EOQ Calculator

What is Economic Order Quantity (EOQ)?

Economic Order Quantity (EOQ) is the order size that minimizes total annual inventory costs by balancing two opposing cost drivers: ordering costs (which decrease with larger orders) and holding costs (which increase with larger orders). The EOQ model, also known as the Wilson formula, finds the mathematical optimum.

Ordering costs include purchase order processing, receiving inspection, shipping, and supplier setup charges. Holding costs encompass warehousing, insurance, capital cost, obsolescence, and shrinkage — typically 20-30% of item value per year.

The EOQ model assumes constant demand, fixed ordering cost, fixed holding cost per unit, and no quantity discounts. Despite these simplifications, EOQ remains the foundation of inventory management and serves as an excellent starting point for more complex models.

Formula: EOQ = √(2DS / H) Orders per Year = D / EOQ Total Annual Cost = (D/Q) × S + (Q/2) × H where D = annual demand, S = order cost, H = holding cost per unit per year

Example Calculation

Annual demand D = 10,000 units, ordering cost S = $50 per order, holding cost H = $2 per unit per year. EOQ = √(2 × 10,000 × 50 / 2) = √500,000 = 707 units. Orders per year = 10,000 / 707 ≈ 14.1. Total cost = 14.1 × $50 + 354 × $2 = $707 + $707 = $1,414 per year.

When to Use This Calculator

• A purchasing manager determining optimal order quantities for repetitive MRO supplies to minimize total inventory cost
• An operations analyst setting up replenishment parameters in a new ERP or WMS system
• A supply chain consultant benchmarking current order sizes against the theoretical optimum to identify savings opportunities
• A small business owner deciding how much product to order from a supplier to balance shipping costs against storage costs

Common Mistakes to Avoid

• Using purchase price instead of holding cost — holding cost includes warehousing, insurance, capital cost, and obsolescence risk, typically 20-30% of item value per year
• Forgetting to include all ordering costs — order cost is not just the PO processing fee; include receiving, inspection, freight surcharges for small orders, and supplier setup charges
• Applying EOQ to items with quantity discount breaks — standard EOQ ignores price breaks; use the quantity discount model instead to compare total cost at each price tier
• Not rounding EOQ to practical units — if EOQ calculates 347 units but items ship in cases of 24, round to the nearest case quantity (336 or 360) with minimal cost impact

How to Interpret Results

• At the EOQ, annual ordering cost equals annual holding cost — this is the mathematical balance point that minimizes total cost
• If the EOQ is much larger than current order sizes, you are ordering too frequently and overpaying in ordering costs
• If the order cycle time seems too long (risk of obsolescence), consider a shorter cycle with slightly higher cost — EOQ is a starting point, not an absolute rule

Related Standards & References

• F. W. Harris (1913) — the original Economic Order Quantity derivation; also known as the Wilson formula
• APICS/ASCM Dictionary — defines EOQ, ordering cost, and carrying (holding) cost as the lot-sizing trade-off
• EOQ assumes constant demand and instantaneous replenishment — extensions (EPQ, quantity discounts, backorders) relax these for real procurement

Frequently Asked Questions

Is EOQ still relevant with modern supply chains?

Yes. While JIT and lean manufacturing reduce the need for large batches, EOQ still provides the baseline economic trade-off. Modern adaptations include incorporating quantity discounts, variable lead times, and multi-item joint replenishment. Even Amazon uses EOQ variants for replenishment decisions.

What if my demand is not constant throughout the year?

For seasonal or variable demand, use periodic EOQ (recalculate quarterly), the Silver-Meal heuristic, or dynamic lot-sizing methods like Wagner-Whitin. However, if demand coefficient of variation is below 0.2, standard EOQ remains a good approximation.

How sensitive is total cost to ordering the 'wrong' quantity?

The EOQ cost curve is relatively flat near the optimum. Ordering 20% more or less than EOQ increases total cost by only about 2%. This robustness means rounding EOQ to convenient lot sizes (full pallets, minimum order quantities) is perfectly acceptable without significant cost penalty.