TAHA Engineering Toolsby TAHA Knowledge Lab

Industrial & Manufacturing

Safety Stock Calculator

Safety stock by four methods: fixed buffer, variable demand, variable lead time, or both.

Inputs

Calculate from
Stock level falling over one cycle: safety stock band at the bottom, expected lead-time demand above it, and the reorder point at the top of that band.Safety stockReorder pointlead time Lexpecteddemand d × Lsafety stockStock
When stock falls to the reorder point, an order is placed. During the lead time, expected demand (d × L) uses up stock down to the safety stock. Reorder point = expected lead-time demand + safety stock. Diagram not to scale.

Demand, lead time and their standard deviations must all use this same period.

In periods (e.g. 9 days).

Probability of not running out during a lead time (cycle service level).

Result

Safety stock (calculated)
19.7382units
Recommended safety stock (rounded up)
20whole units
Expected demand during lead time
180units
Reorder point (lead-time demand + safety stock)
199.738units
Z value used
1.6449

Hold about 20 whole units of safety stock (19.7382 units before rounding). Expected demand during the lead time is 180 units, so reorder when stock falls to about 199.738 units. All figures use one day as the period.

  • Rounding rule: safety stock is rounded UP to the next whole unit, so the buffer is never smaller than calculated.

Educational estimate — check the assumptions below.

About this calculator

Safety stock is extra inventory held to cover uncertainty — days when demand is higher than average, or deliveries that arrive late. Too little causes stock-outs; too much ties up money and space. This calculator offers four clearly separated methods. Choose the one that matches what varies in your situation, and use your own data for every figure.

Formula

Target stock level

Safety stock = Target stock level − d × L

Use this only when you have already decided the stock level at which you reorder; it shows how much of that is a buffer above expected lead-time demand.

Variable demand

SS = Z × σd × √L

σd = standard deviation of demand per period, L = lead time in the same periods. Lead time is assumed constant.

Variable lead time

SS = Z × d × σL

d = average demand per period, σL = standard deviation of lead time in periods. Demand is assumed steady.

Both variable

SS = Z × √(L × σd² + d² × σL²)

A common approximation that assumes demand and lead time vary independently of each other and are roughly normally distributed.

Worked example

Daily demand averages 20 units (σ = 4 units/day); lead time averages 9 days (σ = 2 days); target service level 95% (Z = 1.645).

  • Expected lead-time demand = 20 × 9 = 180 units
  • Variable demand: SS = 1.645 × 4 × √9 = 1.645 × 12 = 19.74 → 20 units
  • Variable lead time: SS = 1.645 × 20 × 2 = 65.79 → 66 units
  • Both: SS = 1.645 × √(9 × 16 + 400 × 4) = 1.645 × √1744 = 1.645 × 41.76 = 68.69 → 69 units
  • Target-level method: if you reorder at 210 units, safety stock = 210 − 180 = 30 units

Assumptions and limitations

  • Service level here means cycle service level: the probability of not running out during one replenishment lead time. Z values come from the standard normal distribution (95% → 1.645, 99% → 2.326).
  • The statistical methods assume demand (and lead time) vary randomly and roughly follow a normal distribution. Seasonal, trending or very lumpy demand needs a different approach.
  • The “both variable” formula assumes demand and lead time are independent.
  • Real inventory policy also depends on minimum order quantities, supplier reliability, shelf life, storage space and the business cost of a stock-out.

References

  • Silver, Pyke & Thomas, Inventory and Production Management in Supply Chains; standard safety-stock formulas for demand and lead-time variability.