Reorder Point Formula with Safety Stock and EOQ, Worked Through
The reorder point formula is reorder point = daily demand x lead time + safety stock. If you sell 10 units a day and stock takes 30 days to arrive, you reorder when you are down to 300 units - plus whatever buffer you hold for late deliveries. That answers when to order. The economic order quantity (EOQ) answers how much, and the two together are a complete ordering rule.
The formulas
- Reorder point: ROP = daily demand x lead time (days) + safety stock
- Safety stock from lead-time history: safety stock = daily demand x (longest lead time you have seen - normal lead time)
- Safety stock from a service level: safety stock = z x standard deviation of daily demand x square root of lead time
- Economic order quantity: EOQ = square root of (2 x D x S / H), where D is annual demand in units, S is the cost of placing one order, and H is the cost of holding one unit for a year
- Holding cost per unit: H = unit cost x your holding rate
Reorder point formula with safety stock: a worked example
An illustrative product: 10 units sold a day, a quoted lead time of 30 days, and a supplier whose slowest delivery so far took 40 days.
- Demand during the lead time: 10 x 30 = 300 units.
- Safety stock to cover the slowest delivery: 10 x (40 - 30) = 100 units, which is 10 days of cover.
- Reorder point: 300 + 100 = 400 units.
When stock on hand (plus anything already on order) falls to 400, place the next order. Here is how the reorder point moves with lead time and days of cover at 10 units a day:
| Lead time | No safety stock | + 7 days cover | + 14 days cover |
|---|---|---|---|
| 7 days | 70 | 140 | 210 |
| 14 days | 140 | 210 | 280 |
| 21 days | 210 | 280 | 350 |
| 30 days | 300 | 370 | 440 |
| 45 days | 450 | 520 | 590 |
The service-level version
If your demand swings from day to day, the textbook safety stock formula uses its standard deviation. For a 95% chance of not running out during the lead time, z = 1.645 (from the normal distribution). With a standard deviation of 3 units a day and a 30-day lead time:
- 1.645 x 3 x 5.48 = 27.0, rounded up to 28 units, for a reorder point of 328.
That buffer is smaller than the 100 units above because it covers a different risk. The service-level formula in this form assumes the lead time is fixed and only demand varies. The lead-time-history formula covers a supplier who is late. If late deliveries are what has actually hurt you, the second one is the one that matches your problem - and you can hold both.
Economic order quantity: how much to order
Same product: 10 units a day over 240 selling days is 2,400 units a year. Each order costs $75 to place and receive, the unit costs $12, and we use an illustrative holding rate of 25%, so holding one unit for a year costs H = $3.00.
EOQ = square root of (2 x 2,400 x $75 / $3.00) = square root of 120,000 = 346.4, call it 346 units.
Here is what different order sizes cost over a year. Ordering cost is orders a year times $75; holding cost is the average stock (half the order size) times $3.00:
| Order size | Orders a year | Ordering cost | Holding cost | Total a year |
|---|---|---|---|---|
| 86 | 27.9 | $2,093 | $129 | $2,222 |
| 173 | 13.9 | $1,040 | $260 | $1,300 |
| 346 | 6.9 | $520 | $519 | $1,039 |
| 692 | 3.5 | $260 | $1,038 | $1,298 |
| 1,385 | 1.7 | $130 | $2,078 | $2,207 |
Ordering 86 at a time costs $2,222 a year. Ordering 346 costs $1,039. Same demand, same product, $1,183 a year apart - the small order size costs 2.1 times as much, almost all of it in the 28 orders a year it forces you to place.
Notice the EOQ row: ordering cost ($520) and holding cost ($519) are equal, give or take rounding. That is not a coincidence. The EOQ is exactly the order size where the two costs cross, which is a quick way to check a calculation.
Reorder point formula and EOQ together
The two numbers fit into one rule: when stock falls to 400, order 346. The reorder point protects against running out; the EOQ keeps the cost of ordering and holding as low as it goes. Changing one does not change the other - lead time and safety stock have no place in the EOQ formula, and order cost has no place in the reorder point.
What the formulas do not make obvious
The bottom of the cost curve is flat. Ordering half or double the EOQ costs only 25% more than the minimum - the table shows 346 and twice that landing close together. So you can round the EOQ to a case size or a supplier’s minimum order with little penalty. What the table also shows is that the curve gets steep fast at the edges: a quarter of the EOQ costs more than twice the minimum.
It is a square root, so it does not scale with sales. Doubling demand to 4,800 units raises the EOQ to 490, only 41% more. Growing your order size in step with sales holds more stock than the math calls for.
The holding rate is yours to build, and it moves the answer. It is meant to cover storage, the cost of the money tied up, insurance, damage and shrinkage, and the risk that some stock never sells. The 25% above is an illustration, not a benchmark. Here is how the EOQ responds when you change it:
| Holding rate (your input) | Holding cost per unit a year | EOQ |
|---|---|---|
| 15% | $1.80 | 447 |
| 25% | $3.00 | 346 |
| 40% | $4.80 | 274 |
Safety stock is cheap next to a stockout. In the example, holding the 100 units of safety stock costs $300 a year at $3.00 a unit. At an illustrative margin of $8 a unit, one week out of stock loses 70 sales and $560 of margin - before counting the customers who buy elsewhere and do not come back.
How these were calculated
Every figure on this page is computed by code, twice: once by the same functions that build the inventory kit below, and once by a separate implementation written from the textbook formulas. The page only builds if the two agree to the cent. The EOQ uses the standard formula, square root of 2DS/H, with holding cost charged on the average inventory of half the order quantity. The z value comes from the inverse of the standard normal distribution. All inputs - demand, lead times, order cost, unit cost, margin and the holding rate - are illustrative; put in your own. This is general arithmetic, not financial or accounting advice.
If you want to run this on your own products, the kit below includes a live Excel workbook that works out the EOQ, the reorder point and the total cost at any order size, plus a script for asking a supplier for their real lead time - the number the safety stock above depends on.