Understanding your result
Safety stock is rounded upward to whole units. The unrounded result and one-sided normal Z-score remain visible for checking. This buffer sits above expected lead-time demand; it is not the total reorder point or an order quantity.
To calculate spread from a daily demand series, use the Standard Deviation Calculator and choose sample or population treatment appropriate to your data.
To combine this buffer with expected demand during delivery, use the Reorder Point Calculator with matching time units.
The formula
Independent daily demand variances add over a fixed lead time, so standard deviation scales with the square root of days. The selected one-sided normal quantile converts that spread into a buffer above mean demand. Cycle service level describes the modeled probability of no stockout during a replenishment cycle, not the fraction of units immediately fulfilled.
Worked example
A daily standard deviation of 10 units over nine fixed lead-time days gives lead-time deviation of 30 units. A 95% cycle service level uses Z ≈ 1.644854. The buffer is 49.345609 units before rounding, or 50 whole units. At 99%, the same inputs require 70 units.
How to use this calculator
- Calculate demand standard deviation from observations using one consistent daily time basis.
- Enter fixed lead time in the matching days and choose a cycle service level.
- Review the rounded buffer and add it to expected lead-time demand when setting a reorder trigger.
Standard deviation is not average demand
Average sales determine expected consumption; standard deviation describes how observations vary around their mean. Entering average sales in the spread field estimates a different and usually misleading quantity. Include appropriate zero-demand days when constructing the daily data, and decide whether calendar or working days match the lead-time definition.
The square-root rule has assumptions
This model assumes independent demand increments and a useful normal approximation for total lead-time demand. Trend, promotions, autocorrelation, intermittent demand, and very small counts can violate those assumptions. Uncertain supplier lead times require an extended model; entering an average lead time does not automatically account for its variability.
Service level has a specific meaning
A 95% cycle service level is not the same as fulfilling 95% of demanded units. It is a probability under the model for avoiding a stockout in a cycle. The tool does not claim the selected level will occur in practice. Validate a policy against historical cycles and operational constraints before relying on it.
Assumptions & limitations
What this calculation assumes
- Lead time is fixed, daily demand increments are independent, and a normal approximation is appropriate.
What to keep in mind
- Does not model lead-time variability, periodic review, forecast error bias, or fill-rate targets.
Common questions
Why is the 95% Z-score about 1.645 rather than 1.96?
This is a one-sided upper demand threshold. The 1.96 value corresponds to a 97.5% one-sided threshold and is commonly seen in two-sided 95% intervals.
Does zero safety stock mean no inventory is needed?
No. Expected lead-time demand still needs coverage. The buffer can be zero when the modeled variability, lead time, or selected Z-score is zero.