Safety stock formula
Safety stock SS = Z * sigma_LT, where Z is the standard normal score corresponding to your target service level and sigma_LT is the standard deviation of demand during lead time. Z values: 90 percent -> 1.282, 95 percent -> 1.645, 97.5 percent -> 1.96, 99 percent -> 2.326, 99.5 percent -> 2.576[1].
Buffer stock above mean lead-time demand to absorb variance at a target service level.
How Z grows non-linearly
Each step up the service ladder costs more in SS. 95 percent (Z = 1.645) to 97.5 percent (Z = 1.96) is a 19 percent SS increase. 97.5 percent to 99 percent (Z = 2.326) is another 19 percent. 99 percent to 99.5 percent (Z = 2.576) is another 11 percent. The cost of the last percentage point of service compounds[2].
Combining demand and lead-time variance
When both demand and lead time vary, the combined variance is sigma_DLT^2 = L * sigma_D^2 + d_bar^2 * sigma_LT^2. Use sigma_DLT in the formula above. The lead-time variability page walks the full derivation.
When SS dominates the inventory total
For high-service A-class items with long, variable lead times, SS can exceed cycle stock (Q*/2). This is normal and not a bug: the safety buffer is doing the stockout-protection work that the EOQ math cannot. The right reaction is to reduce sigma_LT (dual-source, domestic backup) rather than cap SS arbitrarily.