Safety stock is a buffer, not a forecast
A forecast estimates what will sell. Safety stock protects the reorder decision when the forecast is wrong or the supplier is late. It sits on top of the cycle stock you expect to sell during lead time, and it is held until a replenishment arrives.
That distinction matters because adding “two weeks of stock” is a policy choice, not a statistical result. The formula here answers a narrower question: how large must the buffer be to keep the probability of stocking out during a replenishment cycle at a chosen level?
Two sources of variability
Demand variability is the day-to-day spread around average sales, measured by the standard deviation. If average demand is 50 units a day but actual days range from 30 to 75, the standard deviation captures that spread. A stable average with high variability needs more buffer than the average alone suggests.
Lead-time variability is the spread in supplier and transit time. A supplier that usually takes 10 days but sometimes takes 18 creates a different risk from one that always takes 10. The formula combines both sources: SS = Z × √(L × σD² + D² × σL²). When lead time is stable, the second term disappears.
The formula, with two worked examples
Take average daily demand of 50 units, a daily standard deviation of 10, a 10-day lead time and a stable supplier. At 95% cycle service level, Z is 1.645. Safety stock is 1.645 × √(10 × 100) = 52.02, rounded up to 53 units. The reorder point is 50 × 10 + 53 = 553 units.
Now add two days of lead-time standard deviation. The variance term becomes 10 × 100 + 2,500 × 4 = 11,000; the square root is 104.88; safety stock is 172.53, rounded up to 173 units. The reorder point rises to 673 units. The extra 120 units are the cost of supplier unreliability, made visible.
What a 95% service level actually means
The service level here is a cycle service level: the probability that demand does not exceed available stock during one replenishment cycle. At 95%, roughly one cycle in twenty is expected to run short. It is not the same as fill rate, which measures the share of units shipped immediately; fill rate can be higher than cycle service level when shortages are small.
Higher service levels increase safety stock quickly because Z rises and the buffer is linear in Z. The presets show the trade-off: 90% uses 1.282, 95% uses 1.645, 99% uses 2.326 and 99.9% uses 3.090. Choose a level based on the margin lost in a stockout, the cost of holding inventory and how customers react, not on an industry default.
What the model leaves out
The formula assumes demand and lead time are independent and approximately normal. Promotions, seasonality, supplier allocations, MOQ, review-period stock, in-transit inventory and multi-location splits are outside the calculation. A zero lead time is rejected because lead-time variability has no meaning without a replenishment window.
Use the result as one input to a replenishment plan, not as the plan itself. The CSV reorder planner adds review cycles, MOQ, pack multiples and per-SKU purchasing quantities; this calculator supplies the statistical buffer that planner otherwise asks you to guess in days.
How to run it per SKU
Export 60–90 days of daily units sold and calculate the average and standard deviation on the same calendar. Measure lead time from purchase-order placement to units being available to sell, and use the standard deviation of that lead time if your supplier is inconsistent. Start at 95%, inspect the resulting safety days and holding cost, then adjust the service level for the margin at risk.
Review the inputs when suppliers, shipping lanes or demand patterns change. A buffer built for last year's lead time can become either expensive excess stock or an expensive stockout.