Economic Order Quantity Calculator
Compute the order size that minimizes the sum of annual ordering and holding costs, using the classic Wilson EOQ formula. Useful for setting standard purchase quantities, negotiating MOQ with suppliers, and balancing the trade-off between order frequency and inventory carrying cost.
Last updated: May 2026
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About this calculator
Economic Order Quantity (EOQ), also called the Wilson formula after F.W. Harris and R.H. Wilson who popularized it in 1913–1934, is the order size that minimizes the sum of two competing inventory costs: ordering cost (incurred each time you place an order) and holding cost (incurred per unit held in inventory per year). The formula is EOQ = √(2 × D × S / H), where D is annual demand in units, S is ordering cost per order (administrative time, freight, supplier setup), and H is holding cost per unit per year (warehouse space, insurance, capital cost, obsolescence). The total annual cost at EOQ is C(EOQ) = √(2 × D × S × H), and the number of orders per year is N = D / EOQ. Variables and edge cases: holding cost H is typically expressed as a fraction of unit cost (commonly 20–30% per year), making H = unit_cost × holding_rate; the formula assumes constant demand, instantaneous full delivery (no lead time effects), no quantity discounts, and a single-product setup. Sensitivity: the EOQ curve is fairly flat near the optimum — ordering within ±25% of EOQ raises total cost only 3–4%, so small deviations to accommodate MOQs, pallet quantities, or container fills are not costly. Real-world adjustments: with quantity discounts, evaluate total cost at each discount break and at the EOQ; choose the lowest. With MOQ above EOQ, you must order MOQ. With finite production rate (not instantaneous delivery), use the Production Order Quantity model. EOQ is a useful starting benchmark even when assumptions are violated.
How to use
Example 1 — small e-commerce retailer. Annual demand D = 1,200 units, ordering cost S = $50 per order (admin + freight allocation), holding cost H = $3 per unit per year (warehouse + capital). Step 1: 2 × D × S = 2 × 1,200 × 50 = 120,000. Step 2: divide by H = 120,000 / 3 = 40,000. Step 3: EOQ = √40,000 = 200 units per order. Verify with total annual cost: with EOQ = 200, ordering cost = (1,200 / 200) × $50 = 6 orders × $50 = $300/year; holding cost = (200 / 2) × $3 = $300/year. Ordering cost equals holding cost at EOQ — the mathematical signature of the optimum. Total annual cost = $600. Example 2 — distributor with MOQ constraint. Annual demand 24,000 units; ordering cost $200 per order; unit cost $4; holding rate 25% → H = 4 × 0.25 = $1/unit/yr. Step 1: 2 × D × S = 2 × 24,000 × 200 = 9,600,000. Step 2: / H = 9,600,000 / 1 = 9,600,000. Step 3: EOQ = √9,600,000 ≈ 3,098 units. Supplier MOQ is 5,000 units. Verify cost at MOQ vs. EOQ: at 3,098: orders/yr = 7.75 × $200 = $1,549; holding (3,098/2) × $1 = $1,549; total = $3,098. At 5,000: orders/yr = 4.8 × $200 = $960; holding (5,000/2) × $1 = $2,500; total = $3,460. Forced to MOQ, total cost rises $362 (12% premium over EOQ) — accept this cost, or negotiate the MOQ down. Sensitivity confirms the flat-curve property: ordering at 5,000 (61% above EOQ) only adds 12% to total cost.
Frequently asked questions
What assumptions does the EOQ formula make, and how robust is it when they are violated?
EOQ assumes (1) constant, known demand, (2) constant, known costs (ordering and holding), (3) instantaneous full-order delivery with no partial shipments, (4) no quantity discounts, (5) no stockouts allowed, and (6) a single product managed independently. In practice, all six are violated to some degree. Demand variability: EOQ remains useful as a benchmark, but actual order policy should include safety stock and dynamic reorder point. Lead time: ROP fills the lead-time gap; EOQ still works as the order quantity. Quantity discounts: evaluate total cost at the EOQ and at each discount break; pick the lowest — usually the next-larger break is optimal if discount > about 3%. MOQ: order at least the MOQ, recognizing the cost penalty. Multi-product joint replenishment: more sophisticated models (e.g., joint replenishment problem) outperform single-product EOQ for products sharing supplier orders. Despite these limitations, EOQ is taught universally because its conceptual lesson — balancing setup vs. holding cost — is correct even when the precise number is approximate. The EOQ cost curve is flat near the optimum, so being off by 25% raises cost only 3%.
