📋 EOQ Calculator

Every inventory manager faces the same tug-of-war: order big and infrequent to save on ordering costs, or order small and often to save on holding costs. The economic order quantity finds the exact point where the two costs balance and total cost bottoms out. It is nearly a century old, and it still beats gut feel.

How to Use This Calculator

The Formula

The square root is the elegant part: doubling demand raises the optimal order by only 41 percent, because the two costs push in opposite directions. At the EOQ, annual ordering cost exactly equals annual holding cost. For the stock left at period end, see our ending inventory calculator.

Worked Example

A distributor sells 10,000 units a year. Each order costs $50 to place and receive; holding one unit for a year costs $2. EOQ = √((2 × 10,000 × 50) / 2) = √500,000 ≈ 707 units. That means 14.14 orders per year, roughly one every 26 days. Annual ordering cost = 14.14 × $50 ≈ $707; annual holding cost = 353.5 × $2 ≈ $707; the two match, confirming the optimum, with total relevant cost ≈ $1,414.

Tips for Real-World Use

Estimate holding cost honestly: most firms guess 10 percent of unit value when the true all-in cost, including the cost of capital, runs 20 to 25 percent. Round the EOQ to pack sizes; ordering 707 units when cartons hold 100 means ordering 700. Recompute when demand shifts materially, since the square root dampens but does not erase changes. And layer safety stock on top for variability; EOQ assumes beautifully steady demand, which no real business has.

Common Mistakes

Including the purchase cost of goods in S or H double-counts, because EOQ optimizes only the costs that change with order size. Using monthly demand with annual holding cost mixes time units and quietly breaks the math. Ignoring quantity discounts is the costly one: if ordering 1,000 units cuts the unit price 5 percent, the true optimum may sit above the EOQ, so always test discount breakpoints against the EOQ total cost.

When EOQ Breaks Down

The model assumes constant demand, instant replenishment, and no stockouts, which fits stable consumables and fails fashionable goods. Perishables need the newsvendor model instead; lumpy project demand needs MRP. Treat EOQ as the starting bid in the negotiation with reality, then adjust for discounts, shelf life, and cash constraints. A model you adjust beats a gut you cannot audit.

Multi-product businesses complicate EOQ with shared constraints: warehouse space, truck capacity, or a single supplier minimum. The textbook answer computes EOQ per SKU, then adjusts for the binding constraint, often via an exchange curve trading total orders against average inventory. Start with individual EOQs, then tune for the shared limit; the unconstrained optimum is the baseline every compromise is measured against.

EOQ with Quantity Discounts

Suppliers dangle discounts that pull order sizes above the EOQ: order 1,000 units instead of 707 and the unit price drops 5 percent. The EOQ formula ignores purchase price, so the true optimum needs a total-cost comparison. Compute annual cost (purchase + ordering + holding) at the EOQ and at each discount breakpoint, then pick the lowest total.

The arithmetic often favors the discount more than intuition suggests. On 10,000 units at $20 each, a 5 percent discount saves $10,000 yearly in purchase cost, dwarfing the few hundred dollars of extra holding cost from ordering 1,000 at a time. Discounts attack the biggest cost line; EOQ optimizes the smaller ones.

Watch the traps: discounts on perishables inflate spoilage, volume commitments strain cash flow, and "discounts" that merely match the EOQ economics are marketing. Run the total-cost math every time, and remember the supplier offering the discount did the same math from their side.

EOQ vs Just-in-Time

Just-in-time looks like EOQ's opposite but is really its child. JIT attacks the ordering cost S with kanbans, EDI, and supplier partnerships; as S collapses toward zero, the EOQ formula's answer collapses too, and tiny frequent orders become optimal. Toyota did not refute the math; it changed the inputs.

The vulnerability is fragility. EOQ's inventory buffers absorb supply shocks; JIT's thin pipeline snaps when a ship blocks a canal or a pandemic closes a port. The optimal system balances the EOQ's cost logic against resilience value the formula never priced. Post-2020, that resilience premium got much bigger.

The practical synthesis: run EOQ logic for the baseline, then add strategic safety stock for critical components with concentrated supply. Let the formula set the rhythm and let risk management set the buffer. Dogma in either direction, pure EOQ or pure JIT, loses to a hybrid that respects both cost and continuity.

Estimates for planning only, not financial advice.