Economic Order Quantity (EOQ) Calculator

EOQ (Optimal Order Size) Calculator

Economic Order Quantity Formula

Formula

\[ EOQ = \sqrt{ \frac{2 \times D \times S}{H} } \]

Where:

$D$ — annual demand, in units per year
$S$ — ordering cost, in currency per order placed
$H$ — holding cost, in currency per unit per year

The formula finds the order size at which the total of ordering costs and holding costs is at its lowest. Ordering costs fall as orders get larger and less frequent, while holding costs rise with the average inventory level — EOQ is the point where these two effects balance out.

Economic Order Quantity – Calculation Example

Example: a retailer sells 10,000 units of a product per year. Each order placed costs $50 in administrative and shipping expenses, and storing one unit for a year costs $2.

\[ EOQ = \sqrt{ \frac{2 \times 10{,}000 \times 50}{2} } = \sqrt{500{,}000} \approx 707.11 \]

Result: The economic order quantity is approximately 707 units. Ordering about 707 units each time (roughly 14 orders per year) keeps total inventory costs at their minimum.

How to Use the Calculator

Enter the Annual demand (units) — the total number of units you expect to sell or use per year.
Enter the Ordering cost per order — the fixed cost of placing and receiving one order, in dollars.
Enter the Holding cost per unit per year — the cost of storing one unit for a year (warehouse space, insurance, capital tied up in stock).
Read the Economic Order Quantity in units, along with a short interpretation of the result.

What Is Economic Order Quantity?

Economic Order Quantity (EOQ), also known as the Wilson formula, is the order size that minimizes the total cost of managing inventory. Every business that stocks goods faces two opposing costs: the cost of placing orders (paperwork, shipping, receiving, supplier setup) and the cost of holding stock (storage, insurance, spoilage, and capital that could be used elsewhere).

Ordering in large quantities reduces how often you order, cutting ordering costs — but it increases average stock levels and therefore holding costs. Ordering in small amounts does the opposite. The EOQ model finds the quantity where the sum of both costs is lowest, which is also the point where annual ordering cost equals annual holding cost.

The result is best treated as a target, not a rigid rule. If the calculator returns 707 units, you may in practice round to a supplier's packaging size (for example 700 or 750 units) with only a negligible cost penalty — the total cost curve is flat near the optimum. To measure how efficiently you turn that stock over afterwards, pair EOQ with the Days in Inventory and Ending Inventory calculators.

Assumptions and Limitations

The classic EOQ model relies on assumptions that rarely hold perfectly in the real world:

Demand is known and constant — the formula uses a single annual demand figure, with no seasonality or growth.
Costs are fixed — ordering cost per order and holding cost per unit do not change with order size, and quantity discounts are ignored.
Instant replenishment — goods arrive exactly when needed, with no lead-time uncertainty or stockouts.
No capacity limits — warehouse space and cash flow can always accommodate the optimal order.

Despite these simplifications, EOQ remains a valuable baseline. It gives a sensible order size that you can then adjust for quantity discounts, safety stock, or supplier minimum order quantities. If a supplier offers a bulk discount, compare the savings against the extra holding cost before deviating from EOQ — the Find Inventory Cost and Inventory Stock calculators can help you quantify the trade-off.

Practical Tips

Include all relevant costs in the holding cost: storage, insurance, taxes, obsolescence, and the opportunity cost of capital (often estimated as a percentage of the unit's value).
Recalculate EOQ periodically — demand, freight rates, and storage costs change over time, and so does the optimal order size.
Use EOQ per SKU, not for your whole product range, since demand and cost structures differ between items.
Combine EOQ with a reorder point calculation so you know not only how much to order, but when.

Frequently Asked Questions

How do I calculate EOQ by hand without a calculator?

Multiply annual demand by ordering cost, double it, then divide by the holding cost per unit per year and take the square root. For example, with demand of 5,000 units, ordering cost of $40, and holding cost of $5: $EOQ = \sqrt{2 \times 5{,}000 \times 40 / 5} = \sqrt{80{,}000} \approx 283$ units. Keep the units consistent — if demand is annual, holding cost must also be per year.

What is a good or normal EOQ value?

There is no universal "good" number — EOQ depends entirely on your demand, ordering cost, and holding cost. A small shop might have an EOQ of 20 units, while a distributor's could be 20,000. What matters is that your actual order size is close to the calculated EOQ. If you routinely order far more or far less, you are paying noticeably higher total inventory costs than necessary.

How many orders per year should I place at the EOQ?

Divide annual demand by the EOQ. If demand is 10,000 units and EOQ is 707, you place about 14 orders per year, or roughly one every 3.5 weeks. The time between orders is $EOQ / D \times 365$ days. This also tells you your reorder frequency, which you can combine with supplier lead times to set a reorder point.

How do I estimate the holding cost per unit per year?

Add up all costs of keeping one unit in stock for a year: warehouse space, insurance, taxes, spoilage or obsolescence, and the opportunity cost of capital tied up in inventory. A common shortcut is to take 20–25% of the unit's purchase price as the annual holding cost — so a $100 item would have a holding cost of about $20–25 per unit per year. Adjust the percentage to your industry and product risk.

What happens if demand or costs are in different units or time periods?

All three inputs must share the same time basis. If you know monthly demand of 500 units, either multiply by 12 to get annual demand, or convert holding cost to a monthly figure by dividing by 12. Mixing a monthly demand with an annual holding cost will inflate your EOQ by a factor of about $\sqrt{12}$, roughly 3.5 times too large. Currency units must also match between S and H.

Does EOQ account for quantity discounts or safety stock?

No. The classic formula assumes constant per-unit costs, no bulk discounts, and no stockouts. If a supplier offers a price break, calculate the total cost (purchase price + ordering + holding) at both the EOQ and the discount quantity, and choose the cheaper option. For safety stock, keep it separate: EOQ answers how much to order, while safety stock covers demand variability during lead time.

What are the most common mistakes when using the EOQ formula?

The biggest errors are mismatched time periods (monthly demand with annual holding cost), excluding the cost of capital from holding cost, using the purchase price instead of the per-order ordering cost, and applying one EOQ to an entire product range. Also avoid blindly following the exact number — rounding to a supplier's case pack or pallet size costs almost nothing, since total cost barely changes near the optimum. Recalculate when costs or demand shift.

Economic Order Quantity Calculator