Economic Ordering Quantity Formula & How to Use It

The Economic Ordering Quantity (EOQ) formula calculates the ideal order size that minimizes the total cost of ordering and holding inventory. You enter your annual demand, ordering cost per order, and holding cost per unit per year, and the calculator returns the optimal order quantity in units. This page explains the formula, walks through a worked example, and covers the assumptions and limitations you need to know before applying it.

Formula

The EOQ formula is written as:

EOQ = √(2DS / H)

• D = annual demand in units (how many you sell or use in a year)
• S = ordering cost per order in dollars (fixed cost per purchase order, not per unit)
• H = holding cost per unit per year in dollars (storage, insurance, capital tied up, shrinkage)

The result is the number of units to order each time you place an order. It balances two opposing costs: ordering too often (high order cost) versus holding too much inventory (high carrying cost). The square root ensures that as any input grows, the EOQ grows more slowly.

Worked Example

Using the default values from the calculator above:

• Annual demand (D) = 1,000 units
• Ordering cost (S) = $50 per order
• Holding cost (H) = $2 per unit per year

1. Multiply 2 × D × S: 2 × 1,000 × 50 = 100,000
2. Divide by H: 100,000 ÷ 2 = 50,000
3. Take the square root: √50,000 ≈ 223.6

So the EOQ is about 224 units per order. With that order size, you would place about 1,000 ÷ 224 ≈ 4.5 orders per year. The total annual cost is (1,000/224)×50 + (224/2)×2 ≈ $223.61 + $224 = $447.61. Notice that the ordering cost and holding cost are nearly equal at the EOQ—that is the defining property of the optimal point.

When to Use EOQ

EOQ is most useful for businesses that buy or produce items with relatively steady demand and predictable costs. It answers the question: “How much should I order each time to keep total inventory costs as low as possible?” It is commonly applied to raw materials, finished goods, and spare parts where the following conditions hold:

• Demand is known and constant throughout the year.
• Ordering cost is fixed per order, regardless of quantity.
• Holding cost is constant per unit per year.
• No quantity discounts are taken into account.
• Lead time is constant and known.

When these assumptions are met, ordering the EOQ minimizes the sum of ordering and holding costs. If demand is seasonal or highly variable, other models like the newsvendor model or periodic review systems may be more appropriate.

How to Choose Input Values

Getting the inputs right matters more than the math. Here are practical guidelines for each variable:

• Annual demand (D): Use the forecast for the next 12 months, not last year’s actuals if you expect growth or decline. For a new product, use the best estimate from market research or similar products.
• Ordering cost (S): Include all costs that occur each time you place an order: administrative labor, paperwork, shipping, receiving, inspection, and setup costs if you manufacture. Do not include the cost of the items themselves—that is a variable cost per unit, not per order.
• Holding cost (H): This is the cost to carry one unit for one year. It typically includes storage space (rent or depreciation), insurance, taxes, obsolescence, spoilage, and the opportunity cost of capital tied up in inventory. A common rule of thumb is 20–30% of the unit cost, but you should calculate it for your situation.

If you have trouble estimating S or H, try a range of values and see how sensitive the EOQ is. The square root function makes the result relatively forgiving to small errors—a 10% error in an input leads to roughly a 5% error in the EOQ.

Common Mistakes and Misconceptions

One frequent mistake is mixing units. If demand is monthly, convert it to annual before plugging into the formula. Similarly, holding cost must be per unit per year, not per unit per month. Another error is using the purchase price of the item as the holding cost—the holding cost is a percentage of that price, not the price itself.

A common misconception is that EOQ gives the minimum total cost. It does, but only under the stated assumptions. In reality, quantity discounts, storage limits, and fluctuating demand often mean the true optimal order size is different. For example, if a supplier offers a 5% discount for ordering 500 units instead of 224, the discount may outweigh the extra holding cost. You would need to compare total costs at each order size, not just use the raw EOQ.

Another pitfall is ignoring that EOQ assumes instantaneous replenishment. If your supplier delivers gradually (like a production run), you should use the production order quantity model, which adjusts for the usage rate during production.

