EOQ Calculator

What is Economic Order Quantity (EOQ)?

Economic Order Quantity (EOQ) is an established inventory management formula that determines the optimal purchase batch size a company should order from suppliers. First formulated by Ford W. Harris in 1913 and later refined by R. H. Wilson, the model calculates the exact order size that minimizes the combined annual costs of placing orders and carrying inventory in stock.

Every business that stocks physical goods faces a fundamental tension between two opposing costs:

• Ordering costs: Fixed administrative, shipping, invoicing, and inspection charges incurred every time a purchase order is dispatched. Ordering in small, frequent batches multiplies these fixed expenses over the course of a year.
• Holding costs (carrying costs): Expenses associated with storing inventory, including warehouse leases, climate control, handling, insurance, shrinkage, spoilage, and the opportunity cost of working capital locked up in unsold stock. Ordering large batches drives holding costs upward.

The EOQ formula locates the exact mathematical balance point where these two cost curves intersect, producing the lowest possible total inventory expense.

The EOQ formula and mathematical foundation

The classic Wilson-Harris model derives the ideal batch size using three primary variables:

In this equation:

• D (Annual Demand): Total number of units required or sold over the annual planning horizon.
• S (Order Cost): Fixed setup or administrative cost incurred per purchase order, regardless of the quantity ordered.
• H (Holding Cost): Cost to hold and carry one unit of inventory in storage for a full year. If given as a percentage (carrying rate i multiplied by unit purchase cost C), substitute H = i × C.

Total annual inventory cost equation

Total annual inventory management cost equals annual ordering cost plus annual holding cost:

Here, D / Q represents the number of orders placed per year, and Q / 2 represents the average cycle stock maintained in inventory under constant depletion. Setting the derivative of total cost with respect to Q equal to zero proves that minimum cost occurs when annual ordering cost strictly equals annual holding cost.

Step-by-step worked example

Consider a regional industrial equipment distributor with the following operational data:

• Annual demand ($D$): 10,000 units
• Order cost ($S$): $50 per purchase order
• Holding cost ($H$): $4 per unit per year

Applying the formula step by step:

1. Calculate the numerator:
   $2 \times 10{,}000 \times 50 = 1{,}000{,}000$
2. Divide by annual holding cost per unit:
   $\frac{1{,}000{,}000}{4} = 250{,}000$
3. Extract the square root to find EOQ:
   $\mathrm{EOQ} = \sqrt{250{,}000} = 500\text{ units}$
4. Determine order frequency and cycle schedule:
   $N = \frac{10{,}000}{500} = 20\text{ orders/year}, \quad T = \frac{365}{20} \approx 18.25\text{ days}$
5. Verify annual cost balance:
   $\text{Ordering Cost} = 20 \times \$50 = \$1{,}000, \quad \text{Holding Cost} = \frac{500}{2} \times \$4 = \$1{,}000$

   Total annual inventory cost is exactly $2,000, split evenly between ordering and holding.

Integrating EOQ into broader working capital management

Calculating the economic order quantity is only one element of modern supply chain planning. Inventory decisions directly impact liquidity, working capital requirements, and profitability:

• Turnover speed: Monitor your cycle velocity alongside the days inventory outstanding calculator to ensure your replenishment batches align with target days of sales on hand.
• Financial statement valuation: Balance sheet audits require accurate asset tracking through the ending inventory calculator and total inventory absorption via the cost of goods sold calculator.
• Cash conversion cycle: Holding larger batches than necessary ties up working capital. Evaluate the cash drag across receivables, payables, and inventory with the cash conversion cycle calculator.

Practical considerations and adjustments in real operations

While the pure EOQ formula provides a solid theoretical baseline, operational reality often requires sensible adjustments:

• Supplier Minimum Order Quantities (MOQs): If a supplier mandates a minimum batch size of 1,000 units and your EOQ is 650 units, ordering 1,000 units is necessary unless supplier terms can be renegotiated.
• Quantity discounts: Vendors frequently offer price breaks for larger orders. If a price discount outweighs the extra holding cost of holding larger batches, ordering above EOQ can be financially advantageous.
• Packaging and pallet constraints: Goods typically ship in standardized cartons, skids, or full truckloads. Round your calculated EOQ to the nearest case or pallet multiple.
• Safety stock and demand variability: The standard EOQ model assumes uniform, constant demand. In practice, businesses maintain buffer safety stock to protect against lead-time delays and sales spikes.

Frequently asked questions