move through the system.
- Order cost is the fixed cost incurred each time an order is placed, regardless of batch size. It can include buyer time, approvals, supplier setup, receiving, inspection, and fixed freight charges. Higher order cost favors fewer, larger orders and therefore raises EOQ.
- Yearly cost of holding one unit is the annual carrying cost for one unit. Include warehouse space, insurance, handling, shrinkage, obsolescence, deterioration, and the financing or opportunity cost of cash tied up in stock. Higher holding cost makes inventory more expensive and lowers EOQ.
All three inputs are required for a meaningful optimum. Zero demand or zero ordering cost creates a boundary case rather than a normal EOQ decision. A zero holding cost means the classical formula has no finite optimum, because it would never penalize larger batches.
How does the formula work?
In the formula, D is annual demand, S is the fixed cost per order, and H is the annual holding cost per unit. Annual ordering cost equals D ÷ Q × S, where Q is the selected order quantity. Annual holding cost equals Q ÷ 2 × H because the classical model assumes inventory falls evenly from Q units to zero, making average inventory Q ÷ 2.
At the EOQ, annual ordering cost and annual holding cost are equal. That equality is a useful cross-check: if the two values shown in the cost balance differ materially, the assumptions or formula implementation should be reviewed. The combined relevant cost is the sum of those two expenses. Purchase cost is excluded from the optimization when unit price stays constant because the same annual demand is purchased regardless of batch size.
What do the results mean?
Economic order quantity is the recommended theoretical batch size. Operations may round it to a case pack, pallet, container, minimum order quantity, or supplier production multiple. Compare the rounded quantity with the table rather than assuming the exact decimal result is operationally possible.
Orders per year is annual demand divided by EOQ. Days between orders spreads those orders across 365 days and is a planning interval, not a reorder trigger. Average inventory is EOQ divided by two under the no-safety-stock assumption. Annual relevant cost combines ordering and holding costs at the optimum. The cost-per-demanded-unit metric makes that recurring inventory overhead easier to compare across SKUs, while implied inventory turns show how rapidly average stock cycles through demand.
How should the chart and table be read?
The blue ordering-cost line slopes downward because larger orders reduce the number of purchase orders. The teal holding-cost line slopes upward because larger batches increase average inventory. The purple total line combines both effects and reaches its low point around the EOQ. The legend reports each cost at the current optimum, and the accessible summary uses the same calculated data.
The comparison table tests quantities from 25% to 200% of EOQ. “Cost above minimum” shows the annual penalty for choosing a different batch size. EOQ cost curves are often relatively flat near the minimum, so a practical pack size close to EOQ may add little cost. Far smaller or larger quantities usually create a more visible penalty.
What assumptions and limitations matter?
The classical model assumes stable demand, immediate replenishment, no stockouts, constant ordering and holding costs, and no quantity discounts. Seasonal demand, uncertain supplier lead time, capacity constraints, perishable goods, or service-level targets require additional planning. Safety stock and reorder point answer when to order; EOQ answers how much to order. They are related but not interchangeable.
Use the output as a structured baseline and test it against supplier terms, warehouse capacity, cash-flow limits, and forecast error. Recalculate when demand, freight, labor, interest rates, storage fees, or obsolescence risk changes. For additional background, review the OpenStax inventory management overview, the Investopedia EOQ explanation, and the U.S. Small Business Administration finance guidance.