What is the basic safety stock formula?

Safety stock equals Z × σ_demand × √(lead time), where Z is the service-level z-score, σ_demand is the standard deviation of demand per period, and lead time is in the same period units. The square root reflects that variance accumulates over the lead-time window.

How does service level become a z-score?

The z-score is the inverse standard normal at the service level: 90 percent gives 1.28, 95 percent gives 1.65, 98 percent gives 2.05, and 99 percent gives 2.33. A higher service level needs a larger z and therefore more safety stock.

When should I include lead-time variability?

Use the combined (King's) formula when supplier lead times themselves vary. It is √(lead_time × σ_demand² + avg_demand² × σ_leadtime²) × Z. Variable lead time often dominates, so ignoring it understates the buffer.

What units should I use?

Keep demand and lead time in consistent period units. If σ_demand is per day, lead time must be in days. The result is in the same units as demand (e.g. units). Mixing daily demand with weekly lead time gives a wrong answer.

Does more safety stock always mean better service?

Up to a point, with diminishing returns. Moving from 95 to 99 percent service can nearly double safety stock for a small service gain because the normal tail thins quickly. Balance the holding cost against the cost of a stockout.

Safety Stock Calculator

Safety stock is the buffer that absorbs demand and supply uncertainty so you do not stock out during the replenishment lead time. This calculator applies the standard statistical formula and an optional combined model that also captures variable lead times.

How it works

The basic model multiplies a service-level z-score by demand variability scaled over the lead-time window:

basic:    SS = Z × σ_demand × √(lead time)
combined: SS = Z × √( lead_time × σ_demand²  +  avg_demand² × σ_leadtime² )

Z comes from the inverse normal distribution at your target cycle service level. The square root on lead time reflects that demand variance accumulates across the days the order is in transit. The combined (King’s) formula adds the term for lead-time variability, which often dominates the buffer.

Example

With σ_demand = 20 units/day, lead time = 9 days, and a 95% service level (Z = 1.65): SS = 1.65 × 20 × √9 = 1.65 × 20 × 3 = 99 units. Raising the target to 99% (Z = 2.33) increases it to 140 units for the same demand pattern.

Notes

Keep demand and lead time in the same period units. If your supplier’s lead time varies, switch on the combined formula — variable lead time frequently contributes more buffer than demand variability. Service levels above 98% raise safety stock sharply for small service gains, so weigh holding cost against stockout cost.