Safety stock is the buffer that absorbs variability — in how much customers order, in how long suppliers take, or in both. Set it too low and you stock out; too high and you pay to store inventory you did not need. The service level you choose is the explicit statement of which risk you are willing to accept.
This calculator covers the three cases assignment briefs set: demand varies while lead time is fixed, lead time varies while demand is fixed, and both vary at once. It picks the right formula from what you enter, shows the working, and gives you the reorder point alongside it.
When only demand varies, safety stock = z × sd_demand × sqrt(L). The square root of lead time appears because variances add over independent periods, not standard deviations — a point worth stating explicitly in a report, because it is the step most often skipped.
When only lead time varies, safety stock = z × d × sd_lead, where d is the constant demand per period. Here the variability is in how many periods of demand you must cover, so average demand scales it directly.
When both vary, the general form combines them: safety stock = z × sqrt(L × sd_demand² + d² × sd_lead²). The first two formulas are just this one with a term set to zero, which is a clean thing to point out if your brief asks you to compare the cases.
The z value comes from the service level you pick: 90% gives 1.28, 95% gives 1.64, 99% gives 2.33. Note how steeply the cost climbs at the top — moving from 95% to 99% raises safety stock by about 40% for a four-percentage-point gain in protection. That trade-off is usually the actual question a case study is asking.
Be careful to distinguish cycle service level from fill rate. Cycle service level is the probability of not stocking out during any single replenishment cycle, which is what this calculator uses and what the z formula gives. Fill rate is the proportion of demand met from stock. They are different numbers and rubrics do test whether students know that.
Different items deserve different service levels. A cheap component whose absence halts a production line justifies a higher level than an expensive slow-moving item with a ready substitute — and an ABC analysis is the standard way to argue that split.
Every mismatch in this calculation comes from units. If demand is per day, lead time must be in days and the standard deviation of demand must be a daily standard deviation. If your data is weekly and lead time is in days, convert one before you start rather than midway through.
The standard deviation of demand must be the deviation of demand per period, not the deviation of total demand over the lead time. Students who use the latter effectively apply the lead-time adjustment twice and end up with a safety stock that is far too large.
Where a brief provides raw demand history rather than a standard deviation, calculate the sample standard deviation from that series first — the average calculator will do it — then bring the figure here.
With variable demand only: z × sd_demand × sqrt(lead time). With variable lead time only: z × average demand × sd_lead. With both: z × sqrt(L × sd_demand² + d² × sd_lead²). The calculator selects the right one from your inputs.
It follows from the service level: 1.28 for 90%, 1.64 for 95%, 2.33 for 99%. These are one-tailed values, because you are only protecting against demand being higher than expected.
Reorder point = demand during lead time + safety stock, where demand during lead time is average demand × average lead time.
Variances add across independent periods; standard deviations do not. Adding L periods of variance and taking the root gives the sqrt(L) factor. It is a common exam question.
No. Cycle service level is the chance of no stockout in a given cycle; fill rate is the share of demand served from stock. This calculator uses cycle service level.
Then no safety stock is needed and the reorder point is simply demand during lead time. The calculator will tell you rather than returning zero silently.