EOQ Formula: Economic Order Quantity Calculator & Guide

How much should you order at a time? Order too little and you'll face frequent ordering costs and potential stockouts. Order too much and you'll tie up capital in excess inventory with high holding costs.

The Economic Order Quantity (EOQ) formula solves this dilemma by calculating the optimal order size that minimizes total inventory costs. Developed by Ford W. Harris in 1913 and later refined, it remains one of the most widely used inventory models today.

What is Economic Order Quantity (EOQ)?

EOQ is the ideal order quantity that minimizes the total cost of inventory management. It finds the sweet spot between two competing costs:

• Ordering costs: Expenses incurred each time you place an order (processing, shipping, receiving)
• Holding costs: Expenses for keeping inventory in stock (storage, insurance, capital, obsolescence)

Order small quantities frequently, and ordering costs add up. Order large quantities infrequently, and holding costs skyrocket. EOQ finds the balance point where total costs are minimized.

The EOQ Formula

This elegant formula emerges from calculus—finding the order quantity where the derivative of total cost equals zero. But you don't need calculus to use it; just plug in your numbers.

Understanding the Variables

D (Annual Demand): The total number of units you expect to sell or use in one year. Use demand forecasting to estimate this accurately.

S (Ordering Cost per Order): The fixed cost incurred each time you place an order, regardless of order size.

H (Holding Cost per Unit per Year): The annual cost to hold one unit in inventory. Typically calculated as a percentage of unit cost, ranging from 15-30% depending on industry.

Step-by-Step EOQ Calculation

Calculating Order Frequency

With EOQ calculated, determine how often to order:

From our example: 10,000 / 447 = 22.4 orders per year, or roughly every 16 days.

Total Cost at EOQ

Calculate total annual inventory cost to verify savings:

EOQ Model Assumptions

The classic EOQ model makes several simplifying assumptions:

1. Constant demand: Demand is known and steady throughout the year
2. Fixed costs: Ordering and holding costs don't change
3. Instantaneous replenishment: Orders arrive all at once, no lead time
4. No quantity discounts: Unit price is constant regardless of order size
5. No stockouts: Sufficient inventory is always available
6. Single product: Each item is analyzed independently

Real-world conditions often violate these assumptions, requiring adjustments or more sophisticated models.

EOQ Variations for Real-World Scenarios

EOQ with Quantity Discounts

When suppliers offer volume discounts, calculate total cost (including purchase cost) at each price break. The optimal order quantity might be at the EOQ or at a discount breakpoint.

EOQ with Lead Time

Lead time doesn't change the EOQ but affects when to order. Combine EOQ with safety stock calculations to set proper reorder points.

Production EOQ (EPQ)

For manufacturers who produce items gradually rather than receiving them all at once, use the Economic Production Quantity formula, which accounts for the production rate.

When to Use (and Not Use) EOQ

EOQ Works Well For:

• Stable, predictable demand items
• Standard products without customization
• Items with known, consistent costs
• B and C class items in ABC classification

Consider Alternatives For:

• Highly variable or seasonal demand
• Items with significant quantity discounts
• Perishable goods with shelf life constraints
• High-value items requiring tighter control
• New products without demand history

Implementing EOQ in Your Business

1. Gather accurate data: Audit your actual ordering and holding costs
2. Segment your inventory: Apply EOQ to stable items first
3. Calculate EOQ for each SKU: Different items have different optimal quantities
4. Set reorder points: Combine with safety stock for complete policy
5. Review periodically: Recalculate when costs or demand change significantly
6. Track results: Monitor inventory turnover and costs

Common EOQ Mistakes

1. Using purchase cost instead of holding cost: H should include all carrying expenses
2. Forgetting hidden ordering costs: Include all per-order expenses
3. Ignoring rounding: Round EOQ to practical order quantities
4. Static calculations: Update EOQ when demand or costs change
5. Applying to all items: Use judgment for seasonal or volatile items

Summary

The EOQ formula provides a mathematically optimal order quantity that balances ordering and holding costs. While based on simplifying assumptions, it offers a solid foundation for inventory ordering decisions.

Calculate EOQ using √(2DS/H), verify that ordering and holding costs balance, and combine with safety stock for complete inventory policies. Track your inventory KPIs to measure improvement over time.