Economic Order Quantity Formula Calculator

This calculator works out the Economic Order Quantity (EOQ) — the optimal number of units to order at one time to minimize the total cost of inventory, including ordering and holding costs. You enter annual demand, ordering cost per order, and holding cost per unit per year, and it returns the EOQ in units, along with the total annual inventory cost at that quantity.

Formula

The EOQ formula is:

EOQ = √(2DS / H)

• D = annual demand (units per year)
• S = ordering cost per purchase order (dollars per order)
• H = holding cost per unit per year (dollars per unit per year)

The result is the number of units to order each time you place an order. The accompanying total annual inventory cost at that order quantity is √(2DSH), which combines the annual ordering cost and the annual holding cost.

Worked Example

Using the default values from the calculator above:

• Annual demand (D) = 1,200 units
• Ordering cost (S) = $25 per order
• Holding cost (H) = $2 per unit per year

Step 1: Multiply 2 × D × S = 2 × 1,200 × 25 = 60,000.

Step 2: Divide by H: 60,000 ÷ 2 = 30,000.

Step 3: Take the square root: √30,000 = 173.205…, which rounds to 173 units.

The total annual inventory cost at this order quantity is √(2 × 1,200 × 25 × 2) = √120,000 = $346.41.

When to Use EOQ

EOQ is most useful for items with steady, predictable demand throughout the year — not for seasonal products or items with sudden spikes. It works best when:

• Demand is relatively constant and known in advance
• Ordering cost per order is fixed, regardless of order size
• Holding cost per unit is constant per year
• There are no quantity discounts that change the purchase price
• Lead time is constant and orders arrive in full

If your situation deviates from these assumptions, the EOQ still gives a useful baseline, but you may need to adjust for real-world factors like bulk discounts or variable demand.

How to Read the Result

The EOQ tells you the order size that minimizes the sum of two opposing costs:

• Ordering costs — the more often you order, the higher the total ordering cost (because each order has a fixed administrative, shipping, or setup cost).
• Holding costs — the more units you keep in inventory, the higher the storage, insurance, and capital costs.

If you order fewer than the EOQ, your ordering costs rise faster than your holding costs fall. If you order more than the EOQ, your holding costs rise faster than your ordering costs fall. The EOQ is the sweet spot where the two are equal.

For example, with D = 1,200, S = $25, H = $2, ordering 173 units at a time means you place about 7 orders per year (1,200 ÷ 173 ≈ 6.94). Your annual ordering cost is 7 × $25 = $175, and your average inventory is 173 ÷ 2 = 86.5 units, giving an annual holding cost of 86.5 × $2 = $173. The small difference is due to rounding.

Common Mistakes and Unit Mix-ups

The most frequent errors are:

• Mixing time periods — demand must be annual, not monthly or weekly. If you have monthly demand of 100 units, use D = 1,200, not 100.
• Holding cost per unit per year vs. per order — H must be the cost to hold one unit for one full year, not the cost per order or per month.
• Ordering cost per order vs. per unit — S is the fixed cost per order, not the cost per unit shipped.
• Currency units — S and H must be in the same currency. If ordering cost is $25 and holding cost is $2, that’s fine; if holding cost is in cents, convert to dollars first.
• Rounding too early — round the final EOQ, but keep full precision in intermediate steps to avoid a skewed total cost.

Limitations of the EOQ Model

The classic EOQ model makes simplifying assumptions that may not hold in practice:

• Constant demand — real demand fluctuates; EOQ can be recalculated periodically as demand changes.
• No quantity discounts — if a supplier offers lower unit prices for larger orders, the EOQ may be too low; you need to compare total costs at the discount threshold.
• Fixed ordering cost — if ordering cost varies with order size (e.g., shipping cost per unit), the model breaks down.
• Instantaneous replenishment — the model assumes the entire order arrives at once, not gradually over time.
• No stockouts — it assumes you never run out of stock; if stockouts are allowed, the model changes.

Despite these limits, EOQ remains a standard starting point for inventory management because it is simple, transparent, and often close to optimal even when assumptions are slightly violated.

Alternatives and Extensions

If the basic EOQ doesn’t fit your situation, consider these variations:

• Quantity discount model — compares total costs at each price break to find the best order size.
• Production order quantity (POQ) — for items produced internally, where inventory builds up gradually during production.
• Reorder point (ROP) — the inventory level at which you place a new order, based on lead time and safety stock.
• Safety stock — extra inventory to buffer against demand variability and supply delays; EOQ doesn’t include it.
• Periodic review system — instead of ordering a fixed quantity, you review inventory at fixed intervals and order up to a target level.

These methods often use EOQ as a building block, so understanding the basic formula helps with more advanced inventory planning.

Frequently Asked Questions

What is a good EOQ?

A “good� EOQ is simply the order quantity that minimizes total inventory costs for your specific inputs. There is no universal number; it depends entirely on your demand, ordering cost, and holding cost. If your current order size is far from the EOQ, you may be spending more than necessary on inventory.

Can EOQ be used for perishable goods?

Yes, but with caution. The standard EOQ assumes holding cost covers storage and capital, not spoilage. For perishable items, you must include spoilage or expiry costs in H, and you may need to cap the order size at the amount you can sell before the product expires. In practice, many perishable businesses use smaller, more frequent orders than the classic EOQ suggests.

How do quantity discounts affect EOQ?

Quantity discounts break the assumption of a constant unit price. When a supplier offers a lower price for larger orders, you should calculate the total annual cost (purchase + ordering + holding) at each price break and at the basic EOQ, then choose the quantity with the lowest total. Often the discounted price makes a larger order more economical even though it exceeds the basic EOQ.

What is the difference between EOQ and reorder point?

EOQ determines how many units to order each time. The reorder point determines when to place that order, based on lead time and average demand during that lead time. For example, if lead time is 2 weeks and weekly demand is 20 units, you reorder when inventory drops to 40 units, but the order size is still the EOQ.

Is EOQ still relevant for small businesses?

Yes. Even a small business with a handful of products can benefit from the EOQ framework because it forces you to think about the trade-off between ordering frequency and inventory holding. The formula is simple enough to compute on a spreadsheet, and the result gives a clear benchmark for order sizes, even if you adjust it for practical constraints like minimum order quantities or storage space.

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in d | Annual demand (units) | units/year | 1200 | 0
in s | Ordering cost per order | $ | 25 | 0
in h | Holding cost per unit per year | $ | 2 | 0
out eoq | Economic Order Quantity | units | sqrt((2 * d * s) / h) | 0
out tc | Total annual inventory cost | $ | sqrt(2 * d * s * h) | 2