EOQ Calculator

The EOQ Calculator finds the Economic Order Quantity — the order size that minimizes the total cost of buying and holding inventory. Order too much and you tie up cash and pay to store it; order too little and you place (and pay for) far too many orders. EOQ is the sweet spot between these two. This tool also returns your orders per year, days between orders, reorder point, and the lowest possible total inventory cost, and draws the cost curve and inventory cycle so you can see exactly why the answer is what it is.

What is Economic Order Quantity (EOQ)?

Economic Order Quantity (EOQ) is a classic inventory-management formula, developed by Ford W. Harris in 1913, that determines the ideal quantity to order each time you restock. It balances two opposing costs: the ordering cost (a fixed cost incurred every time you place an order — paperwork, shipping, receiving, setup) and the holding cost (the cost of keeping a unit in stock for a year — warehousing, insurance, spoilage, and the opportunity cost of tied-up capital). EOQ is the order quantity at which the sum of these two costs is at its minimum.

EOQ Formula

The EOQ formula comes from minimizing the total annual cost with respect to order quantity:

where D is the annual demand (units per year), S is the ordering cost per order, and H is the holding cost per unit per year. Two related results follow directly:

Reorder Point Formula

The reorder point tells you when to order, while EOQ tells you how much. It is the stock level that covers demand during the supplier's lead time, plus any safety stock:

where d is daily demand, L is lead time in days, and SS is safety stock.

Why Ordering Cost Equals Holding Cost at the EOQ

One of the most elegant features of EOQ is that, at the optimal quantity, your annual ordering cost and annual holding cost are exactly equal. As you order in bigger batches, you place fewer orders (ordering cost falls) but carry more stock on average (holding cost rises). Total cost is a U-shaped curve, and its lowest point sits precisely where the falling ordering-cost line crosses the rising holding-cost line. The interactive chart above this section makes that crossing visible.

EOQ Worked Example

Suppose a shop sells 12,000 units a year, it costs $50 to place an order, and holding one unit for a year costs $3. Then:

How to Estimate Holding (Carrying) Cost

Holding cost is the hardest input to pin down. A common shortcut is to express it as a percentage of the item's unit cost — typically 15% to 30% per year — covering storage, insurance, taxes, shrinkage, obsolescence, and the cost of capital. This calculator's Unit cost × carrying rate % mode does that conversion for you: enter a $20 item at a 25% carrying rate and it uses $5 per unit per year as H.

What Affects Your EOQ?

Assumptions and Limitations

The basic EOQ model assumes demand is constant and known, lead time is fixed, the whole order arrives at once, and there are no quantity discounts or stockouts. Real demand is lumpier than that, so treat EOQ as a strong starting point rather than an exact rule. Fortunately, the total-cost curve is flat near its minimum, so the EOQ is forgiving: rounding it to a convenient pack, case, or pallet size usually costs very little.

How to Use This Calculator

1. Enter annual demand: The number of units you expect to sell or use in a year.
2. Enter the ordering cost: The fixed cost of placing one order, regardless of size.
3. Enter the holding cost: Either directly as a cost per unit per year, or switch to the percentage mode and enter the unit cost and an annual carrying rate.
4. Add lead time and safety stock (optional): To also compute your reorder point and inventory cycle.
5. Click Calculate: Review your EOQ, orders per year, days between orders, total cost, the cost curve, and the inventory sawtooth diagram.

Frequently Asked Questions

What is Economic Order Quantity (EOQ)?

Economic Order Quantity (EOQ) is the order size that minimizes the combined cost of ordering inventory and holding it in stock. Ordering in larger batches lowers the number of orders but raises carrying costs, while ordering in smaller batches does the opposite. EOQ is the quantity where these two costs balance and total cost is lowest.

What is the EOQ formula?

EOQ equals the square root of (2 × annual demand × ordering cost per order ÷ holding cost per unit per year). In symbols, EOQ = √(2DS / H), where D is annual demand, S is the cost per order, and H is the annual holding cost per unit.

How do I find the holding (carrying) cost?

Holding cost is the cost of keeping one unit in stock for a year, including storage, insurance, obsolescence, and tied-up capital. It is often estimated as a percentage of the item's unit cost, typically 15% to 30% per year. This calculator lets you enter it directly or as a percentage of unit cost.

What is the reorder point?

The reorder point is the inventory level at which you should place a new order so stock arrives before you run out. It equals daily demand multiplied by lead time in days, plus any safety stock you want to hold as a buffer against demand or supply variability.

Why are ordering cost and holding cost equal at the EOQ?

At the EOQ the annual ordering cost and the annual holding cost are exactly equal. This is a mathematical property of the cost curves: total cost is minimized at the point where the falling ordering-cost curve crosses the rising holding-cost curve, and at that crossing the two costs are the same.

What happens if I do not order exactly the EOQ?

The total-cost curve is flat near its minimum, so the EOQ is forgiving. Ordering 50% more or less than the EOQ usually raises total inventory cost by only around 8%, so rounding the EOQ to a convenient pack or pallet size has a very small cost penalty.

Additional Resources

• Economic Order Quantity - Wikipedia
• Reorder Point - Wikipedia