EOQ Calculator (Economic Order Quantity)

EOQ = √(2 × D × S / H). The Wilson formula, published by Ford W. Harris in 1913 and popularized by R.H. Wilson. It finds the order quantity that minimizes total inventory cost, balancing the cost of ordering frequently against the cost of sitting on a large batch.

Where:

• D = annual demand (units per year)
• S = setup or order cost per order ($)
• H = holding cost per unit per year ($)

The trade-off the formula solves. Two costs move in opposite directions:

• Ordering cost: small batches mean many orders per year, each with admin overhead, shipping minimums, vendor processing time. Annual ordering cost = (D / Q) × S.
• Holding cost: large batches mean lots of inventory sitting in the warehouse paying rent, insurance, obsolescence, and capital cost. Annual holding cost = (Q / 2) × H.

EOQ is the Q where those two curves cross, and that crossing is the total-cost minimum. That is not a coincidence of the algebra, it is the most useful property of the model: at the economic order quantity, your annual ordering cost and your annual holding cost are exactly equal. If you already know both numbers for a part and one is triple the other, you do not need this calculator to tell you the batch size is wrong.

Worked derivation (the math sanity check).

• Total annual cost = (D / Q) × S + (Q / 2) × H
• Take derivative with respect to Q: -D × S / Q² + H / 2 = 0
• Solve: Q² = 2 × D × S / H
• Q = √(2DS / H)

Holding cost components (H per unit per year):

• Capital cost (cost of money tied up in inventory): typically 10-15% of unit value
• Storage (warehouse rent, utilities, security): 2-5% of unit value
• Insurance and taxes: 1-3%
• Obsolescence and shrinkage: 2-10% (huge for fashion, electronics, food)
• Total H is typically 15-30% of unit value annually

Order cost (S per order):

• Purchase order processing: $50-$200 in admin
• Inbound logistics (receiving, putting away): $20-$100 per order
• Quality inspection: varies
• Vendor minimum charges, freight tier breaks
• Total S typically $50-$500 for routine orders, much higher for capital purchases

Typical EOQ-driven decisions.

• A widget with D = 10,000/year, S = $100, H = $5: EOQ = √(2 × 10,000 × 100 / 5) = √400,000 = 632 units per order. Orders per year = 10,000 / 632 = 15.8 (every ~3.3 weeks).
• A high-value, slow-moving part: D = 50, S = $500, H = $200: EOQ = √(2 × 50 × 500 / 200) = √250 = 16 units per order. Orders per year = 3.

EOQ assumes constant demand and instantaneous replenishment. Both are oversimplifications. The model breaks down for:

• Seasonal demand (Christmas spikes, summer peaks): use period-specific EOQ or different model.
• Stochastic demand: add safety stock above EOQ-based reorder point.
• Quantity discounts: a vendor offering price breaks at higher volumes needs the tiered-pricing version of EOQ, not this one.
• Backorders allowed: introduces shortage cost as a third variable.

The reorder point. EOQ tells you HOW MUCH to order; reorder point tells you WHEN. ROP = (daily demand × lead time in days) + safety stock. Take the widget above: 10,000 units a year is 27.4 a day, so a 14-day lead time puts the reorder point at 384 units plus whatever safety stock the demand variability justifies.

Note the day basis. This calculator divides annual demand by 365, so the lead time you type has to be calendar days, which is how suppliers quote them anyway. If your demand figure only covers working days, divide by 250 instead and adjust the lead time to match.

Sensitivity is forgiving. EOQ uses a square root, so doubling your estimate of D, S, or H moves the answer by only 41%. And the cost penalty is gentler still: misjudge the batch size by 20% in either direction and total inventory cost rises by at most 2.5%. That is why nobody agonizes over the third decimal place of a holding-cost estimate, and why rounding 632 up to a 650-unit pallet costs you almost nothing.

Where EOQ fails. Just-in-time inventory inverts the logic. Toyota’s lean approach minimizes inventory through frequent small orders supported by tight supplier integration. EOQ takes the order cost as a given; JIT engineers it down to near zero, which drives the economic quantity down with it. Same formula, different lever.