Optimal Order Quantity Calculator & Formula

This calculator works out the Economic Order Quantity (EOQ) — the ideal number of units to order at one time so that the combined cost of ordering and holding inventory is at its lowest. You enter annual demand, ordering cost per order, and holding cost per unit per year, and the calculator returns the optimal order quantity in units, plus the total annual inventory cost at that quantity.

Formula

The Economic Order Quantity is given by the classic EOQ formula:

EOQ = √(2DS / H)

Where:

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

The total annual inventory cost at the EOQ is √(2DSH), which is the sum of annual ordering costs (D/EOQ × S) and annual holding costs (EOQ/2 × H). At the optimal quantity, these two costs are exactly equal.

Worked Example

Using the default values from the calculator above:

• Annual demand (D) = 1,200 units
• Ordering cost (S) = $50 per order
• Holding cost (H) = $2 per unit per year

Step 1: Multiply 2 × D × S = 2 × 1,200 × 50 = 120,000

Step 2: Divide by H = 120,000 ÷ 2 = 60,000

Step 3: Take the square root = √60,000 ≈ 245 units

So the optimal order quantity is 245 units per order.

Total annual cost = √(2 × 1,200 × 50 × 2) = √240,000 ≈ $489.90. You can verify: ordering cost = (1,200 ÷ 245) × $50 ≈ $244.90, and holding cost = (245 ÷ 2) × $2 ≈ $245.00 — the two are nearly equal, as expected.

When to Use the EOQ Model

The EOQ model is best suited for items with steady, predictable demand throughout the year. Use it when you replenish a single product and the following assumptions hold reasonably well:

• Demand is constant and known in advance.
• Ordering cost per order is fixed, regardless of order size.
• Holding cost is a fixed percentage or dollar amount per unit per year.
• No quantity discounts are offered.
• Lead time is constant and orders arrive in full at once.

In practice, few businesses meet all these conditions perfectly, but EOQ still provides a useful baseline for inventory decisions, especially for stable, non-seasonal products.

How to Choose the Input Values

Getting accurate inputs matters more than the formula itself. Here is what each number should represent:

• Annual demand (D): Total units sold or used in a year. Use historical sales data adjusted for growth or decline. Do not use monthly demand without multiplying by 12.
• Ordering cost (S): All costs incurred each time you place an order — administrative time, paperwork, shipping, receiving, inspection. This is per order, not per unit.
• Holding cost (H): Cost to store one unit for one full year. Include storage space, insurance, taxes, spoilage, obsolescence, and the opportunity cost of capital tied up in inventory. Often estimated as 20–30% of the unit cost.

If you are unsure about a cost, run the calculation with a range of values. EOQ is fairly robust — a 20% error in an input usually produces only a small increase in total cost.

Common Mistakes and Misconceptions

A frequent error is mixing time periods: using monthly demand with annual holding cost, or vice versa. Keep everything on an annual basis. Another mistake is treating ordering cost as the price of the goods themselves — that is a separate variable and does not enter the EOQ formula because it does not change with order size.

A common misconception is that EOQ minimizes the cost of goods purchased. It does not — it only minimizes the sum of ordering and holding costs. If suppliers offer quantity discounts, the EOQ must be adjusted by comparing total costs at discount thresholds. Also, EOQ assumes demand is constant; for seasonal products, a fixed order quantity will be too high in slow months and too low in peak months.

Rounding matters: order quantities are usually whole units, so round the result to the nearest sensible number (e.g., 245 units, not 244.9). If the result is very small, it may indicate that ordering more frequently in smaller lots is better.

Limitations of the EOQ Model

The EOQ formula is a simplification. Real-world inventory systems face variable demand, stochastic lead times, stockouts, and multi-product constraints. The model also assumes that holding cost is linear with quantity, which may not hold for very large orders that require additional warehouse space.

For many businesses, a periodic review system (ordering at fixed intervals) or a reorder point system (ordering when stock hits a threshold) works better than a fixed order quantity. EOQ is still taught and used as a starting point because it is simple and gives a reasonable approximation for stable items.

Alternatives to the EOQ Model

• Reorder Point (ROP): Order a fixed quantity (often EOQ) when inventory falls to a predetermined level. Useful when demand or lead time varies.
• Periodic Review: Order at fixed intervals (e.g., weekly) to bring inventory up to a target level. Simpler to schedule but may require more safety stock.
• Just-in-Time (JIT): Order very small lots frequently to minimize holding costs. Requires reliable suppliers and stable demand.
• ABC Analysis: Classify items by annual value and apply different ordering policies to each class.

For products with quantity discounts, you must compare the total cost (ordering + holding + purchase) at the EOQ and at each discount breakpoint, choosing the quantity with the lowest overall cost.

Frequently Asked Questions

What is a good EOQ value?

There is no universal “good” value. The EOQ is the quantity that minimizes your specific ordering and holding costs. A small EOQ (e.g., 10 units) means ordering costs are low relative to holding costs, so frequent small orders make sense. A large EOQ (e.g., 10,000 units) means holding costs are low and ordering costs are high, so fewer large orders are better.

What happens if I order more or less than the EOQ?

Total inventory cost increases, but the increase is gradual near the optimum. Ordering 20% above or below EOQ typically raises total cost by only a few percent. The penalty becomes larger the further you deviate. That is why EOQ is often called a “sweet spot” — but it is not a sharp cliff.

How do I calculate holding cost per unit per year?

Add all storage-related costs for one unit over a year: warehouse rent (allocated per unit), insurance, taxes, shrinkage, and the opportunity cost of capital (often 10–15% of unit value). A common shortcut is to take 20–30% of the product’s unit cost. For example, a $10 item might have a holding cost of $2–$3 per year.

Does EOQ work for perishable goods?

Only if the shelf life is longer than the order cycle. If goods spoil before they are used, EOQ will overestimate the optimal quantity. For perishables, you need to cap the order quantity at the amount that can be sold or used before expiry, and consider spoilage as part of holding cost.

Can I use EOQ for multiple products at once?

The standard EOQ formula is for a single product. For multiple products, you would calculate EOQ for each separately, but this ignores shared ordering costs (e.g., one delivery truck for several items). In that case, you may need a joint replenishment model or simply group orders pragmatically.

Why is the total cost at EOQ equal to √(2DSH)?

At the EOQ, annual ordering cost (D/EOQ × S) equals annual holding cost (EOQ/2 × H). The total cost is the sum of these two equal parts, which simplifies to 2 × (EOQ/2 × H) = EOQ × H. Substituting EOQ = √(2DS/H) gives √(2DSH).

Related

• Arc Length of a Half Circle Calculator
• Area of a Circle Calculator: Formula & Examples
• Area Percent Change Calculator: Formula & Examples

in d | Annual demand | units/year | 1200 | 0
in s | Ordering cost per order | $ | 50 | 0
in h | Holding cost per unit per year | $ | 2 | 0
out eoq | Optimal order quantity | units | sqrt((2 * d * s) / h) | 0
out total | Total annual inventory cost | $ | sqrt(2 * d * s * h) | 2