Economic Order Quantity (EOQ) Calculator

About the Economic Order Quantity (EOQ) Calculator

The Economic Order Quantity (EOQ) is the ideal order size that minimizes the combined cost of ordering and holding inventory. Developed by Ford W. Harris in 1913 and later refined by R.H. Wilson, the EOQ model remains one of the most widely used inventory management tools in manufacturing and supply chain operations.

The core insight behind EOQ is that ordering costs and carrying costs move in opposite directions as order size changes. Larger orders reduce the number of orders placed per year (lowering ordering costs) but increase average inventory on hand (raising carrying costs). The EOQ formula finds the exact point where these two cost curves intersect, yielding the lowest total inventory cost.

This calculator lets you enter annual demand, cost per order, and annual holding cost per unit to quickly compute your optimal order quantity, the number of orders per year, and the total annual inventory cost at that optimum.

When This Page Helps

Without EOQ analysis, companies often order in round lots or based on gut feel, leading to excess inventory or excessive ordering frequency. The EOQ calculation provides a data-driven starting point for order quantity decisions, potentially saving thousands of dollars annually in combined inventory costs.

How to Use the Inputs

1. Enter the annual demand for the item in units.
2. Enter the fixed cost per order (setup, shipping, admin).
3. Enter the annual holding cost per unit (storage, capital, insurance).
4. Review the optimal EOQ result.
5. Note the suggested number of orders per year.
6. Compare the total annual cost against your current ordering pattern.
7. Adjust inputs for sensitivity analysis on key variables.

Example Calculation

Tips & Best Practices

• EOQ assumes constant demand — adjust for seasonality by recalculating quarterly.
• Include all ordering costs: purchase orders, receiving inspection, freight, and payment processing.
• Holding cost per unit = unit value × carrying rate (typically 20-30%).
• Round EOQ to practical pack sizes or pallet quantities for real-world application.
• Recalculate EOQ when supplier pricing, freight rates, or warehouse costs change.
• Use EOQ as a starting point, then layer on constraints like shelf life and storage capacity.

History of the EOQ Model

The EOQ formula was first published by Ford W. Harris in 1913 and popularized by R.H. Wilson in 1934, which is why it is sometimes called the Wilson EOQ model. Despite being over a century old, the formula remains relevant because its core trade-off — balancing ordering frequency against inventory investment — is fundamental to every supply chain.

Practical Adjustments to EOQ

In practice, companies rarely order exactly the EOQ amount. Orders are rounded to case packs, pallet quantities, or truckload multiples. Minimum order quantities imposed by suppliers may exceed EOQ. Seasonal demand spikes may require temporarily larger orders. The key is to use EOQ as a baseline and document why actual orders deviate.

EOQ and Lean Manufacturing

Lean practitioners sometimes view EOQ skeptically because it can justify large batch sizes. However, the lean approach of reducing setup costs and lead times directly lowers the S variable in the formula, naturally reducing EOQ toward single-piece flow. EOQ and lean thinking are complementary when setup reduction is part of the improvement strategy.

Frequently Asked Questions

• What is Economic Order Quantity?

  EOQ is the mathematically optimal number of units to order each time you replenish inventory. It minimizes the sum of ordering costs and holding costs over a year, assuming constant demand and lead time.

• What assumptions does the EOQ model make?

  The classic EOQ model assumes constant and known demand, fixed ordering cost, constant holding cost per unit, instantaneous replenishment, and no quantity discounts. Real-world adjustments are often needed for seasonality, lead time variability, and bulk pricing.

• How do I estimate holding cost per unit?

  Multiply the unit cost by the annual carrying rate. Carrying rates typically range from 20% to 35% and include capital cost, storage, insurance, obsolescence, and shrinkage. For a $10 item at 25%, holding cost is $2.50/unit/year.

• Can EOQ be used for multiple items?

  Yes, calculate EOQ separately for each SKU. Some companies use joint replenishment models when multiple items share a supplier or shipment, adjusting the ordering cost allocation.

• What if demand is uncertain?

  EOQ handles the order quantity decision. Pair it with safety stock calculations to handle demand variability. The reorder point (ROP) determines when to order, while EOQ determines how much.

• How sensitive is EOQ to input changes?

  EOQ is relatively robust because of the square root function. A 50% error in demand only changes EOQ by about 22%. This makes EOQ practical even with moderate forecasting uncertainty.

• Does EOQ account for quantity discounts?

  The basic EOQ model does not. For quantity discounts, calculate EOQ at each price break and compare total costs (purchase + ordering + carrying) to find the overall minimum cost order quantity.