How to use this calculator
- Enter or choose average daily demand.
- Enter or choose standard deviation of daily demand.
- Enter or choose average lead time.
- Enter or choose standard deviation of lead time.
- Enter or choose cycle service level.
- The safety stock updates as you type. Use Copy result or Share to keep it.
Method
Safety stock = z × √(L × σd² + d² × σL²); Reorder point = d × L + Safety stock
- z
- standard normal quantile for the cycle service level
- d, σd
- mean and standard deviation of daily demand
- L, σL
- mean and standard deviation of lead time in days
Worked example
- σ over the lead time = √(9 × 10²) = 30 units.
- Safety stock = 1.644854 × 30 = 49.35, so hold 50 units.
- Reorder point = 50 × 9 + 49.35 = 499.35 units.
For a 95% cycle service level, demand of 50 ± 10 units a day and a 9-day lead time need about 50 units of safety stock.
What the result means
A 95% cycle service level means about 1 replenishment cycle in 20 runs out before the delivery arrives. Going from 95% to 99% raises safety stock by about 41% (z 1.64 → 2.33).
Assumptions and limits
- Daily demand is roughly normally distributed and independent from day to day.
- Demand and lead time vary independently.
- Service level means the probability of no stock-out during a replenishment cycle (cycle service level), not fill rate.
- Slow-moving or very lumpy items do not follow a normal distribution; this method under- or over-states their buffer.
Questions
How do I get the standard deviation of demand?
Take daily sales for a recent, typical period and use the Standard Deviation Calculator on them.
Is service level the same as fill rate?
No. Cycle service level is the chance of not running out in a cycle; fill rate is the share of demand met from stock, which is usually higher.