EOQ Calculator
Enter annual demand, the cost per order and the holding cost to find the economic order quantity, how often to order, the total annual cost and your reorder point with safety stock. Everything is calculated privately in your browser.
| Annual ordering cost (D ÷ Q × S) | – |
| Annual holding cost (Q ÷ 2 × H) | – |
| Safety stock holding (SS × H) | – |
| Purchase cost (D × unit cost) | – |
| Total annual cost | – |
Cost curve
Sensitivity: what if you order more or less?
| Order size | Orders / yr | Ordering cost | Holding cost | Total (excl. purchase) | vs EOQ |
|---|
The EOQ model assumes steady demand, a fixed cost per order, a constant holding cost and no quantity discounts. Holding cost usually includes capital, storage, insurance, shrinkage and obsolescence (often 20–30% of unit cost per year).
How to use the EOQ Calculator
- Enter annual demand in units, the cost of placing one order and the unit cost.
- Enter the holding cost as a % of unit cost per year (often 20–30%) or as an amount per unit per year.
- Add lead time and safety stock to get the reorder point; pick Calculate from service level if you know how much daily demand varies.
- Press Calculate EOQ (results update as you type) and read the order size, orders per year and total cost.
- Compare with your current order size, check the cost curve and sensitivity table, and export a CSV.
EOQ formulas
| Quantity | Formula |
|---|---|
| Economic order quantity | EOQ = √(2DS ÷ H) |
| Orders per year | N = D ÷ Q |
| Time between orders | T = working days ÷ N |
| Annual ordering cost | D ÷ Q × S |
| Annual holding cost | Q ÷ 2 × H (+ safety stock × H) |
| Minimum ordering + holding cost | √(2DSH) |
| Reorder point | daily demand × lead time + safety stock |
| Safety stock (service level) | Z × σd × √L |
D = annual demand (units), S = cost per order, H = holding cost per unit per year (for example 25% × unit cost), Q = order quantity, L = lead time in days.
Worked example
A shop sells 12,000 units a year, each order costs $50 to place and receive, and a unit costs $20 with a 25% annual holding rate, so H = $5. EOQ = √(2 × 12,000 × 50 ÷ 5) = √240,000 ≈ 490 units. That means about 24.5 orders a year, one every 10.2 working days (250-day year). Ordering and holding costs are both $1,224.74, a total of $2,449.49 a year. If the shop currently orders 1,000 units at a time, it pays $600 + $2,500 = $3,100, so switching to the EOQ saves about $651 a year. With 48 units sold per working day, a 7-day lead time and 100 units of safety stock, the reorder point is 436 units.
Service level Z values
| Service level | 80% | 90% | 95% | 97.5% | 99% | 99.9% |
|---|---|---|---|---|---|---|
| Z factor | 0.842 | 1.282 | 1.645 | 1.960 | 2.326 | 3.090 |
- Flat bottom: ordering 50% more than the EOQ raises ordering + holding cost by only about 8%; ordering half the EOQ raises it by 25%. Rounding to a pack or pallet size is usually fine.
- Quantity discounts: if suppliers give price breaks, compare total cost (including purchase cost) at the EOQ and at each break quantity.
- Track the result: a good ordering policy should show up as higher stock turns; check with the inventory turnover calculator.
Frequently asked questions
What is the EOQ formula?
EOQ = √(2 × D × S ÷ H), where D is annual demand in units, S is the fixed cost of placing one order and H is the cost of holding one unit in stock for a year. With D = 12,000, S = $50 and H = $5, EOQ = √240,000 ≈ 490 units.
What does the economic order quantity minimize?
It minimizes the sum of annual ordering cost (D ÷ Q × S) and annual holding cost (Q ÷ 2 × H). At the EOQ these two costs are exactly equal, and the minimum total is √(2DSH).
How do I calculate the reorder point?
Reorder point = average daily demand × lead time in days + safety stock. If you sell 48 units a day, the supplier takes 7 days and you keep 100 units of safety stock, reorder when stock falls to 48 × 7 + 100 = 436 units.
How is safety stock calculated from a service level?
A common formula is safety stock = Z × σd × √L, where Z is the normal-distribution factor for the service level (1.645 for 95%), σd is the standard deviation of daily demand and L is the lead time in days. It assumes the lead time itself is constant.
What should I include in holding cost?
Holding (carrying) cost includes the cost of capital tied up in stock, warehouse space, insurance, taxes, handling, shrinkage and obsolescence. Many businesses estimate it at roughly 20–30% of the unit cost per year.
What if I order a bit more or less than the EOQ?
The total cost curve is flat near the minimum, so small deviations cost little. Ordering 25% more than the EOQ raises ordering plus holding cost by only about 2.5%. The sensitivity table shows the exact figures for your inputs.
When does the EOQ model not apply?
It assumes steady demand, a constant order cost and holding cost, instant delivery of the whole order and no quantity discounts. With strong seasonality, perishable goods or price breaks, use EOQ as a starting point and adjust.