The EOQ formula is: EOQ = √(2DS/H), where D is annual demand, S is the ordering cost per order, and H is the holding cost per unit per year. It answers a simple question that every stock-holding business faces: how much should we order each time? Order too much and money sits on shelves. Order too little and you pay to place orders constantly. The economic order quantity is the order size that balances those two costs. It keeps total inventory cost as low as possible. This guide explains the EOQ formula, works through an example with clear numbers, and shows how EOQ connects to the reorder point.
EOQ is one of the oldest tools in inventory management. It remains useful precisely because it is simple. It needs three inputs, a square root, and an honest understanding of its limits. Used well, it replaces guesswork about order sizes with a reasoned starting point.
What Is the EOQ Formula?
Economic order quantity is the order size that minimises the total cost of ordering and holding inventory. Two costs pull in opposite directions. Ordering costs fall as order size grows, because fewer orders are placed each year. Holding costs rise as order size grows, because larger orders mean more stock sitting in the warehouse on average. Total cost is the sum of the two, and it forms a U-shaped curve. It is high at small order sizes, falls to a minimum, then rises again as orders get larger. EOQ is the bottom of that curve.
At the EOQ, ordering cost and holding cost are equal. That is a useful check. If your two annual cost figures are not roughly equal at the EOQ, something has gone wrong in the arithmetic. The model deliberately ignores some real-world costs, such as stockout costs and quantity discounts. That is why EOQ is a starting point, not a final answer in itself.
The EOQ Formula, Term by Term
EOQ = √(2DS/H)
Each letter in the formula stands for one input. Getting these three inputs right matters more than the arithmetic itself.
D: annual demand
D is the total demand for the item over one year, in units. Use actual usage or sales for the year, not purchases, because purchases can be distorted by bulk buying or stock building. If demand is seasonal, an annual average still works for the basic model. Treat the result as a guideline rather than a precise instruction, and adjust order sizes through the year.
S: ordering cost per order
S is the cost of placing one order, regardless of its size. It includes the staff time spent raising and processing the order. It also covers supplier communication, delivery and receiving checks, and invoice handling. Exclude the price of the goods themselves from S. Many businesses underestimate S because the costs are spread across salaries and systems. Even a rough estimate is better than ignoring ordering cost altogether. Ordering cost is what stops the model from recommending tiny, frequent orders.
H: holding cost per unit per year
H is the cost of holding one unit in stock for one year. It includes warehouse space, handling, insurance, and the cost of capital tied up in stock. It also allows for damage, obsolescence, and shrinkage. Holding cost is often estimated as a percentage of the unit’s value. For example, if an item costs $20 and the annual holding rate is 10%, H is $2 per unit per year. Holding cost is what stops the model from recommending one giant annual order.
EOQ Formula: A Worked Example
Let us work through the formula with simple round numbers. Please note: all figures in this example are purely illustrative, chosen to show the arithmetic clearly, not data from any real company.
Suppose a business stocks a standard component with the following illustrative inputs:
Annual demand (D): 10,000 units. Ordering cost per order (S): $50. Holding cost per unit per year (H): $2.
Step 1: multiply 2 × D × S. That is 2 × 10,000 × 50 = 1,000,000.
Next, divide by H. That is 1,000,000 ÷ 2 = 500,000.
Then take the square root. The square root of 500,000 is approximately 707. So EOQ is about 707 units per order.
Finally, check the result. Orders per year = annual demand ÷ EOQ = 10,000 ÷ 707 ≈ 14.1. That is roughly one order every 26 days. Annual ordering cost = 14.1 × $50 ≈ $707. Average inventory = EOQ ÷ 2 ≈ 354 units, so annual holding cost = 354 × $2 ≈ $707. The two costs match, which confirms the calculation. Total relevant cost at the EOQ is about $1,414 per year.
Notice how forgiving the model is near the optimum. Ordering 600 or 800 units instead of 707 would raise total cost only slightly. The cost curve is flat near the bottom. That is good news in practice. An approximately right order size captures most of the benefit, and rounding to a convenient pack size is perfectly sensible.
Ordering Costs vs Holding Costs in the EOQ Formula
Understanding the two costs helps you judge whether your EOQ result is trustworthy.
Ordering costs are mostly fixed per order. Whether you order 100 units or 1,000, the processing costs are roughly the same. The purchase order, the supplier call, the delivery booking, and the goods-in check barely change. That is why ordering cost per unit falls as order size grows. Businesses that automate ordering or consolidate suppliers effectively lower S. A lower S pushes EOQ down, favouring smaller, more frequent orders.
Holding costs grow with stock levels. More stock means more space, more handling, more capital tied up, and more risk of damage or obsolescence. Warehouse budgets and finance charges often hide these costs. That is why holding cost is the input most often underestimated. If you set H too low, EOQ comes out too high. Then the warehouse quietly fills with slow-moving stock.
When either cost changes, EOQ moves in a predictable direction. Higher demand pushes EOQ up. A higher ordering cost also pushes EOQ up, because fewer orders are better. A higher holding cost pushes EOQ down, because leaner stock is better. Because the formula uses a square root, EOQ moves more slowly than its inputs. Doubling demand increases EOQ by only about 41%, not 100%.
