What is the Economic Order Quantity?

EOQ is the order size that minimises the combined cost of placing orders and holding inventory. Order too much and holding cost rises; order too little and you pay ordering cost too often. The EOQ is the balance point where both costs are equal.

What is the Wilson EOQ formula?

EOQ equals the square root of (2 times annual demand times ordering cost, divided by annual holding cost per unit). It comes from setting the derivative of the total cost curve to zero, which occurs where annual ordering cost equals annual holding cost.

What counts as a holding cost?

Holding cost (H) covers everything tied to storing one unit for a year: warehouse space, capital tied up, insurance, shrinkage, and obsolescence. It is often estimated as a percentage of unit value, for example 20 to 30 percent of the item cost.

Does EOQ account for quantity discounts or lead time?

The basic Wilson model assumes constant demand, fixed costs, and no discounts. It does not set a reorder point, which depends on lead time and safety stock. For volume price breaks you compare EOQ total cost against each discount tier separately.

Why does total cost barely change near the EOQ?

The total cost curve is flat near its minimum, so ordering 10 to 20 percent above or below the EOQ raises total cost only slightly. This makes EOQ robust to imperfect cost estimates and lets you round to a convenient pack or pallet size.

What is the Economic Order Quantity (EOQ) Calculator?

Compute the Economic Order Quantity with the Wilson formula sqrt(2DS/H) from annual demand, cost per order, and per-unit holding cost. Returns optimal order size, orders per year, cycle length, and total annual inventory cost. Runs in your browser. It runs free in your browser on Gera Tools, with nothing uploaded.

Economic Order Quantity (EOQ) Calculator

Name: Economic Order Quantity (EOQ) Calculator
Creator: Gera Tools
License: https://creativecommons.org/licenses/by/4.0/

The Economic Order Quantity answers a core procurement question: how much should you order at a time? Order in large batches and you tie up cash and warehouse space in holding cost; order frequently in small batches and you rack up ordering cost. The EOQ is the sweet spot that minimises the two combined.

How it works

The classic Wilson EOQ formula is derived by minimising the total annual cost:

total cost = ordering cost + holding cost
           = (D / Q) × S  +  (Q / 2) × H

EOQ (Q*) = sqrt( 2 × D × S / H )

where D is annual demand in units, S is the fixed cost per order, and H is the cost to hold one unit for a year. At the EOQ the annual ordering cost and the annual holding cost are exactly equal, which is the condition that minimises the sum. Average inventory is Q / 2 because stock draws down linearly from Q to 0 between deliveries.

Worked example

Suppose annual demand is 12,000 units, each order costs 75 to place (including paperwork, receiving, and setup), and holding one unit for a year costs 3 (warehouse space, insurance, and capital cost combined). Then:

EOQ = sqrt(2 × 12,000 × 75 / 3) = sqrt(600,000) ≈ 775 units

With this order size:

Orders per year: 12,000 / 775 ≈ 15.5 orders, roughly one every 24 days
Annual ordering cost: 15.5 × 75 ≈ 1,162
Annual holding cost: (775/2) × 3 ≈ 1,163
Total minimised cost: approximately 2,325 per year

Notice that ordering cost and holding cost are nearly equal at the optimum — that is the mathematical signature of the EOQ.

How to estimate your inputs

The three inputs are straightforward to define but can be tricky to measure accurately:

Annual demand (D)

Use historical sales or usage data, ideally from the past year adjusted for any known trend. If demand is seasonal, the basic EOQ uses the average — you may want to run separate EOQs for peak and off-peak seasons.

Ordering cost (S)

This is the fixed cost of placing and receiving one order, regardless of quantity. It typically includes staff time to raise and process a purchase order, freight if delivery is a flat fee, receiving and inspection labour, and any supplier setup fee. Do not include the unit cost of the goods themselves — that is absorbed into the holding cost calculation.

Holding cost (H)

Also called carrying cost, this is everything it costs to store one unit for one year. The most common approach is to estimate it as a percentage of the unit value — industry rules of thumb often suggest 20–30% annually, covering:

Capital cost — the cost of money tied up in inventory (interest rate or opportunity cost)
Storage — warehouse rent or depreciation, utilities, handling equipment
Shrinkage and obsolescence — expected spoilage, theft, or items going out of date
Insurance — typically a small fraction of stock value

The flat minimum and rounding

The total cost curve is unusually flat near the EOQ. Ordering 10–20% above or below the optimum raises total cost by only a percent or two. This is practically useful: round the EOQ to the nearest convenient pack size, pallet quantity, or supplier minimum order quantity with almost no penalty. In the example above, rounding 775 up to 800 units — a round number the supplier may prefer — costs only a few extra units per year.

What EOQ does not cover

The basic Wilson model assumes constant, known demand and fixed costs with no volume discounts. In practice you may also need to account for:

Reorder point and safety stock — EOQ tells you how much to order but not when. The reorder point depends on lead time and acceptable stockout risk.
Quantity discounts — if your supplier offers a price break at, say, 1,000 units, compare the total cost at the EOQ against the total cost at the minimum discount quantity.
Perishable goods — items with expiry dates may need a shelf-life constraint applied on top of the EOQ result.