Calculate safety stock levels based on demand variability, lead time, and service level targets with stockout probability curves.
Safety stock is the buffer that sits between forecast and reality, and this calculator sizes it from demand variability, lead time, and the service level you commit to. You enter average demand, its standard deviation, lead time, and a service level target, and it returns safety stock in units, a reorder point, and a stockout-probability curve showing how the risk falls as the buffer grows. The surprise: safety stock scales with the square root of lead time, so doubling lead time grows the buffer by only about 40 percent, while moving from 95 to 99 percent service adds roughly 40 percent more units.
A concrete input and expected output from the current implementation.
Input
Mean demand: 100 units/day | Demand standard deviation: 20 units/day | Lead time: 7 days (constant) | Service level: 95%
Expected output
Safety stock: 87 units. Reorder point: 787 units (700 units of average lead-time demand plus 87 units of buffer). Stockout probability at this reorder point: 5% per replenishment cycle.
A 95 percent service level corresponds to a z-score of 1.645, and with a constant lead time the formula reduces to SS = 1.645 x 20 x sqrt(7) = 87 units. Adding the 700 units of average demand during the 7-day lead time gives the 787-unit reorder point.
The service level is converted to a z-score of the standard normal distribution: 90 percent gives 1.28, 95 percent gives 1.645, 99 percent gives 2.33. The z-score is how many standard deviations of lead-time demand the buffer must span, and stockout probability per cycle is exactly 1 minus the service level: 5 percent at 95 percent. The stockout-probability curve is the tail area of the same distribution.
The model pools demand and lead-time uncertainty into one term: SS = Z x sqrt(LT x sd_d^2 + d^2 x sd_LT^2), where d is mean demand, sd_d its standard deviation, LT mean lead time, and sd_LT lead-time spread. With a constant lead time this collapses to Z x sd_d x sqrt(LT), which is why the buffer grows with the square root of lead time rather than in proportion to it.
No. The 5 percent is the chance of a stockout in each replenishment cycle, not in a year. With 12 cycles a year you would expect about 0.05 x 12 = 0.6 stockouts per year on average. If your business needs a different annual exposure, raise the per-cycle service level accordingly and re-run the calculation.
With constant demand and a fixed lead time the variability terms are zero and the formula returns no safety stock, because steady demand needs cycle stock (ordering earlier), not buffer stock. Safety stock exists only to absorb spread: the wider the demand or lead-time variation you enter, the larger the buffer. A long but reliable lead time raises the reorder point, not the safety stock.
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