Economic Order Quantity (EOQ) Calculator
Calculate the optimal order quantity that minimizes total inventory costs — the sum of ordering costs and holding costs — using the classic Wilson EOQ formula.
How to use this tool
- Enter annual demand (d), ordering cost per order (s) and annual holding cost per unit (h) in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your economic order quantity (eoq) and the full breakdown beneath it.
⚠ This tool provides general estimates for education only and is not financial, tax or legal advice. Figures may not reflect your situation — verify with a qualified professional.
Formula
EOQ = √(2DS / H)
Where D is annual demand in units, S is the fixed cost per order (ordering/setup cost), and H is the annual holding (carrying) cost per unit.
Total Annual Cost = (D/EOQ) × S + (EOQ/2) × H
How it works
The Economic Order Quantity model, also known as the Wilson EOQ formula, finds the order size that minimizes total inventory cost — the sum of ordering costs (which decrease as order size increases) and holding costs (which increase with order size). The minimum occurs where these two cost components are equal, which the square-root formula captures directly. The model assumes constant demand, fixed ordering and holding costs, instantaneous replenishment, and no quantity discounts.
Worked example
Widget Manufacturer with 1,000 Units/Year Demand
- Inputs: D = 1,000 units/year, S = $50 per order, H = $2 per unit per year
- EOQ = √(2 × 1,000 × 50 / 2) = √(100,000 / 2) = √50,000
- EOQ = 223.61 units per order
- Number of orders/year = 1,000 / 223.61 ≈ 4.47; Order cycle ≈ 365 / 4.47 ≈ 81.6 days
EOQ = 223.61 units. Total annual inventory cost = (1000/223.61)×50 + (223.61/2)×2 = $223.61 + $223.61 = $447.21.
Common mistakes to avoid
- Using unit purchase cost as the holding cost — holding cost H should be expressed as the cost per unit per year (storage, insurance, opportunity cost), not the purchase price itself.
- Plugging monthly demand into D without annualizing — EOQ uses annual demand; using monthly demand underestimates EOQ by a factor of sqrt(12).
- Ignoring quantity discounts by applying EOQ in isolation — when suppliers offer discounts at higher order quantities, the total cost comparison must include the lower per-unit price, which can make ordering more than the EOQ optimal.
Key terms
- What is EOQ?
- Economic Order Quantity (EOQ) is the optimal number of units a company should order to minimize the combined costs of ordering and holding inventory. Ordering fewer, larger batches reduces order frequency but increases storage costs; EOQ balances these two opposing cost drivers.
- What is ordering cost?
- Ordering cost (S) is the fixed cost incurred each time an order is placed, including administrative processing, transportation, and receiving costs. It is expressed per order, not per unit.
- What is holding cost?
- Holding cost (also called carrying cost) is the annual cost of storing one unit of inventory, including warehousing, insurance, obsolescence, and the opportunity cost of capital tied up in stock.
- What are the limitations of the EOQ model?
- The classic EOQ model assumes constant demand, fixed costs, and instantaneous replenishment — conditions rarely met in practice. Extensions such as the Economic Production Quantity (EPQ) or reorder-point models address variable demand, lead times, and quantity discounts.
Frequently asked questions
- What assumptions does the EOQ model make?
- EOQ assumes constant and known demand, fixed ordering cost, constant holding cost per unit, and instantaneous replenishment. Violating these (e.g., seasonal demand) reduces its accuracy.
- How does EOQ change if ordering costs double?
- EOQ = sqrt(2DS/H), so doubling S increases EOQ by sqrt(2) — roughly 41%. Higher ordering costs favor larger, less frequent orders.
- What is the reorder point and how does it relate to EOQ?
- The reorder point is the inventory level at which a new order should be placed. It equals lead-time demand (daily demand x lead time in days) and is independent of EOQ, which only determines how much to order.