Safety stock calculator
Safety stock is the extra inventory that covers demand spikes and late deliveries while a reorder is on its way. With a steady lead time, safety stock = z × σd × √L: the service-level factor z, times the standard deviation of daily demand, times the square root of the lead time in days. When the lead time varies too, use z × √(L × σd² + d̄² × σL²).
Standard deviation is how far a typical day, or delivery, strays from the average.
218units
Safety stock for a 95% service level.
Demand over the 14-day lead time averages 560 units, give or take 132.5. 1.645 × 132.5 = 218 units of safety stock, so reorder at 778.
That is about 1 stockout every 20 reorder cycles.
How safety stock is calculated
- From daily sales history, find average daily demand and its standard deviation. If your supplier’s lead time varies, find its standard deviation in days too.
- Pick a service level: the share of reorder cycles you want to end without running out. Look up its z, or use =NORM.S.INV(level) in Excel.
- Work out how much demand over the lead time varies: σd × √L with a steady lead time, or √(L × σd² + d̄² × σL²) when it varies too.
- Multiply by z and round up to whole units.
1.645 × √(14 × 15² + 40² × 3²) = 218 units
Add the safety stock to average lead-time demand and you have your reorder point; the reorder point calculator shows what that does to stock over 90 days. To decide how much to order each time, use the EOQ calculator.
Each extra point of service costs more stock
Safety stock rises faster than the service level. Going from 95% to 99% takes about 41% more buffer for any SKU, because z climbs from 1.645 to 2.326 while the stockouts you avoid get rarer.
| Service level | z | Safety stock | Runs short about |
|---|---|---|---|
| 80% | 0.842 | 112 units | 1 in 5 cycles |
| 85% | 1.036 | 138 units | 1 in 7 cycles |
| 90% | 1.282 | 170 units | 1 in 10 cycles |
| 95% | 1.645 | 218 units | 1 in 20 cycles |
| 97.5% | 1.960 | 260 units | 1 in 40 cycles |
| 99% | 2.326 | 309 units | 1 in 100 cycles |
| 99.5% | 2.576 | 342 units | 1 in 200 cycles |
| 99.9% | 3.090 | 410 units | 1 in 1,000 cycles |
No standard deviation? Use max minus average
If you don’t have daily demand history, take the worst case you have seen and subtract the average one: your busiest day times your slowest delivery, minus an average day times an average delivery.
It sizes the buffer for your busiest day and your slowest delivery happening together. That is rare, so it can hold more stock than the statistical method above; with a short history, it can also miss a worse case.
58 × 18 − 40 × 14 = 484 units of safety stock
Common questions
What is the safety stock formula?
With a steady lead time, safety stock = z × σd × √L, where z comes from your service level, σd is the standard deviation of daily demand and L is the lead time in days. For a 95% service level (z = 1.645), a standard deviation of 15 units a day and a 14-day lead time, that is 1.645 × 15 × √14 ≈ 93 units. When the lead time also varies, use z × √(L × σd² + d̄² × σL²), where d̄ is average daily demand and σL is the standard deviation of the lead time.
What z-score goes with each service level?
z is the inverse of the standard normal distribution at your service level: about 1.28 for 90%, 1.65 for 95%, 1.96 for 97.5% and 2.33 for 99%. In Excel, =NORM.S.INV(0.95) returns it for any level.
What does the service level mean here?
It is the cycle service level: the share of replenishment cycles that end without running out. At 95%, about 1 cycle in 20 runs short before the next delivery lands. It is not the same as fill rate, the share of ordered units shipped from stock.
How do I find the standard deviation of demand?
Export daily unit sales for the SKU over several months and use STDEV.S in Excel on the daily figures. Keep days with zero sales, and leave out days you were out of stock, because they hide real demand.
What if I don’t know the standard deviation?
Use the max-minus-average method: maximum daily sales × longest lead time, minus average daily sales × average lead time. It needs no statistics, but it plans for your worst recorded day and your slowest delivery at once, so it can hold more stock than you need, or miss a worse case your history never saw.
How is safety stock different from the reorder point?
Safety stock is the buffer. The reorder point is the stock level that triggers the next order: average demand during the lead time plus that buffer.
Sources
Checked 2026-10-28. Rules change; confirm with the carrier or agency before you rely on a number.
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