How do I estimate holding cost per unit per year in practice?
Holding cost includes both direct and opportunity-cost components. Direct: warehouse space (rent or owned-warehouse depreciation, utilities, insurance) — typically 3–8% of unit cost per year; labor for picking, moving, cycle counting — 2–5%; risk of obsolescence, damage, shrinkage — 2–10% depending on product type; insurance — 0.5–2%. Opportunity cost: capital tied up in inventory that could earn returns elsewhere — set to your cost of capital, typically 8–15% for established businesses, 15–25% for startups or capital-constrained firms. Total holding cost rate is usually 20–30% of unit cost per year for typical products, higher for technology (35%+, due to obsolescence), perishables (40%+, due to spoilage), or seasonal goods. To convert to dollars per unit, multiply unit cost by the rate: $10 unit cost × 25% rate = $2.50/unit/year. For accurate EOQ, use marginal holding cost (extra cost of holding one more unit), not average — for owned warehouses with excess capacity, marginal space cost is near zero, but capital and obsolescence still apply.
When does the EOQ formula give the wrong answer, and what alternatives exist?
EOQ fails or gives suboptimal answers in several common scenarios. For products with significant quantity discounts (e.g., 10% off at 1,000 units, 15% off at 2,500), use the quantity-discount EOQ algorithm: compute EOQ at the unit cost for each tier, check whether the EOQ falls in or above that tier, and compare total costs at the EOQ or at each tier's minimum quantity. For products produced internally with a finite production rate (not instantaneous), use the Production Order Quantity (POQ) model: EPQ = EOQ × √(1 / (1 − d/p)) where d is demand rate and p is production rate. For multiple products sharing the same supplier order (joint replenishment problem), solve for a coordinated replenishment cycle and synchronize order frequencies. For perishable products or fashion goods with one-time selling windows, EOQ does not apply — use newsvendor or similar single-period models. For consignment or vendor-managed inventory, the supplier optimizes the order quantity, often using EOQ on the joint cost function. For very-low-volume slow movers, EOQ may recommend years of supply per order; floor the quantity at some minimum order frequency (e.g., quarterly) instead.
What are common mistakes when applying EOQ?
The most common mistake is using inaccurate ordering or holding costs — small errors in either input lead to over-stating EOQ by 20–50%. Many companies set S to just purchase-order processing time (5–15 dollars) when true ordering cost including freight, supplier setup, and receiving can be 50–500 dollars. Another error is using a year-old demand figure for D when demand has shifted 20–30% since; recalculate annually or quarterly. Holding cost rate is often understated by ignoring obsolescence and capital cost — a typical 'physical storage' figure of 5–8% misses the much larger 15–20% from capital + obsolescence. Treating EOQ as a hard rule rather than a starting point and ignoring MOQ, pallet quantities, container fills, or supplier minimums causes friction with operations and procurement. Applying EOQ to multi-SKU shared-truck supplier orders (where ordering cost is shared) overstates per-SKU ordering cost by ignoring the sharing. Finally, forgetting that EOQ is the order quantity but not the reorder point — these are two different decisions and need to be set separately.
When should I NOT use this calculator?
Skip EOQ for products with highly variable or seasonal demand where the constant-demand assumption is so far off that the answer is misleading — use demand-period-by-period or stochastic models instead. Do not use it for new product launches where there is no demand history; use forecast scenarios and ramp-up planning. Avoid EOQ for perishable goods (food, flowers, pharmaceuticals with expiry) where holding too many even briefly leads to write-offs; use shelf-life-constrained models. For one-time event purchases (seasonal apparel, custom inventory for a campaign), the newsvendor model is the right tool. For high-mix manufacturers with many components sharing supplier orders, joint-replenishment models work better than per-component EOQ. For consigned inventory or VMI relationships, the supplier sets the order quantity. For drop-ship or zero-inventory models, the framing does not apply — there is no order quantity to optimize. Finally, EOQ is a rough heuristic, not a precision tool — for high-stakes decisions, run real total-cost simulation (Monte Carlo) including demand variability, lead-time variability, stockout cost, and capacity constraints rather than the closed-form formula.