What this calculator does
Ordering in large batches means fewer orders but more stock sitting in the warehouse. Ordering in small batches means less stock but more orders to place. The economic order quantity is the size that balances the two.
At that balance point, annual ordering cost and annual holding cost are exactly equal. Ordering 671 units at a time gives $1,341.64 of each, and that equality is not a coincidence: it is the mathematical signature of the optimum.
The formula
The optimal quantity is the square root of twice the annual demand times the cost per order, divided by the annual holding cost per unit. Annual demand divided by that quantity gives the number of orders.
| Term | Meaning |
|---|---|
| Economic order quantity | The order size that minimises total inventory cost. |
| Ordering cost | The fixed cost of placing an order, regardless of its size. |
| Holding cost | The annual cost of keeping one unit in stock, including capital, storage and obsolescence. |
The inputs explained
| Field | What to enter |
|---|---|
| Annual demand (units) | Annual demand in units. |
| Cost per order ($) | The fixed cost of placing one order, regardless of quantity. |
| Annual holding cost per unit ($) | The cost of holding one unit in stock for a year. |
When to use it
Setting a reorder quantity
The optimal batch size follows directly from demand and the two cost figures.
Justifying a change in ordering frequency
The total cost curve shows what moving away from the optimum actually costs.
Assessing a bulk discount
A supplier discount for larger orders has to beat the extra holding cost it creates.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does the ordering cost change the batch size?
Three levels of cost per order.
| Cost per order | Economic order quantity | Total annual inventory cost |
|---|---|---|
| $25 | 387 units | $1,549.19 |
| $75 | 671 units | $2,683.28 |
| $200 | 1,095 units | $4,381.78 |
Questions
Why are ordering and holding costs equal at the optimum?
Because the total cost curve is minimised where the two opposing costs balance. Ordering more often raises one and lowers the other, and the lowest total occurs precisely where they meet.
What assumptions does EOQ make?
Constant demand, instant replenishment, no stockouts, and costs that do not change with order size. Real supply chains violate all of these, which is why EOQ is a starting point rather than a rule.
How sensitive is the answer?
Not very, which is the model's most useful property. The cost curve is flat near the optimum, so ordering 20 per cent above or below the ideal quantity raises total cost by only about 2 per cent.
What about bulk discounts?
They break the basic model, since the unit price is no longer constant. The usual approach is to calculate total cost at the EOQ and at each discount break point, then choose whichever is cheapest overall.
For how fast stock moves, see the turnover ratios calculator. For the cash tied up in that stock, see the cash conversion cycle calculator.