Economic Order Quantity Calculator: Formula & Example

This calculator works out the Economic Order Quantity (EOQ) – the optimal number of units to order at a time to minimize total inventory costs. You enter the annual demand, the cost per order, and the annual holding cost per unit, and you get the ideal order quantity, plus the total annual cost at that quantity. It applies the classic Harris–Wilson formula used in supply-chain management.

Formula

The EOQ formula is:

EOQ = √(2DS / H)

• D = annual demand in units (how many you sell or use in a year)
• S = cost per order (setup cost, shipping, administrative handling – in dollars)
• H = holding cost per unit per year (storage, insurance, capital tied up – in dollars)

The result is in units per order. The total annual cost at that quantity is √(2DSH), which includes both ordering and holding costs.

Worked Example

Using the default values from the calculator: D = 10,000 units/year, S = $50 per order, H = $2 per unit per year.

1. Multiply 2 × D × S: 2 × 10,000 × 50 = 1,000,000
2. Divide by H: 1,000,000 / 2 = 500,000
3. Take the square root: √500,000 ≈ 707.1

So the EOQ is 707 units (rounded to the nearest whole unit). The total annual cost is √(2 × 10,000 × 50 × 2) = √2,000,000 ≈ $1,414.21. That is the minimum total cost – ordering more or less than 707 units would increase the total.

When to Use EOQ

EOQ is useful when you have steady, predictable demand and want to balance two competing costs:

• Ordering costs – placing more orders increases these costs, so you want larger, less frequent orders.
• Holding costs – keeping more inventory increases storage and capital costs, so you want smaller, more frequent orders.

It works best for items with constant demand, known costs, and no quantity discounts. Retailers, manufacturers, and wholesalers use it for raw materials, components, and finished goods. It is also taught in operations management and supply-chain courses as the foundation for more advanced inventory models.

How to Read the Result

The EOQ tells you the order quantity that minimizes total annual inventory cost. If you currently order a different amount, you can compare your total cost with the EOQ total. For example, if you order 1,000 units at a time, your total cost would be:

• Ordering: (10,000 / 1,000) × $50 = $500
• Holding: (1,000 / 2) × $2 = $1,000
• Total: $1,500 – which is higher than the EOQ total of $1,414.21

The EOQ is the point where ordering cost equals holding cost. In the example, at 707 units: ordering cost = (10,000 / 707) × $50 ≈ $707, and holding cost = (707 / 2) × $2 ≈ $707.

Common Mistakes and Limitations

• Unit mismatch: Ensure D is annual demand, S is per order, and H is per unit per year. If you use monthly demand, the result will be wrong.
• Rounding too early: Do not round intermediate steps. Round only the final EOQ to a practical whole number (you cannot order half a unit).
• Ignoring lead time: EOQ tells you how much to order, not when to order. You still need a reorder point based on lead time and safety stock.
• Variable demand: EOQ assumes constant demand. If demand fluctuates, consider a safety stock or a different model like the newsvendor model.
• Quantity discounts: EOQ does not consider discounts for larger orders. If discounts are available, compare the total cost at the discount breakpoints with the EOQ cost.

Alternatives to EOQ

EOQ is not the only inventory model. Depending on your situation, you might use:

• Periodic review system: Order a fixed interval (e.g., every month) and adjust the quantity based on current stock.
• Min-max system: Order when stock falls below a minimum level, and order enough to reach a maximum level.
• ABC analysis: Classify items by value and apply different ordering policies to each class.
• Just-in-time (JIT): Order very small quantities frequently to minimize holding costs, often used in lean manufacturing.
• Newsvendor model: For perishable items with uncertain demand, where you must decide how much to stock before demand is known.

These alternatives address some of EOQ’s limitations, but EOQ remains a simple and effective starting point for many products.

Frequently Asked Questions

What does EOQ stand for?

EOQ stands for Economic Order Quantity. It is the order quantity that minimizes the total cost of ordering and holding inventory.

How do I calculate holding cost per unit?

Holding cost per unit per year is the sum of storage costs (rent, utilities, insurance) and the opportunity cost of capital tied up in inventory, divided by the average number of units held. A common approximation is 20–30% of the unit cost per year.

Can EOQ be used for perishable items?

EOQ assumes items can be stored indefinitely without spoilage. For perishable items, the holding cost should include spoilage, but if spoilage is significant, a different model (like the newsvendor) may be more appropriate.

What if my demand is not constant?

EOQ is less accurate with variable demand. You can use an average demand, but you may need to add safety stock to prevent stockouts. Consider a probabilistic inventory model if demand is highly variable.

Does EOQ include the cost of the product itself?

No, the EOQ formula only includes ordering and holding costs. The purchase cost of the units is constant regardless of order size (assuming no quantity discounts), so it does not affect the optimal order quantity.

Why is my EOQ not a whole number?

The formula often gives a decimal. In practice, you round to the nearest whole unit, but you can also round up to the next whole number if you prefer to have a little extra stock. The cost difference is usually negligible.

Related

• Exponent Equation Calculator: Solve for x
• Exponent Factor Calculator: How to Use It
• Exponent Addition Calculator: Rules & Examples

in d | Annual demand (units) | units/year | 10000 | 0
in s | Order cost per order | $ | 50 | 0
in h | Holding cost per unit per year | $ | 2 | 0
out eoq | Economic Order Quantity | units | sqrt((2 * d * s) / h) | 0
out total | Total annual cost | $ | sqrt(2 * d * s * h) | 2