Economic Order Quantity Calculator Formula
Understand the math behind the economic order quantity calculator. Each variable explained with a worked example.
Formulas Used
Economic Order Quantity
eoq = holding_cost > 0 ? sqrt(2 * annual_demand * ordering_cost / holding_cost) : 0Orders Per Year
orders_per_year = holding_cost > 0 ? annual_demand / sqrt(2 * annual_demand * ordering_cost / holding_cost) : 0Total Annual Inventory Cost
total_annual_cost = holding_cost > 0 ? sqrt(2 * annual_demand * ordering_cost * holding_cost) : 0Variables
| Variable | Description | Default |
|---|---|---|
annual_demand | Annual Demand (units) | 10000 |
ordering_cost | Cost Per Order(USD) | 50 |
holding_cost | Annual Holding Cost Per Unit(USD) | 4 |
How It Works
How to Calculate Economic Order Quantity
Formula
EOQ = sqrt(2 x Annual Demand x Ordering Cost / Holding Cost Per Unit)
The EOQ model, developed by Ford W. Harris in 1913, finds the sweet spot between ordering too frequently (high ordering costs) and ordering too much at once (high holding costs). At the EOQ, total ordering costs equal total holding costs, producing the lowest combined inventory expense. While the model assumes constant demand and lead times, it provides an excellent starting point for inventory optimization.
Worked Example
Annual demand is 10,000 units. Each order costs $50 to place, and holding one unit for a year costs $4.
- 01EOQ = sqrt(2 x 10,000 x $50 / $4) = sqrt(250,000) = 500 units
- 02Orders Per Year = 10,000 / 500 = 20 orders
- 03Total Annual Cost = sqrt(2 x 10,000 x $50 x $4) = $2,000
Frequently Asked Questions
What are the limitations of EOQ?
EOQ assumes constant demand, fixed ordering and holding costs, and no quantity discounts. Real-world demand fluctuates, suppliers offer volume discounts, and lead times vary. Use EOQ as a baseline, then adjust for these factors.
What costs go into ordering cost?
Ordering cost includes purchase order processing, supplier communication, receiving and inspection labor, invoice processing, payment handling, and any shipping surcharges that are fixed per order regardless of quantity.
Ready to run the numbers?
Open Economic Order Quantity Calculator