EOQ Calculator
Find the optimal order quantity that minimises total inventory cost. The Economic Order Quantity balances two opposing forces: ordering too frequently drives up ordering costs, while ordering too rarely drives up holding costs. EOQ finds the exact minimum between them.
EOQ is derived by finding the order quantity Q that minimises the sum of two cost functions: ordering cost = (D/Q) × S, which decreases as Q increases; and holding cost = (Q/2) × H, which increases as Q increases. The minimum of their sum occurs precisely where the two are equal — a result that emerges from setting the derivative of total cost to zero and solving for Q.
At EOQ, annual ordering cost always equals annual holding cost. This “golden cross” property is useful for validation: if your calculated ordering and holding costs are not approximately equal, recheck your inputs.
The formula assumes constant demand, fixed costs per order, and instantaneous replenishment. For variable demand or lead times, consider safety stock calculations and reorder point models.
History of the EOQ Model
The Economic Order Quantity formula was first published by Ford Whitman Harris, an engineer at Westinghouse Electric, in a 1913 paper titled “How Many Parts to Make at Once” in the journal Factory, The Magazine of Management. Harris derived the formula to solve a practical problem: how large a production run minimises the combined cost of setup and inventory carrying?
The model was independently rediscovered and popularised by R.H. Wilson, a management consultant, whose 1934 paper spread the technique widely. For decades it was known as the “Wilson Formula” — Harris’s original derivation was largely forgotten until researchers traced the credit back to him in the 1980s.
EOQ became foundational to Operations Research (OR) and supply chain management, forming the basis of more sophisticated inventory models including the Economic Production Quantity (EPQ), the Newsvendor Model, and multi-echelon inventory theory. Despite the rise of just-in-time (JIT) and demand-driven supply chains, EOQ remains a core analytical tool for establishing baseline order policies in classical inventory management.
How the Calculator Works
The calculator computes EOQ as the square root of (2 × D × S / H). It then calculates the number of orders per year as D/EOQ, and the order interval as 365/orders per year.
The cost curve chart plots total cost, ordering cost, and holding cost as functions of order quantity across a range from zero to 3× EOQ. This reveals the shape of the cost landscape: total cost has a flat, shallow minimum — meaning order quantities near but not exactly at EOQ are nearly as efficient as the theoretical optimum. A 20% deviation from EOQ typically results in less than 2% cost increase, which has important practical implications for rounding to practical lot sizes.
The chart also visually confirms the key property: at EOQ, the ordering cost and holding cost lines intersect — they are always equal at the optimum.
How to Use This Tool
Annual demand (D): Use 12-month actuals or a demand forecast. For new items, use comparable item demand or a market-based estimate.
Ordering cost (S): This is the total cost of one purchase cycle — typically staff time to raise a PO, supplier processing fees, receiving and inspection costs, and any administrative overhead. For most organisations, this ranges from ₹500 to ₹5,000 per order depending on the complexity of the procurement process.
Holding cost (H): The most commonly underestimated input. Include: warehouse space cost allocated to the item, insurance, spoilage and obsolescence risk, and most importantly, the opportunity cost of capital tied up in inventory. A practical formula: H = unit cost × 25% per year is a widely used approximation.
Once you have EOQ, round to the nearest practical lot size (pallet quantity, minimum order quantity, etc.) — the flat cost curve means this rounding has minimal cost impact.