The economic order quantity balances the cost of placing orders against the cost of holding inventory. Calculate the EOQ, the reorder point that covers lead-time demand, and the safety stock needed for your target service level.
How it works
Find the order quantity that minimizes ordering and holding costs, the reorder point that covers lead-time demand, and the safety stock for a target service level.
EOQ = √(2 × Annual demand × Cost per order ÷ Holding cost per unit)
Holding cost per unit = Unit cost × Holding %
Safety stock = z(service level) × σ(daily demand) × √Lead time
Reorder point = Daily demand × Lead time + Safety stockCommon uses
- Inventory replenishment policies
- Purchasing and supply chain planning
- Reducing working capital tied up in inventory
Worked example
The calculator above opens with this example. Change any input to see the results update instantly, or select Reset to return to these figures.
| Annual demand (units) | 24,000 |
| Cost per order | $85 |
| Unit cost | $12.50 |
| Annual holding cost (% of unit cost) | 22% |
| Lead time | 12 days |
| Operating days per year | 365 |
| Std. deviation of daily demand (optional) | 18 |
| Service level | 95% |
| Economic order quantity | 1,218 |
| Reorder point | 892 |
| Safety stock | 103 |
| Orders per year | 19.70 |
| Annual ordering + holding cost | $3,632 |
| Average inventory value | $8,895 |
Total cost is flat near the EOQ, so rounding to a convenient case or pallet quantity costs little.
Interpreting the results
- Holding cost typically runs 20% to 30% of unit cost a year, including capital, storage, insurance and obsolescence.
- Raising the service level from 95% to 99% increases safety stock by about 40%.
- EOQ assumes steady demand and no quantity discounts; check volume price breaks separately.
Frequently asked questions
What is the EOQ formula?
EOQ equals the square root of two times annual demand times the cost per order, divided by the annual holding cost per unit. It is the order quantity at which total ordering and holding costs are lowest.
How is safety stock calculated?
Safety stock equals the z-score for the target service level times the standard deviation of daily demand times the square root of lead time in days. A 95% service level corresponds to a z-score of about 1.645.
What are the limitations of EOQ?
EOQ assumes steady demand, constant costs and no quantity discounts or capacity limits. Real purchasing decisions should also consider supplier minimums, volume price breaks and shelf life.
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