Supply Chain & Procurement worked example

Safety Stock Calculator with service-level factor of 0.83 σ: a worked example

Here is what the math looks like when conditions slip. We hold every other input steady and drop service-level factor to 0.83 σ, then walk the calculation through step by step. Calculate statistical safety stock for Supply Chain & Procurement from service level, demand variability, and lead time.

The inputs for this scenario

  • Service-level factor (Z): 0.83 σ (the input this scenario stresses; the baseline uses 1.65)
  • Demand standard deviation: 40 units (held at the documented default)
  • Lead time: 9 periods (held at the documented default)

Working through the calculation

  • The calculation starts from the formula this tool documents: Safety stock = service-level factor (Z) × demand std dev × √(lead time).
  • Safety stock works out to 99.6 units at these inputs, and this is the headline figure for the scenario.
  • Service factor (Z) works out to 0.83 σ at these inputs.
  • Demand std dev works out to 40 units at these inputs.
  • Lead-time factor (√LT) works out to 3 x at these inputs.

How this compares with the baseline

  • Against the tool's baseline example, where service-level factor sits at 1.65 σ and the headline result is 198 units, this scenario comes in 49.7% below the baseline at 99.6 units.
  • The practical read: the gap between this scenario and the baseline is entirely attributable to service-level factor, so recovering it is worth quantifying in dollars before considering equipment or staffing changes. This standard form assumes lead time is fixed and demand variability is the only uncertainty; if supplier lead time itself swings, you need the dual-variability formula, which this version does not model.

Results at a glance

  • Safety stock: 99.6 units (headline result)
  • Service factor (Z): 0.83 σ
  • Demand std dev: 40 units
  • Lead-time factor (√LT): 3 x

Run it with your numbers

  • To rerun this with your own numbers, open the live Safety Stock Calculator calculator, set service-level factor to your actual value, and adjust the remaining inputs to match your operation.

Last reviewed 2026-05-12.