What is safety stock?
Safety stock is the buffer inventory you hold on top of expected demand during lead time. Its job is to absorb the two things that go wrong between reorders: demand comes in higher than forecast, or replenishment takes longer than planned. Size it right and you hit your target service level without drowning in working capital.
The full safety stock formula
σd = std dev of daily demand · d = average daily demand · σL = std dev of lead time (days)
Turning a service level into Z
You don't need a Z-table — enter the service level you want and the calculator converts it with the inverse normal distribution. But if you want to look the value up or sanity-check a number someone handed you, here is the full table. "Stockout risk" is simply 100% minus the service level: the chance of running out during any one replenishment cycle.
| Cycle service level | Z-score | Stockout risk per cycle |
|---|---|---|
| 50% | 0.00 | 50% |
| 75% | 0.67 | 25% |
| 80% | 0.84 | 20% |
| 85% | 1.04 | 15% |
| 90% | 1.28 | 10% |
| 95% | 1.64 | 5% |
| 96% | 1.75 | 4% |
| 97% | 1.88 | 3% |
| 98% | 2.05 | 2% |
| 99% | 2.33 | 1% |
| 99.5% | 2.58 | 0.5% |
| 99.9% | 3.09 | 0.1% |
Look at what happens above 95%: going from 95% to 99% raises Z from 1.64 to 2.33, so the buffer grows by about 42% to buy back just four points of risk. Going to 99.9% nearly doubles the 95% buffer. This is why blanket "99% on everything" policies quietly consume working capital — set high service levels on the items where a stockout actually costs you, not across the whole catalogue.
Safety stock formula variations (and which to use)
There is no single canonical safety stock formula. Which one is correct depends entirely on which sources of variability you can actually measure. Here are the three you will meet, weakest to strongest.
1. Max/average method (no statistics needed)
Popular because it needs no standard deviations — just the worst case you have seen. The catch is that it has no service level: you cannot dial the risk up or down, and the answer depends on how extreme your single worst historical observation happened to be. One freak event permanently inflates the buffer. Use it when you have too little history to compute a standard deviation.
2. Demand-variability only
This is what most free calculators implement. It has a real service level, which makes it a genuine improvement — but it assumes lead time never varies. If your supplier is reliable to the day, it is correct and simple. If not, it under-buffers, sometimes badly.
3. Demand and lead-time variability (what this calculator uses)
The complete form. It adds the d² × σL² term for lead-time variability, and treats the two sources as independent — which is why they combine as a root-sum-of-squares rather than a simple sum.
Which method fits your data
| Your situation | Use |
|---|---|
| No usable history, just a known worst case | Max/average method |
| Demand varies, lead time is reliable to the day | Z × σd × √L |
| Both demand and lead time vary | Full formula (this tool) |
| Lead time varies a lot, demand is steady | Full formula — the lead-time term will dominate |
Safety stock worked example
A distributor sells an average of 480 units a day with a standard deviation of 60. Replenishment takes 7 days on average, with a standard deviation of 2 days. The target is a 95% cycle service level.
| Input | Value |
|---|---|
| Average daily demand d | 480 units / day |
| Std dev of daily demand σd | 60 units |
| Average lead time L | 7 days |
| Std dev of lead time σL | 2 days |
| Cycle service level | 95% |
Step 1 — convert the service level to Z. From the table above, 95% gives
Z = 1.645
Step 2 — compute the demand-variability term. Variance, not standard deviation, is what adds:
L × σd² = 7 × 60² = 7 × 3,600 = 25,200
Step 3 — compute the lead-time-variability term.
d² × σL² = 480² × 2² = 230,400 × 4 = 921,600
Step 4 — combine and take the square root.
25,200 + 921,600 = 946,800
√946,800 = 973.04
SS = 1.645 × 973.04 = 1,601 units
Step 5 — see what lead-time variability cost you. Had we used the demand-only formula, the answer would have been Z × σd × √L = 1.645 × 60 × √7 = 261 units. The full formula returns 1,601 — 1,339 units more. Look at where the variance actually comes from:
| Source of variability | Variance | Share of total |
|---|---|---|
| Demand (L × σd²) | 25,200 | 3% |
| Lead time (d² × σL²) | 921,600 | 97% |
Almost all the risk on this item is the supplier, not the customer. A demand-only calculator would have told you to hold 261 units and you would have stocked out repeatedly — while the real fix is either a buffer of 1,601 units or a more reliable lead time. That diagnostic is the reason to carry both terms.
A tempting mistake: adding the two buffers instead of combining their variances. That would give 261 + 1,579 = 1,840 units — about 15% too much. Independent risks do not both peak at the same moment, which is why the correct combination is the square root of the summed variances.
From safety stock to reorder point
Safety stock on its own does not tell you when to reorder. The reorder point is expected demand during lead time plus the buffer:
Continuing the example: expected demand during lead time is 480 × 7 = 3,360 units, so
ROP = 3,360 + 1,601 = 4,961 units
When stock on hand falls to 4,961 units, place the order. If demand and lead time both land on their averages you will receive the replenishment with the 1,601-unit buffer still intact; the buffer is there for the cycles that do not cooperate. Continue into the Reorder Point calculator to carry these numbers over, or start upstream with the EPQ calculator to size the production run itself.