Reorder Quantity Formula: How to Calculate It

This calculator works out the economic order quantity (EOQ), the reorder quantity that minimizes the total cost of ordering and holding inventory. You enter annual demand, ordering cost per order, and holding cost per unit per year, and the calculator returns the optimal order size in units. The result tells you how many units to order each time you place a purchase order.

Formula

The reorder quantity is given by the economic order quantity (EOQ) formula:

EOQ = √(2DS / H)

• D = annual demand in units per year (how many units you sell or use in a year)
• S = ordering cost in dollars per order (fixed cost to place and receive one order, not per unit)
• H = holding cost in dollars per unit per year (cost to store one unit for one year, including capital, storage, insurance, and obsolescence)

The result is in units, and it represents the quantity to order each time you replenish stock to minimize the sum of annual ordering costs and annual holding costs.

Worked Example

Using the default values from the calculator:

• Annual demand (D) = 1200 units/year
• Ordering cost (S) = $50 per order
• Holding cost (H) = $2 per unit per year

Plug into the formula:

EOQ = √(2 × 1200 × 50 / 2) = √(120000 / 2) = √60000 ≈ 244.95 units

Rounded to the nearest whole unit, the reorder quantity is 245 units per order. The calculator rounds to 0 decimals, so it displays 245. The number of orders per year is 1200 / 245 ≈ 4.9 orders.

What Is the Reorder Quantity?

The reorder quantity is the number of units you order each time you replenish inventory. It is a core decision in inventory management because it directly affects two opposing costs:

• Ordering costs – administrative costs, shipping, receiving, and inspection. These are incurred each time you place an order, so ordering more frequently (smaller quantities) increases total ordering cost.
• Holding costs – storage space, insurance, depreciation, and the opportunity cost of capital tied up in inventory. Ordering larger quantities means you hold more stock on average, which increases holding cost.

The EOQ model finds the quantity that balances these two costs, giving the lowest total annual cost. It assumes demand is constant and known, and that orders arrive instantly and in full.

How to Choose the Right Reorder Quantity

To use the EOQ formula effectively, you need accurate estimates for the three inputs:

1. Estimate annual demand (D) – use historical sales data or forecasts. Be realistic; overestimating leads to overstocking, underestimating leads to stockouts.
2. Determine ordering cost (S) – include all costs that occur per order, such as purchase order processing, freight, receiving labor, and quality inspection. Do not include the cost of the items themselves.
3. Calculate holding cost (H) – include storage rent, utilities, insurance, shrinkage, and the cost of capital (often 20-30% of the item’s value per year).

Once you have these, the formula gives the optimal order quantity. In practice, you may adjust the result to match supplier minimums, truckload capacities, or storage constraints. The EOQ is a starting point, not a rigid rule.

Common Mistakes and Misconceptions

• Using the wrong cost basis – ordering cost is per order, not per unit. Holding cost is per unit per year, not per order or per total inventory value.
• Mixing time periods – if demand is given monthly, multiply by 12 to get annual demand. If holding cost is quoted per month, multiply by 12 to get annual holding cost.
• Ignoring lead time – EOQ tells you how much to order, but not when. The reorder point (ROP) is a separate calculation: ROP = daily demand × lead time in days. The reorder quantity and reorder point work together.
• Assuming constant demand – real demand fluctuates. For seasonal or variable demand, the basic EOQ may not be optimal; consider safety stock or a periodic review system.
• Rounding incorrectly – the EOQ is often a fractional number. Round to a practical quantity (e.g., whole units or case sizes), but rounding to the nearest whole number is usually fine.

Limitations of the EOQ Formula

The EOQ model relies on several simplifying assumptions:

• Demand is constant and known with certainty.
• Ordering cost is fixed and independent of order size.
• Holding cost is linear and proportional to the number of units held.
• No quantity discounts are considered.
• Orders arrive instantly (zero lead time) or lead time is constant.

In real life, these assumptions are rarely perfectly met. If you have quantity discounts, the EOQ may not be optimal because a larger order could reduce the unit price enough to offset higher holding costs. In that case, compare the total cost at the EOQ with the total cost at each discount breakpoint. For variable demand, you may need safety stock to avoid stockouts, which the basic EOQ does not include.

Alternatives to EOQ

When the EOQ assumptions are too restrictive, other methods can be used:

• Periodic review (fixed interval) – order a variable quantity at fixed time intervals (e.g., every week). The order quantity is the amount needed to bring inventory up to a target level.
• Min-max system – order up to a maximum level when inventory drops to a minimum (reorder point). The order quantity is the difference between the max and current inventory.
• Just-in-time (JIT) – order very small quantities frequently, often daily, to minimize holding costs. This requires reliable suppliers and stable demand.
• Material requirements planning (MRP) – for dependent demand (e.g., components in manufacturing), MRP calculates order quantities based on the production schedule.

Each method has trade-offs. EOQ is simple and works well for independent, steady demand. The others handle variability better but require more data or closer supplier coordination.

Frequently Asked Questions

What is the difference between reorder quantity and reorder point?

The reorder quantity (EOQ) is how many units to order each time. The reorder point is when to place the order, based on lead time and daily demand. For example, if daily demand is 10 units and lead time is 5 days, the reorder point is 50 units. When inventory drops to 50, you place an order for the EOQ (e.g., 245 units).

How do I calculate reorder quantity if I have a quantity discount?

The basic EOQ ignores discounts. To handle discounts, calculate the total annual cost (ordering + holding + purchase cost) at the EOQ and at each discount breakpoint. Choose the order quantity with the lowest total cost. For example, if the EOQ is 245 units but a discount applies at 500 units, compare the total cost at 245 and at 500.

What if my demand is not constant?

If demand varies, the EOQ may still be a good average, but you should add safety stock to cover variability. Alternatively, use a periodic review system where you order up to a target level at fixed intervals. The target level is calculated to cover demand during the review period plus lead time, plus safety stock.

Can I use EOQ for a single product or multiple products?

EOQ is typically calculated per product because each product has its own demand, ordering cost, and holding cost. For multiple products from the same supplier, you might combine orders to save on ordering cost, but then the per-order cost is shared, and the optimal quantity for each product changes. This is a more advanced joint replenishment problem.

How often should I recalculate the reorder quantity?

Recalculate whenever your demand, ordering cost, or holding cost changes significantly. Many businesses review EOQ annually or quarterly, or when they renegotiate supplier contracts. If demand is stable, the EOQ remains valid for a long time.

Does EOQ work for perishable goods?

For perishable items, the EOQ may overestimate the order quantity because it does not account for spoilage or expiration. In that case, you should limit the order quantity to the amount that can be sold before expiration. Consider using a shorter review period and smaller, more frequent orders to reduce waste.

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in d | Annual demand | units/year | 1200 | 1
in s | Ordering cost | $/order | 50 | 0
in h | Holding cost | $/unit/year | 2 | 0.01
out eoq | Economic order quantity | units | sqrt((2 * d * s) / h) | 0
out orders | Orders per year | orders | d / eoq | 1