Understanding your result
The main result compares the integer quantities immediately below and above the continuous optimum, using at least one unit. Annual orders and order interval are long-run averages, so they may be fractional. Relevant cost includes ordering and cycle-stock holding only.
For the stock level that triggers replenishment, use the Reorder Point Calculator with lead-time demand and an appropriate buffer.
The formula
The basic model treats stock as falling steadily from an order quantity to zero, giving average cycle stock Q/2. Increasing Q reduces order frequency but raises average stock. The square-root result is continuous; comparing the neighboring whole quantities selects the cheaper integer under this model.
Worked example
Demand of 10,000 units per year, an order cost of 50, and holding cost of 2 per unit-year give EOQ 707.107. Ordering 707 units produces about 707.21 annual ordering cost and 707.00 holding cost, totaling 1,414.21. At 250 operating days, the average interval is about 17.675 days.
How to use this calculator
- Enter expected annual demand and the fixed administrative or delivery cost per order.
- Enter holding cost per unit per year, expressed as money rather than a percentage.
- Set operating days and review the order size, interval, and cost balance.
Convert holding percentages before entry
If your holding assumption is a percentage of purchase cost, multiply the percentage fraction by unit cost first. For example, 20% of a 10-unit currency purchase cost means 2 currency units of annual holding cost. The calculator expects that resulting amount, not the number 20.
Order size is not a reorder trigger
EOQ answers how much to order in a simplified cost model. Supplier lead time and safety stock determine when to trigger replenishment. A long-run frequency such as 14.14 orders per year does not mean a fractional purchase order is created; it describes the model’s average cycle across time.
Operational constraints can dominate the optimum
Minimum quantities, carton multiples, storage, perishability, discounts, changing demand, and limited cash can make the unconstrained optimum impractical. Review feasible supplier quantities separately. Purchase cost is excluded because a constant unit price contributes the same annual total at every Q; quantity discounts break that assumption.
Assumptions & limitations
What this calculation assumes
- Demand and costs are constant, replenishment is instantaneous, and shortages are not allowed in the basic model.
What to keep in mind
- No quantity discounts, production replenishment, safety-stock carrying cost, or pack multiples are optimized.
Common questions
Why not always round EOQ upward?
The lower neighboring integer can have lower combined cost. This tool evaluates both rather than assuming one rounding direction.
Why must holding cost be positive?
With no holding cost, the simple model has no finite interior tradeoff that yields the usual square-root optimum.