Inventory planning
Service level z-score.
Convert a target cycle service level into the z-value used in safety stock, or convert a z-value back to a service level.
z = inverse standard normal of the service level. 95% gives z = 1.645; 99% gives z = 2.326.
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Result
Worked example
A 97.5% cycle service level corresponds to z = 1.960: the standard normal distribution has 97.5% of its area below 1.96, leaving a 2.5% chance of a stockout in a cycle. Going the other way, z = 1.645 gives a service level of 95.0%.
How it works
The service level is the cumulative probability of the standard normal distribution at z. The NIST/SEMATECH e-Handbook table of the standard normal CDF lists areas for z values (for example 1.645 corresponds to a cumulative probability of about 0.95); this calculator computes the same function and its inverse numerically, so any level works, not only table rows.
Cycle service level is the probability of no stockout during one replenishment cycle (Wikipedia, Service level). In the safety stock formula, the z-score is multiplied by the standard deviation of demand during the lead time.
The normal distribution is an assumption. It fits poorly for intermittent or very low-volume demand. Results are accurate to about three decimals for z.
Sources (opened 2026-10-18): NIST/SEMATECH e-Handbook: Cumulative Distribution Function of the Standard Normal Distribution; Service level - Wikipedia. The formula wording above follows these pages; the example figures and all arithmetic are ours.
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FAQ
What is the z-score for a 95% service level?
About 1.645.
What is the z-score for 99%?
About 2.326. For 90% it is about 1.282 and for 97.5% about 1.960.
Can I use 100%?
No. A normal distribution has no upper limit, so a 100% cycle service level would need infinite safety stock.
How much more safety stock does a higher service level need?
Going from 95% to 99% raises z from 1.645 to 2.326, about 41% more safety stock for 4 points of service level, and the cost rises faster still near 100%.