Economic Order Quantity (EOQ): formula, calculator, and worked example

Economic order quantity (EOQ) is the order size that costs you the least once you add the cost of ordering to the cost of holding stock. It matters because those two costs pull against each other: When you order in big batches, you tie up cash and shelf space, but when ordered little and often, you rack up order fees and receiving time.

Across dozens of SKUs, guessing the batch size on each one wastes money on both sides. This guide gives you a calculator, the formula, a worked example, and how EOQ sets up your reorder point.

EOQ calculator 

Enter three numbers, your annual demand for the item, the cost of placing one order, and the cost of holding one unit for a year, and the calculator returns the economic order quantity, how many orders that means per year, and the total annual cost at that size.

What is Economic Order Quantity? 

Economic order quantity is the order size that minimizes the combined cost of ordering and holding inventory. It also goes by optimal order quantity, and the formula behind it was first published by Ford W. Harris in 1913. The idea is simple. For any item there is one order size where the money spent placing orders and the money spent holding stock add up to the smallest total. Above that size, holding cost dominates; below it, ordering cost does. EOQ is the bottom of that curve.

The EOQ formula

The economic order quantity comes from three inputs:

EOQ = √(2DS ÷ H)

Where:

• D is annual demand, the units you sell or use in a year.

• S is the ordering cost per order, the fixed cost of placing one order, delivery, and receiving.

• H is the holding cost per unit per year: storage, tied-up capital, insurance, and obsolescence.

Holding cost is often written as the unit cost times a holding rate. A $10 item at a 20% holding rate gives an H of $2 a year.

Worked example 

Take an item with annual demand of 1,000 units, an ordering cost of $20 per order, and a holding cost of $1 per unit per year. The figures are illustrative.

EOQ = √(2 × 1,000 × 20 ÷ 1) = √40,000 = 200 units

So the cheapest batch is 200 units, which works out to 1,000 ÷ 200 = 500 orders a year, roughly one every 73 days. At that size, the annual ordering cost is (1,000 ÷ 200) x $20 = $100, and the annual holding cost is (200 ÷ ) x $1 = $100. The two come out equal, which is the fingerprint of the EOQ.

Ordering cost vs. holding cost (why EOQ works) 

As the order size changes, the two costs move opposite ways. Bigger orders mean fewer of them, so ordering cost falls while more stock sits on the shelf and holding cost climbs. Smaller orders flip it. The EOQ is the one size where the two balance and their sum is lowest, which the same example makes concrete:

Ordering 200 at a time totals $200. Ordering 500 pulls ordering cost down to $40 but pushes holding cost to $250, landing at $290. Ordering 100 pulls holding cost down to $50 but pushes ordering cost to $200, landing at $250. Both cost more than the $200 at the EOQ.

EOQ assumptions and limitations 

The formula is exact only when a set of tidy assumptions holds, and in a real business several rarely do, so treat the EOQ as a starting number, not a finished rule. The main assumptions:

• Demand is steady and known.

• Ordering and holding costs stay fixed as the order size changes.

• The unit price is constant, with no bulk discounts.

• Stock arrives all at once, with no stockouts.

Where they break and what to do:

• Quantity discounts: If a supplier drops the price at a higher quantity, it can pay to order up to that tier even past the EOQ. The formula cannot see the discount, so check it on its own.
   

• Fixed pack sizes and minimum orders: An EOQ of 200 may need rounding to the nearest carton or pallet or up to a supplier minimum.
   

• Seasonal or variable demand: When demand swings through the year, recalculate the EOQ per season instead of once annually.

How EOQ connects to reorder point and safety stock 

EOQ answers how much to order. It says nothing about when, and that is the reorder point's job: the stock level at which you place the next order. Put together, they make one rule: when stock falls to the reorder point, order a single EOQ. The reorder point itself is built from your lead time and a safety-stock buffer.

Reorder Point = (Average Daily Usage × Lead Time) + Safety Stock

So EOQ sizes the order, the reorder point triggers it, and safety stock covers the demand and supply wobble in the gap between placing an order and receiving it.