EOQ Calculator
Free Eoqcalculator Calculator for operations & inventory. Enter your numbers to see returns, costs, and optimized scenarios instantly.
Formula
EOQ = √(2DS / H)
The Economic Order Quantity formula calculates the optimal order size by taking the square root of (2 times annual demand D times ordering cost per order S, divided by annual holding cost per unit H). This minimizes total inventory costs by balancing ordering and holding costs.
Worked Examples
Example 1: Manufacturing Parts Ordering
Problem: A factory uses 10,000 widgets per year. Each order costs $150 to place, and annual holding cost is $2 per widget. Lead time is 7 working days with 250 working days per year.
Solution: D = 10,000 units/year, S = $150/order, H = $2/unit/year\nEOQ = sqrt(2 × 10,000 × 150 / 2) = sqrt(1,500,000) = 1,225 units\nOrders per year = 10,000 / 1,225 = 8.16 orders\nAnnual ordering cost = 8.16 × $150 = $1,224\nAnnual holding cost = (1,225/2) × $2 = $1,225\nReorder point = (10,000/250) × 7 = 280 units
Result: EOQ = 1,225 units | 8.16 orders/year | Total cost = $2,449 | ROP = 280 units
Example 2: Retail Store Inventory
Problem: A store sells 5,200 units annually. Ordering cost is $75 per order, and holding cost is $4.50 per unit per year. Lead time is 3 days.
Solution: D = 5,200 units/year, S = $75/order, H = $4.50/unit/year\nEOQ = sqrt(2 × 5,200 × 75 / 4.50) = sqrt(173,333) = 416 units\nOrders per year = 5,200 / 416 = 12.5 orders\nOrder cycle = 250/12.5 = 20 working days\nReorder point = (5,200/250) × 3 = 62 units
Result: EOQ = 416 units | 12.5 orders/year | Total cost = $1,873 | ROP = 62 units
Frequently Asked Questions
What is the Economic Order Quantity (EOQ) model?
The Economic Order Quantity (EOQ) model is a fundamental inventory management formula that determines the optimal order quantity to minimize total inventory costs. Developed by Ford W. Harris in 1913 and later refined by R.H. Wilson, the EOQ model balances two opposing costs: ordering costs (which decrease as order size increases because fewer orders are needed) and holding costs (which increase as order size increases because more inventory is stored). The classic EOQ formula is Q* = sqrt(2DS/H), where D is annual demand, S is the ordering cost per order, and H is the annual holding cost per unit. The model assumes constant demand, fixed ordering costs, constant holding costs, instantaneous replenishment, and no quantity discounts, making it a starting point that many businesses adapt to their specific circumstances.
What are the limitations of the EOQ model?
The classic EOQ model has several important limitations that practitioners should understand. It assumes constant and known demand, which rarely occurs in practice as demand fluctuates seasonally and unpredictably. It assumes instantaneous replenishment, ignoring lead times and production schedules. It does not account for quantity discounts, which are common in real purchasing situations. The model assumes a single product in isolation, ignoring interactions between multiple products sharing warehouse space or transportation. It does not consider stockout costs or service level targets. Holding and ordering costs are assumed constant, when in reality they may vary with volume. Despite these limitations, EOQ remains valuable as a baseline calculation. Many extensions have been developed, including EOQ with quantity discounts, EOQ with backorders, the production EOQ model, and stochastic demand models.
How does lead time affect the EOQ reorder point?
Lead time does not affect the EOQ quantity itself but critically determines when to place an order, known as the reorder point (ROP). The basic reorder point formula is ROP = daily demand multiplied by lead time in days. For example, if daily demand is 20 units and lead time is 5 days, you should reorder when inventory drops to 100 units. In practice, companies add safety stock to account for variability in both demand and lead time: ROP = (average daily demand multiplied by average lead time) plus safety stock. Safety stock is typically calculated using the standard deviation of demand during lead time multiplied by a service level factor (z-score). Longer lead times require higher reorder points and often more safety stock, increasing average inventory levels and costs. Reducing lead times through supplier management, better logistics, or local sourcing can significantly reduce inventory investment.
How do I calculate EOQ with quantity discounts?
When suppliers offer quantity discounts, the standard EOQ formula must be extended because the unit purchase cost changes at different order quantities. The procedure involves several steps: first, calculate the EOQ at each price level using the standard formula. Then, check if each calculated EOQ falls within its valid price range. If an EOQ falls below its price break quantity, adjust it up to the minimum quantity for that price level. Next, calculate the total annual cost (ordering plus holding plus purchase cost) at each viable order quantity. Finally, select the quantity with the lowest total cost. The total cost formula is TC = (D/Q) multiplied by S plus (Q/2) multiplied by H plus D multiplied by the unit price. Sometimes ordering more than the EOQ is justified because the price discount savings exceed the additional holding cost. This analysis is essential for procurement professionals making bulk purchasing decisions.
What formula does EOQ Calculator use?
The formula used is described in the Formula section on this page. It is based on widely accepted standards in the relevant field. If you need a specific reference or citation, the References section provides links to authoritative sources.
Can I use EOQ Calculator on a mobile device?
Yes. All calculators on NovaCalculator are fully responsive and work on smartphones, tablets, and desktops. The layout adapts automatically to your screen size.