How the EOQ Formula Connects to the Reorder Point
EOQ answers “how much to order”. The reorder point answers “when to order”. The two work together, and neither is complete alone.
Calculate the reorder point as expected demand during lead time plus safety stock. Lead time demand is average daily demand multiplied by lead time in days. Safety stock is the buffer against demand spikes and delivery delays. When stock falls to the reorder point, you place an order for the EOQ quantity.
Returning to our illustrative example: annual demand of 10,000 units means average daily demand of about 27 units. That assumes a 365-day year. If lead time is 7 days, lead time demand is 27 × 7 = 189 units. Add a safety stock of, say, 50 units, and the reorder point is 239 units. In practice, when stock reaches 239 units, you order 707 units. If demand and delivery behave as expected, you will use 189 units during the 7-day wait. The 50-unit buffer will remain untouched.
This pairing is the backbone of simple stock control. It is closely related to the pull systems used in just-in-time inventory management and kanban, where stock levels trigger replenishment rather than calendar dates.
Assumptions and Limitations of the EOQ Model
EOQ is a model, and models simplify reality. Knowing its assumptions helps you know when to trust it and when to adjust it.
First, the basic model assumes demand is constant and known. Real demand fluctuates. For seasonal or erratic items, recalculate EOQ for different periods or treat it as a guideline. Second, it assumes lead time is constant and deliveries arrive complete. Unreliable suppliers undermine any fixed order quantity, which is why supplier management and lead time reliability matter as much as the calculation. Third, it assumes no quantity discounts: the unit price does not change with order size. If a supplier offers a meaningful discount for a larger order, compare the saving against the extra holding cost.
Fourth, the model assumes no stockouts and ignores stockout costs. Running out can carry a high penalty, such as stopping production or losing a key customer. In that case, safety stock and service-level thinking matter more than EOQ alone. Finally, the model treats each item independently. In reality, buyers often combine orders across items from the same supplier. That changes the effective ordering cost and may justify different order sizes.
None of this makes EOQ useless. It makes EOQ a starting point. Calculate it, then adjust for discounts, seasonality, supplier reliability, and practical constraints such as pack sizes and minimum order values. A model you understand and adjust beats a precise-looking answer nobody questions.
Common EOQ Formula Mistakes to Avoid
Guessing holding cost as zero or near-zero
Warehouse space, handling, insurance, and capital all cost money even when they are not charged to a single product line. A holding cost of zero would imply an infinite order size, which is obviously wrong. Estimate H properly, even roughly, and revisit it when warehousing or financing costs change.
Treating EOQ as a rule rather than a guide
EOQ gives an order quantity. But pack sizes, supplier minimums, shelf life, and cash flow may justify ordering a little more or less. The cost curve is flat near the optimum, so sensible rounding costs almost nothing. Follow the model, not the decimal places.
Setting EOQ once and forgetting it
Demand, ordering costs, and holding costs all change. Review EOQ at least annually, and whenever a major input shifts. That could be a new supplier, a warehouse move, a change in product range, or a sustained change in demand. In a well-run warehouse management routine, EOQ is a living number, not a one-time calculation.
Watch: EOQ Explained on Video
The video below walks through the economic order quantity model and its assumptions. It shows how ordering and holding costs balance at the optimum.
Frequently Asked Questions About the EOQ Formula
What is the EOQ formula?
The EOQ formula is EOQ = √(2DS/H). D stands for annual demand in units. S is the ordering cost per order. H is the holding cost per unit per year. It gives the order quantity that minimises the combined annual cost of ordering and holding inventory.
How do you calculate EOQ with an example?
Apply the formula to annual demand, ordering cost, and holding cost. Example, using illustrative figures: D = 10,000 units, S = $50, H = $2, so EOQ = √(2 × 10,000 × 50 ÷ 2) ≈ 707 units per order.
What are ordering costs in EOQ?
Ordering costs are the fixed costs of placing one order. They cover staff time, supplier communication, delivery arrangement, goods-in checks, and invoice handling. They exclude the price of the goods.
What are holding costs in EOQ?
Holding costs are the annual cost of keeping one unit in stock. They cover space, handling, insurance, capital tied up, and allowances for damage and obsolescence. They are often estimated as a percentage of unit value.
How does EOQ relate to the reorder point?
EOQ decides how much to order; the reorder point decides when to order. The reorder point equals expected demand during lead time plus safety stock. When stock falls to the reorder point, you place an order for the EOQ quantity.
When should you not use EOQ?
EOQ is less useful when demand is highly erratic or seasonal. It also struggles when suppliers offer large quantity discounts that outweigh extra holding cost. The same applies when lead times are unreliable, or for very low-value items where the cost of managing the calculation exceeds the saving. In those cases, use EOQ as a reference and adjust for the real conditions.
Putting It All Together
Start with honest inputs: true annual demand, a realistic ordering cost, and a holding cost that includes space, handling, and capital. Apply the formula, check that ordering and holding costs balance at the result, and round to a practical order size. Pair EOQ with a reorder point based on lead time and safety stock. Review both when conditions change, and adjust for discounts, seasonality, and supplier reliability. Used that way, the EOQ formula turns one of the most common procurement and stock decisions from a guess into a repeatable, defensible routine. It also supports the wider supply chain planning process with numbers the whole business can understand.