Costs: Ordering vs. Holding

The EOQ model focuses on two types of costs that move in opposite directions:

• Ordering costs decrease as order size increases because you place fewer orders per year. If you order 1,000 units at a time, you order once per year; if you order 100 units, you order ten times.
• Holding costs increase as order size increases because you carry more average inventory. With an order size of Q, the average inventory is Q/2 (assuming steady usage and no safety stock).

The EOQ is the point where these two costs are equal. At that point, the total cost curve is at its minimum. If you plot total cost against order quantity, you get a U-shaped curve—the EOQ is at the bottom. This balance is why the formula uses the square root of (2DS/H): it finds the quantity where the marginal savings from one more unit of order size equals the marginal cost of holding that unit.

Safety Stock and Reorder Point

EOQ tells you how much to order, but not when to order. The reorder point (ROP) determines when to place the order: ROP = (daily demand × lead time in days) + safety stock. Safety stock is extra inventory held to protect against demand variability or supply delays. EOQ assumes constant demand and lead time, so it does not include safety stock. In practice, you would add safety stock based on the desired service level and the variability of demand and lead time. The EOQ remains the order quantity, but you place the order earlier to avoid stockouts.

For example, if daily demand is 10 units and lead time is 5 days, the reorder point is 50 units. If you want a safety stock of 20 units, you order when inventory drops to 70 units. The order size is still the EOQ (say, 224 units), but you trigger the order at 70 units remaining.

Alternatives to EOQ

EOQ is a classic model, but it is not always the best fit. Several alternatives address its limitations:

• Quantity discount model: Extends EOQ by comparing total costs at different price breaks. You calculate EOQ at each price and then check if the discount makes a larger order cheaper overall.
• Periodic review system: Orders are placed at fixed intervals (e.g., every month) rather than at a fixed quantity. The order size varies based on current inventory. This is simpler to manage but may require more safety stock.
• Just-in-Time (JIT): Aims for very small order quantities and frequent deliveries to minimize inventory. This works well in stable, high-volume environments but requires reliable suppliers.
• Material Requirements Planning (MRP): Uses a bill of materials to calculate exact quantities needed over time, often for manufacturing. It handles dependent demand (where demand for one item depends on another) better than EOQ.
• Newsboy model: For perishable items with a single selling season, where you must choose a quantity before demand is known. It balances the cost of overstocking versus understocking.

Choose the model that matches your demand pattern, cost structure, and operational constraints. EOQ is a great starting point, but real-world complexity often requires adjustments.

Frequently Asked Questions

What if my demand is not constant?

EOQ assumes constant, known demand. If your demand varies seasonally or randomly, the basic EOQ may still give a reasonable average order size, but you should consider safety stock and possibly a periodic review system. For highly variable demand, simulation or more advanced inventory models are better.

How do I handle quantity discounts?

Calculate the EOQ at each price level, then compare the total cost (ordering + holding + purchase cost) for each candidate order quantity. The lowest total cost is the optimal order size. Often the discount threshold is higher than the EOQ, so you need to decide if the extra holding cost is worth the lower unit price.

What is the difference between EOQ and reorder point?

EOQ determines how much to order each time, while the reorder point determines when to place the order. EOQ is about order quantity; reorder point is about timing. Both are needed for a complete inventory policy. The reorder point depends on lead time and demand during that lead time, plus safety stock.

Can EOQ be used for manufacturing?

Yes, but with a modification. The production order quantity model (also called EPQ) accounts for the fact that items are produced and used simultaneously. The formula is similar but includes a production rate term. If production is instantaneous (all at once), the basic EOQ applies.

Why is the holding cost often a percentage of unit cost?

Because many holding costs—like capital tied up, insurance, and taxes—scale with the value of the inventory. If a unit costs $100, the capital cost of holding it for a year might be $10 (10% interest), plus storage and other costs. Using a percentage makes it easy to estimate H for different items.

What happens if I order more than the EOQ?

Your total cost will be higher than the minimum. Ordering more reduces ordering costs but increases holding costs. The total cost curve is relatively flat near the EOQ, so a small deviation (e.g., 10% more) might only increase total cost by a few percent. However, large deviations can be costly.

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in d | Annual demand | units/year | 1000 | 0
in s | Ordering 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 orders | Orders per year | - | d / eoq | 1
out total_cost | Total annual cost | $ | (d / eoq) * s + (eoq / 2) * h | 2