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Economic Order Quantity (EOQ) Calculator

Find the order size that minimizes combined ordering and holding cost, using the classic Wilson EOQ formula: EOQ = √(2DS/H).

Economic order quantity
223.6 units
Orders per year
4.47
Time between orders
81.6 days
Total annual ordering + holding cost
$447.21

How it works

Ordering inventory involves two opposing costs: a fixed cost each time an order is placed (shipping, processing, setup), and a holding cost for keeping unsold stock in inventory. Ordering in large batches means fewer orders (lower ordering cost) but more average stock sitting around (higher holding cost); ordering in small batches flips that trade-off. The Wilson EOQ formula, published by R.H. Wilson in 1934, finds the exact order quantity that minimizes their sum: EOQ = √(2DS ⁄ H), where D is annual demand, S is the cost per order, and H is the annual holding cost per unit.

At that optimal quantity, annual ordering cost (D ⁄ EOQ × S) and annual holding cost (EOQ ⁄ 2 × H) always come out exactly equal to each other — this calculator also reports how many orders that works out to per year, the time between them, and the resulting total annual cost.

The model assumes steady, known demand, a fixed cost per order, and instant restocking with no quantity discounts — it's the standard textbook starting point for an ordering policy, not a substitute for one that accounts for bulk-pricing breaks or demand variability.

FAQ

What if my supplier gives a discount for larger orders?

The plain EOQ formula doesn't account for quantity discounts — it assumes a constant cost per unit. If bulk pricing is available, you'd compare the total cost (purchase + ordering + holding) at the EOQ against the total cost at each discount break point and pick whichever is actually lowest, which can mean ordering more than the EOQ.

Why do ordering cost and holding cost come out equal at the EOQ?

Total cost as a function of order quantity Q is (D/Q)S + (Q/2)H — one term shrinks and the other grows as Q increases. Minimizing that sum (setting its derivative to zero) is what produces the EOQ formula in the first place, and the algebra that falls out of that minimization happens to make the two terms equal at the minimum — it's a property of this particular cost shape, not a coincidence.

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