EOQ Calculator (Economic Order Quantity)

Find the order size that minimizes total inventory cost using EOQ = √(2DS/H). Enter annual demand, ordering cost, and holding cost to get the optimal order quantity, orders per year, total annual inventory cost, and reorder point.

Quick Facts

Formula
EOQ = √(2 × D × S / H)
D = annual demand, S = cost per order, H = annual holding cost per unit.
Optimal point
Ordering cost = Holding cost
At the EOQ, total ordering cost per year exactly equals total holding cost per year.

Your Results

Calculated
Optimal order quantity
-
Units per order (EOQ)
Orders per year
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Annual demand ÷ EOQ
Total annual inventory cost
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Ordering cost + holding cost at EOQ
Reorder point
-
Stock level that triggers the next order

Ready

Enter annual demand, ordering cost, holding cost, and lead time, then press Calculate.

How the EOQ Calculator works

Economic Order Quantity (EOQ) is the classic inventory-management formula for finding the order size that minimizes total inventory cost: the cost of placing orders plus the cost of holding stock. Order too little at a time and you pay ordering costs (staff time, shipping, setup) too often; order too much at a time and you tie up cash and warehouse space in holding costs. EOQ finds the balance point.

The formula

For annual demand D (units), a fixed cost per order S ($), and an annual holding cost per unit H ($), the economic order quantity is:

EOQ = √(2 × D × S / H)

The calculator also reports orders per year (D ÷ EOQ), total annual inventory cost at that order size — (D ÷ EOQ) × S + (EOQ ÷ 2) × H — and the reorder point, which uses average daily demand (D ÷ 365) multiplied by your supplier's lead time in days.

Worked example

Suppose annual demand is 12,000 units, each order costs $75 to place, and holding one unit in stock for a year costs $3.50. EOQ = √(2 × 12,000 × 75 / 3.5) ≈ 717 units per order. That works out to about 16.7 orders per year, roughly one every 22 days, with total annual ordering-plus-holding cost around $2,510. With a 10-day lead time and daily demand of about 33 units, the reorder point is about 329 units.

Why ordering cost equals holding cost at the optimum

At the true EOQ, annual ordering cost — (D ÷ EOQ) × S — is exactly equal to annual holding cost — (EOQ ÷ 2) × H. This is not a coincidence; it falls out of setting the derivative of total cost with respect to order quantity to zero. Ordering in smaller batches raises ordering cost faster than it lowers holding cost, and vice versa for larger batches, so the two curves cross exactly at the minimum-cost point.

Model assumptions

  • Constant, known demand: the model assumes annual demand is steady and predictable, not seasonal or volatile.
  • Fixed costs per order and per unit held: S and H are treated as constants that do not change with order size or time.
  • No quantity discounts: the basic EOQ model does not account for bulk-purchase price breaks — those require an extended EOQ-with-discounts calculation.
  • No stockouts: the model assumes you never run out, so it does not include a shortage-cost term or safety-stock buffer beyond the reorder point.

Frequently Asked Questions

What is the EOQ formula?
Economic Order Quantity is EOQ = √(2 × D × S / H), where D is annual demand in units, S is the fixed cost of placing one order, and H is the annual holding cost per unit. The formula finds the order size that minimizes the sum of ordering costs and holding costs over a year.
How is total annual inventory cost calculated?
Total annual cost at the EOQ is ordering cost plus holding cost: (D ÷ EOQ) × S + (EOQ ÷ 2) × H. At the true EOQ these two terms are equal, and the total simplifies to √(2 × D × S × H). Ordering smaller or larger batches than the EOQ raises the total.
What is the reorder point and why does lead time matter?
The reorder point is the inventory level that triggers a new order so stock does not run out while the order is in transit. It is calculated as average daily demand (annual demand ÷ 365) multiplied by supplier lead time in days. Longer lead times require placing the next order earlier, at a higher stock level.
What does the EOQ model assume?
The classic EOQ model assumes constant, known annual demand, a fixed ordering cost per order, a constant holding cost per unit per year, no quantity discounts, no stockouts, and instantaneous or fixed-lead-time replenishment. Real inventories with variable demand or bulk discounts need extended models, but EOQ remains a solid baseline.

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