Economic Order Quantity Calculator
The order size that minimises ordering plus holding cost.
Economic order quantity
673
- Orders per year
- 17.8 orders
- Days between orders
- 20.5 days
- Annual ordering cost
- $1,515
- Annual holding cost
- $1,515
- Total annual cost
- $3,030
Economic order quantity solves a specific trade-off: order often in small batches and you pay too much in ordering cost; order rarely in large batches and you pay too much to hold the stock. EOQ is the quantity where those two costs are exactly equal, and total cost is at its minimum. It is one of the oldest results in operations research — Harris derived it in 1913 — and it is still the reference point every more sophisticated model is compared against.
The most useful insight is not the quantity itself but the shape of the cost curve around it. Total cost is flat near the optimum, so being 20% off the EOQ typically raises total cost by only about 2–5%. That means you can round the answer to something practical — a full pallet, a container load, a supplier’s price break quantity — without materially hurting the economics. Where EOQ hurts is when the two input assumptions are wrong.
How the result is calculated
EOQ = √(2 × D × S ÷ H)- D = annual demand in units
- S = cost to place one order
- H = holding cost per unit per year
- Orders per year = D ÷ EOQ; days between orders = 365 ÷ orders per year
- Annual ordering cost = (D ÷ EOQ) × S; annual holding cost = (EOQ ÷ 2) × H
Variables
| Symbol | Meaning | Unit |
|---|---|---|
D | Annual demand | units/yr |
S | Cost per order | currency |
H | Holding cost per unit per year | currency |
Q | Order quantity | units |
Worked example
A plant consumes 12,000 units a year. Placing an order costs $85 in purchasing and receiving effort. Holding one unit for a year costs $4.50 in storage, capital and insurance.
- EOQ = √(2 × 12,000 × 85 ÷ 4.5)
- EOQ = √(2,040,000 ÷ 4.5) = √453,333
- EOQ ≈ 673 units per order
- Orders per year = 12,000 ÷ 673 ≈ 17.8, or roughly every 20 days
- Ordering cost ≈ $1,515; holding cost ≈ $1,515; total ≈ $3,030 per year
Order about 673 units at a time, roughly 18 times a year. Note that ordering and holding costs come out equal — that is the defining property of the EOQ optimum, and a quick way to sanity-check the answer. Rounding to a 700-unit pallet quantity changes total cost by well under 1%.
What this calculation does not cover
- Assumes demand is constant and known. For lumpy or seasonal demand, EOQ understates the right order size; use a period order quantity or a min-max policy instead.
- Assumes a constant unit price with no quantity discounts. Where price breaks exist, compare total cost (purchase + ordering + holding) at each break quantity against the EOQ — the discount often wins.
- Assumes instantaneous replenishment. With a long or unreliable lead time, the reorder point matters more than the order quantity; combine EOQ with the reorder point calculator.
- Ignores storage capacity, shelf life and minimum order quantities. Any of these can override the calculated quantity in practice.
- Holding cost is the input most often guessed and most often wrong. It should include cost of capital, storage, handling, insurance, shrinkage and obsolescence — typically 15–30% of unit value per year, not a flat dollar guess.
Frequently asked questions
How do I estimate the holding cost per unit per year?
Multiply the unit value by an annual carrying rate. A typical carrying rate is 20–30%, covering cost of capital (5–10%), storage and handling (5–10%), insurance and taxes (2–3%), and obsolescence and shrinkage (5–10%). A $20 part therefore costs roughly $4 to $6 a year to hold, which is the order of magnitude most people underestimate.
Does EOQ still make sense with modern low-inventory thinking?
Yes, as a cost baseline rather than a target. JIT deliberately accepts higher ordering cost in exchange for lower inventory, so JIT order quantities are intentionally below EOQ. EOQ tells you what the pure cost optimum would be, which is exactly what you need to quantify what lean is buying you.
What if my supplier offers a quantity discount?
Calculate total annual cost — purchase cost plus ordering plus holding — at the EOQ and at each discount break quantity. Choose the lowest total. A 5% price break on a high-volume part frequently justifies tripling the order size even though the holding cost rises, because purchase cost dominates the other two components.