BYTETOOLS

Safety Stock Calculator

Calculate safety stock with the full demand and lead-time variability formula, with Z from an inverse normal, plus the reorder point and days of cover.

Demand and lead time

1.6449
Service factor (Z)
345
Safety stock (units)
1,345
Reorder point (units)
3.5
Days of cover
1,000
Cycle stock (d × LT)
$4,140
Safety stock value
$911
Annual cost to hold it
FormulaWhat it coversSafety stock (units)
Z × √(LT·σd² + d²·σLT²)Demand and lead-time variability together345
Z × σd × √LTDemand variability only (fixed lead time)104
Z × d × σLTLead-time variability only (steady demand)329
Service levelZSafety stockReorder pointStock value
90%1.28162691,269$3,226
95%1.64493451,345$4,140
97.5%1.96004111,411$4,934
99%2.32634881,488$5,856
99.9%3.09026481,648$7,779

SS = Z × √(LT × σd² + d² × σLT²)  ·  ROP = d × LT + SS

Worked example: 100 units a day with a daily standard deviation of 20, a 10-day lead time with a standard deviation of 2 days, at a 95% service level. Z = 1.6449, so SS = 1.6449 × √(10 × 400 + 100² × 2²) = 1.6449 × √44,000 = 345 units, and the reorder point is 1,000 + 345 = 1,345. The Z values come from Acklam's inverse-normal approximation and match published tables to better than 1e-8: 95% → 1.6449, 97.5% → 1.9600, 99% → 2.3263.

This is the cycle-service-level form: Z is chosen so that the chance of running out during any one replenishment cycle is (100 − service level)%. It is not a fill rate — a 95% cycle service level usually corresponds to a higher unit fill rate, because most stock-outs are small. The formula also assumes demand is roughly normal and independent from day to day, which breaks down for lumpy or highly seasonal items. Everything runs locally in your browser; nothing is uploaded. Estimates for planning, not financial advice.

What is the Safety Stock Calculator?

Safety stock is the buffer that absorbs the two things you cannot control: demand that spikes and lead times that slip.

  • Full formula covering demand and lead-time variability together
  • Z from Acklam's inverse-normal approximation, not a lookup table
  • Reorder point, cycle stock and days of cover
  • Safety stock value and annual holding cost at your carrying rate
  • Side-by-side comparison of the three common safety stock formulas
  • Service-level sweep from 90% to 99.9% with the stock each one needs

How to use the Safety Stock Calculator

  1. 1

    Enter average daily demand and the standard deviation of that demand.

  2. 2

    Enter the average lead time in days and the standard deviation of the lead time.

  3. 3

    Pick a target service level from the presets, or choose Custom and type your own.

  4. 4

    Add the unit cost and annual holding rate to value the buffer.

  5. 5

    Compare the full formula with the demand-only and lead-time-only forms in the table.

About the Safety Stock Calculator

Safety stock is the buffer that absorbs the two things you cannot control: demand that spikes and lead times that slip. This calculator uses the full form, Z × √(LT × σd² + d² × σLT²), which accounts for both sources of variability rather than assuming lead time is fixed.

The service factor Z is derived from your target service level using Acklam's inverse-normal approximation rather than a five-row lookup table, so any service level between 0 and 100 gives an exact figure. The tool also returns the reorder point, days of cover, the value of the buffer and what it costs to hold for a year.

Two simpler formulas are shown alongside for comparison, and a table sweeps the service level from 90% to 99.9% so you can see what each extra nine actually costs. Everything runs locally in your browser and nothing is uploaded. Estimates for planning, not financial advice.

Frequently asked questions

What is the safety stock formula?

The full form is SS = Z × √(lead time × demand variance + demand² × lead-time variance). With 100 units a day at a standard deviation of 20, a 10-day lead time with a 2-day standard deviation and a 95% service level, that is 1.6449 × √44,000 = 345 units.

How do you find Z for a service level?

Z is the inverse of the standard normal distribution at that probability. 90% gives 1.28, 95% gives 1.64, 97.5% gives 1.96 and 99% gives 2.33. This tool computes it directly, so a 96.4% target gives an exact Z instead of forcing you to round to the nearest table row.

What is the difference between safety stock and the reorder point?

Safety stock is the buffer that sits below the normal cycle. The reorder point is the level at which you place the order: average demand × lead time, plus the safety stock. Ordering at the reorder point means the buffer is only consumed when demand or the lead time misbehaves.

Why does a 100% service level not work?

A 100% guarantee against every possible demand spike would need infinite stock, because the normal distribution has no upper bound. That is why Z rises steeply past 99% — going from 99% to 99.9% costs about a third more buffer for a tenth of the remaining risk.

Is cycle service level the same as fill rate?

No. Cycle service level is the chance of not running out during any one replenishment cycle. Fill rate is the share of demand met from stock. A 95% cycle service level usually corresponds to a higher fill rate, because most stock-outs are small and short.

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